Magic State Factory Catalog

[\![684,\,132,\,3]\!] factory

\mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7}\cdot \mathrm{T}_{8}\cdot \mathrm{T}_{9}\cdot \mathrm{T}_{10}\cdot \mathrm{T}_{11}\cdot \mathrm{T}_{12}\cdot \mathrm{T}_{13}\cdot \mathrm{T}_{14}\cdot \mathrm{T}_{15}\cdot \mathrm{T}_{16}\cdot \mathrm{T}_{17}\cdot \mathrm{T}_{18}\cdot \mathrm{T}_{19}\cdot \mathrm{T}_{20}\cdot \mathrm{T}_{21}\cdot \mathrm{T}_{22}\cdot \mathrm{T}_{23}\cdot \mathrm{T}_{}\cdots

distance, proved here
d=3
error coefficient
A_{3}=5{,}760
\gamma_\rho
1.4975
V_{\mathrm{ex}}
132
wires
N=168
Clifford correction
none with T powers
found by
AI search pure T

The circuit

The 168\times684 matrix. Rows are wires and columns are rotations. A 1 means the wire takes part in the rotation, and the number beside each wire is its row weight. Scroll sideways to see every column.

  • output wires
  • check wires, measured and postselected
wire
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680
out 0 (151)111111111111111111111111111·····················································································································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111······························································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111····
out 1 (151)11111111111111·············1111111111111···············································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111······························································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····························································
out 2 (181)111111········111111·······1111111······1111111·································································································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111····
out 3 (7)······11············11············11···········1····························································································································································································································································································································································································································································································································································································································································
out 4 (213)11111·11111···111·····111··1111···11····111·····11·····································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111····
out 5 (153)1111··1·1111··1··11·1······111·11·1·1···11111··1111····································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·······················································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111····
out 6 (115)11····111·····1111·1111··········1··111·11·1·11···················································································································································································································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111····
out 7 (63)····1111·1··1·111111111111·11·1111··111···1111··1······································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·································································································································································································································································································
out 8 (179)111·1·111·1···1···1·111···1···111···11··111·1···1·······························································································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111····
out 9 (149)1····1··11·111····1···11··1111·1·1······1111111·1·1····································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·······················································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····1·1··1·111·11·11·111·11··111···111·1·1····11··111111····
out 10 (93)1·1·1·1··1·11·····111·11·1·11··1··1··1··111··1·1·11111111················································································································································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111······························································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····························································
out 11 (151)·························································111111111111111111111111111····························································································································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·····························································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1···
out 12 (151)·························································11111111111111·············1111111111111······················································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·····························································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····························································
out 13 (181)·························································111111········111111·······1111111······1111111········································································································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1···
out 14 (7)·······························································11············11············11···········1···································································································································································································································································································································································································································································································································································································
out 15 (213)·························································11111·11111···111·····111··1111···11····111·····11············································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1···
out 16 (153)·························································1111··1·1111··1··11·1······111·11·1·1···11111··1111···········································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1······················································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1···
out 17 (115)·························································11····111·····1111·1111··········1··111·11·1·11··························································································································································································································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1···
out 18 (63)·····························································1111·1··1·111111111111·11·1111··111···1111··1·············································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1································································································································································································································································································
out 19 (179)·························································111·1·111·1···1···1·111···1···111···11··111·1···1······································································································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1···
out 20 (149)·························································1····1··11·111····1···11··1111·1·1······1111111·1·1···········································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1······················································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1···
out 21 (93)·························································1·1·1·1··1·11·····111·11·1·11··1··1··1··111··1·1·11111111·······················································································································································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·····························································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····························································
out 22 (151)··················································································································111111111111111111111111111····································································································································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·····························································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111··
out 23 (151)··················································································································11111111111111·············1111111111111······························································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·····························································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111···························································
out 24 (181)··················································································································111111········111111·······1111111······1111111················································································································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111··
out 25 (7)························································································································11············11············11···········1··········································································································································································································································································································································································································································································································································
out 26 (213)··················································································································11111·11111···111·····111··1111···11····111·····11····················································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111··
out 27 (153)··················································································································1111··1·1111··1··11·1······111·11·1·1···11111··1111···················································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111······················································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111··
out 28 (115)··················································································································11····111·····1111·1111··········1··111·11·1·11··································································································································································································································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111··
out 29 (63)······················································································································1111·1··1·111111111111·11·1111··111···1111··1·····················································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·······························································································································································································································································································
out 30 (179)··················································································································111·1·111·1···1···1·111···1···111···11··111·1···1··············································································································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111··
out 31 (149)··················································································································1····1··11·111····1···11··1111·1·1······1111111·1·1···················································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111······················································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111··
out 32 (93)··················································································································1·1·1·1··1·11·····111·11·1·11··1··1··1··111··1·1·11111111·······························································································································································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·····························································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111···························································
out 33 (151)···········································································································································································111111111111111111111111111·········································································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11··························································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·
out 34 (151)···········································································································································································11111111111111·············1111111111111···································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11··························································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11··························································
out 35 (181)···········································································································································································111111········111111·······1111111······1111111·····················································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·
out 36 (7)·················································································································································································11············11············11···········1·················································································································································································································································································································································································································································································
out 37 (213)···········································································································································································11111·11111···111·····111··1111···11····111·····11·························································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·
out 38 (153)···········································································································································································1111··1·1111··1··11·1······111·11·1·1···11111··1111························································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11···················································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·
out 39 (115)···········································································································································································11····111·····1111·1111··········1··111·11·1·11·······································································································································································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·
out 40 (63)···············································································································································································1111·1··1·111111111111·11·1111··111···1111··1··························································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11······························································································································································································································································································
out 41 (179)···········································································································································································111·1·111·1···1···1·111···1···111···11··111·1···1···················································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·
out 42 (149)···········································································································································································1····1··11·111····1···11··1111·1·1······1111111·1·1························································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11···················································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·
out 43 (93)···········································································································································································1·1·1·1··1·11·····111·11·1·11··1··1··1··111··1·1·11111111····································································································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11··························································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11··························································
out 44 (151)····································································································································································································································111111111111111111111111111················································································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·························································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11
out 45 (151)····································································································································································································································11111111111111·············1111111111111··········································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·························································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·························································
out 46 (181)····································································································································································································································111111········111111·······1111111······1111111····························································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11
out 47 (7)··········································································································································································································································11············11············11···········1························································································································································································································································································································································································································
out 48 (213)····································································································································································································································11111·11111···111·····111··1111···11····111·····11································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11
out 49 (153)····································································································································································································································1111··1·1111··1··11·1······111·11·1·1···11111··1111·······························································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11··················································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11
out 50 (115)····································································································································································································································11····111·····1111·1111··········1··111·11·1·11··············································································································································································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11
out 51 (63)········································································································································································································································1111·1··1·111111111111·11·1111··111···1111··1·································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·····························································································································································································································································································
out 52 (179)····································································································································································································································111·1·111·1···1···1·111···1···111···11··111·1···1··························································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11
out 53 (149)····································································································································································································································1····1··11·111····1···11··1111·1·1······1111111·1·1·······························································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11··················································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···111111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11
out 54 (93)····································································································································································································································1·1·1·1··1·11·····111·11·1·11··1··1··1··111··1·1·11111111···········································································································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·························································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·························································
out 55 (151)·····························································································································································································································································································111111111111111111111111111·······················································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1·························································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1
out 56 (151)·····························································································································································································································································································11111111111111·············1111111111111·················111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1·························································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1·························································
out 57 (181)·····························································································································································································································································································111111········111111·······1111111······1111111···································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1
out 58 (7)···································································································································································································································································································11············11············11···········1·······························································································································································································································································································································································
out 59 (213)·····························································································································································································································································································11111·11111···111·····111··1111···11····111·····11·······111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1
out 60 (153)·····························································································································································································································································································1111··1·1111··1··11·1······111·11·1·1···11111··1111······111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1··················································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1
out 61 (115)·····························································································································································································································································································11····111·····1111·1111··········1··111·11·1·11·····················································································································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1
out 62 (63)·································································································································································································································································································1111·1··1·111111111111·11·1111··111···1111··1········111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1·····························································································································································································································································································
out 63 (179)·····························································································································································································································································································111·1·111·1···1···1·111···1···111···11··111·1···1·································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1
out 64 (149)·····························································································································································································································································································1····1··11·111····1···11··1111·1·1······1111111·1·1······111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1··················································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1
out 65 (93)·····························································································································································································································································································1·1·1·1··1·11·····111·11·1·11··1··1··1··111··1·1·11111111··················································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1·························································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1·························································
out 66 (31)·························································································································································································································································································································································1111····11·11·111·1·1·11·11···1·111···1111·111·1··11·······························································································································································································································································································
out 67 (31)·························································································································································································································································································································································1·1··1··111·1···1111··1··1·11·111·1111·11·1··11·1··111·····························································································································································································································································································
out 68 (7)························································································································································································································································································································································1··1····1·1·····························1·····1···1·································································································································································································································································································
out 69 (7)····························································································································································································································································································································································11············11············11···········1······································································································································································································································································································
out 70 (25)·······················································································································································································································································································································································111···1··1··1·111··1···1·111··1···11·1···1··1111·11··································································································································································································································································································
out 71 (25)························································································································································································································································································································································11·1··1·····1·11··11·1·11·111···11·1···1·1·1··11··1·1·······························································································································································································································································································
out 72 (25)·······················································································································································································································································································································································1·1·111···1111·11·······1··1·11··111····11···1·11·1··1·······························································································································································································································································································
out 73 (25)·······················································································································································································································································································································································1·111·11·1··11··1···1··111···11··1··1····1··1·1·1111·································································································································································································································································································
out 74 (25)························································································································································································································································································································································11··111···1··111·1111···1111···1··11····11·11·····1·································································································································································································································································································
out 75 (25)·······················································································································································································································································································································································1····1·1·1·11··1····11··1··111·11·111···1·1··111···1·1·······························································································································································································································································································
out 76 (25)·······················································································································································································································································································································································11··11·1·1·11·1····1·1·1111··1··11·11··1····111··1···································································································································································································································································································
out 77 (31)··················································································································································································································································································································································································································1111····11·11·111·1·1·11·11···1·111···1111·111·1··11······································································································································································································································
out 78 (31)··················································································································································································································································································································································································································1·1··1··111·1···1111··1··1·11·111·1111·11·1··11·1··111····································································································································································································································
out 79 (7)·················································································································································································································································································································································································································1··1····1·1·····························1·····1···1········································································································································································································································
out 80 (7)·····················································································································································································································································································································································································································11············11············11···········1·············································································································································································································································
out 81 (25)················································································································································································································································································································································································································111···1··1··1·111··1···1·111··1···11·1···1··1111·11·········································································································································································································································
out 82 (25)·················································································································································································································································································································································································································11·1··1·····1·11··11·1·11·111···11·1···1·1·1··11··1·1······································································································································································································································
out 83 (25)················································································································································································································································································································································································································1·1·111···1111·11·······1··1·11··111····11···1·11·1··1······································································································································································································································
out 84 (25)················································································································································································································································································································································································································1·111·11·1··11··1···1··111···11··1··1····1··1·1·1111········································································································································································································································
out 85 (25)·················································································································································································································································································································································································································11··111···1··111·1111···1111···1··11····11·11·····1········································································································································································································································
out 86 (25)················································································································································································································································································································································································································1····1·1·1·11··1····11··1··111·11·111···1·1··111···1·1······································································································································································································································
out 87 (25)················································································································································································································································································································································································································11··11·1·1·11·1····1·1·1111··1··11·11··1····111··1··········································································································································································································································
out 88 (31)···········································································································································································································································································································································································································································································1111····11·11·111·1·1·11·11···1·111···1111·111·1··11·············································································································································································
out 89 (31)···········································································································································································································································································································································································································································································1·1··1··111·1···1111··1··1·11·111·1111·11·1··11·1··111···········································································································································································
out 90 (7)··········································································································································································································································································································································································································································································1··1····1·1·····························1·····1···1···············································································································································································
out 91 (7)··············································································································································································································································································································································································································································································11············11············11···········1····················································································································································································
out 92 (25)·········································································································································································································································································································································································································································································111···1··1··1·111··1···1·111··1···11·1···1··1111·11················································································································································································
out 93 (25)··········································································································································································································································································································································································································································································11·1··1·····1·11··11·1·11·111···11·1···1·1·1··11··1·1·············································································································································································
out 94 (25)·········································································································································································································································································································································································································································································1·1·111···1111·11·······1··1·11··111····11···1·11·1··1·············································································································································································
out 95 (25)·········································································································································································································································································································································································································································································1·111·11·1··11··1···1··111···11··1··1····1··1·1·1111···············································································································································································
out 96 (25)··········································································································································································································································································································································································································································································11··111···1··111·1111···1111···1··11····11·11·····1···············································································································································································
out 97 (25)·········································································································································································································································································································································································································································································1····1·1·1·11··1····11··1··111·11·111···1·1··111···1·1·············································································································································································
out 98 (25)·········································································································································································································································································································································································································································································11··11·1·1·11·1····1·1·1111··1··11·11··1····111··1·················································································································································································
out 99 (31)····································································································································································································································································································································································································································································································································1111····11·11·111·1·1·11·11···1·111···1111·111·1··11····················································································································
out 100 (31)····································································································································································································································································································································································································································································································································1·1··1··111·1···1111··1··1·11·111·1111·11·1··11·1··111··················································································································
out 101 (7)···································································································································································································································································································································································································································································································································1··1····1·1·····························1·····1···1······················································································································
out 102 (7)·······································································································································································································································································································································································································································································································································11············11············11···········1···························································································································
out 103 (25)··································································································································································································································································································································································································································································································································111···1··1··1·111··1···1·111··1···11·1···1··1111·11·······················································································································
out 104 (25)···································································································································································································································································································································································································································································································································11·1··1·····1·11··11·1·11·111···11·1···1·1·1··11··1·1····················································································································
out 105 (25)··································································································································································································································································································································································································································································································································1·1·111···1111·11·······1··1·11··111····11···1·11·1··1····················································································································
out 106 (25)··································································································································································································································································································································································································································································································································1·111·11·1··11··1···1··111···11··1··1····1··1·1·1111······················································································································
out 107 (25)···································································································································································································································································································································································································································································································································11··111···1··111·1111···1111···1··11····11·11·····1······················································································································
out 108 (25)··································································································································································································································································································································································································································································································································1····1·1·1·11··1····11··1··111·11·111···1·1··111···1·1····················································································································
out 109 (25)··································································································································································································································································································································································································································································································································11··11·1·1·11·1····1·1·1111··1··11·11··1····111··1························································································································
out 110 (31)·····························································································································································································································································································································································································································································································································································································1111····11·11·111·1·1·11·11···1·111···1111·111·1··11···························································
out 111 (31)·····························································································································································································································································································································································································································································································································································································1·1··1··111·1···1111··1··1·11·111·1111·11·1··11·1··111·························································
out 112 (7)····························································································································································································································································································································································································································································································································································································1··1····1·1·····························1·····1···1·····························································
out 113 (7)································································································································································································································································································································································································································································································································································································11············11············11···········1··································································
out 114 (25)···························································································································································································································································································································································································································································································································································································111···1··1··1·111··1···1·111··1···11·1···1··1111·11······························································
out 115 (25)····························································································································································································································································································································································································································································································································································································11·1··1·····1·11··11·1·11·111···11·1···1·1·1··11··1·1···························································
out 116 (25)···························································································································································································································································································································································································································································································································································································1·1·111···1111·11·······1··1·11··111····11···1·11·1··1···························································
out 117 (25)···························································································································································································································································································································································································································································································································································································1·111·11·1··11··1···1··111···11··1··1····1··1·1·1111·····························································
out 118 (25)····························································································································································································································································································································································································································································································································································································11··111···1··111·1111···1111···1··11····11·11·····1·····························································
out 119 (25)···························································································································································································································································································································································································································································································································································································1····1·1·1·11··1····11··1··111·11·111···1·1··111···1·1···························································
out 120 (25)···························································································································································································································································································································································································································································································································································································11··11·1·1·11·1····1·1·1111··1··11·11··1····111··1·······························································
out 121 (31)······················································································································································································································································································································································································································································································································································································································································1111····11·11·111·1·1·11·11···1·111···1111·111·1··11··
out 122 (31)······················································································································································································································································································································································································································································································································································································································································1·1··1··111·1···1111··1··1·11·111·1111·11·1··11·1··111
out 123 (7)·····················································································································································································································································································································································································································································································································································································································································1··1····1·1·····························1·····1···1····
out 124 (7)·························································································································································································································································································································································································································································································································································································································································11············11············11···········1·········
out 125 (25)····················································································································································································································································································································································································································································································································································································································································111···1··1··1·111··1···1·111··1···11·1···1··1111·11·····
out 126 (25)·····················································································································································································································································································································································································································································································································································································································································11·1··1·····1·11··11·1·11·111···11·1···1·1·1··11··1·1··
out 127 (25)····················································································································································································································································································································································································································································································································································································································································1·1·111···1111·11·······1··1·11··111····11···1·11·1··1··
out 128 (25)····················································································································································································································································································································································································································································································································································································································································1·111·11·1··11··1···1··111···11··1··1····1··1·1·1111····
out 129 (25)·····················································································································································································································································································································································································································································································································································································································································11··111···1··111·1111···1111···1··11····11·11·····1····
out 130 (25)····················································································································································································································································································································································································································································································································································································································································1····1·1·1·11··1····11··1··111·11·111···1·1··111···1·1··
out 131 (25)····················································································································································································································································································································································································································································································································································································································································11··11·1·1·11·1····1·1·1111··1··11·11··1····111··1······
check 132 (62)·1·1··1·111·11·11·111·11··111···111·1·1····11··111111··································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·································································································································································································································································································
check 133 (62)·111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1··························································································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111········································································································································································································································
check 134 (62)··111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111··················································································································································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111···············································································································································································
check 135 (62)1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11··········································································································································································································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111······················································································································
check 136 (62)1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11··································································································································································································································································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····························································
check 137 (62)111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1···························································································································································································································································································································································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111····
check 138 (62)··························································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·········································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1································································································································································································································································································
check 139 (62)··························································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·································································································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·······································································································································································································································
check 140 (62)···························································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·························································································································································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1··············································································································································································
check 141 (62)·························································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·················································································································································································································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·····················································································································
check 142 (62)·························································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·········································································································································································································································································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····························································
check 143 (62)·························································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1··································································································································································································································································································································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1···
check 144 (62)···················································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·················································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·······························································································································································································································································································
check 145 (62)···················································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·········································································································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111······································································································································································································································
check 146 (62)····················································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·································································································································································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·············································································································································································
check 147 (62)··················································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·························································································································································································································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····················································································································
check 148 (62)··················································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·················································································································································································································································································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111···························································
check 149 (62)··················································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1··········································································································································································································································································································································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111··
check 150 (62)············································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111······················································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11······························································································································································································································································································
check 151 (62)············································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1··············································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·····································································································································································································································
check 152 (62)·············································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111······································································································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11············································································································································································
check 153 (62)···········································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11······························································································································································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11···················································································································
check 154 (62)···········································································································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11······················································································································································································································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11··························································
check 155 (62)···········································································································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1···············································································································································································································································································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·
check 156 (62)·····································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111·····························································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·····························································································································································································································································································
check 157 (62)·····································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1·····················································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11····································································································································································································································
check 158 (62)······································································································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111·············································································································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11···········································································································································································
check 159 (62)····································································································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11·····································································································································································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11··················································································································
check 160 (62)····································································································································································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·····························································································································································································································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11·························································
check 161 (62)····································································································································································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1······················································································································································································································································································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11
check 162 (62)······························································································································································································································································································1·1··1·111·11·11·111·11··111···111·1·1····11··111111····111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1·····························································································································································································································································································
check 163 (62)······························································································································································································································································································111·1·1·1111··11··1·1··11···111··1·1·1·11··1111·111·1····························································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1····································································································································································································································
check 164 (62)·······························································································································································································································································································111··111··1111·1111·1·1··1··111··111··1·1··1·1··1·111····················································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1···········································································································································································
check 165 (62)·····························································································································································································································································································1···1·111·111··111··11··1·1··11·11··1111·1···1··1·111·11············································································································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1··················································································································
check 166 (62)·····························································································································································································································································································1111·1·1··111·1··1··1·11··111···11·1·1··11···111·111···11····································································································································································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1·························································
check 167 (62)·····························································································································································································································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1·····························································································································································································································································································111·1·1····1111·1··11··111·1·1·1·11·11·1··11·111···11···1

The gate is read off the output rows. An output row of odd weight gives a T, a pair of output rows with odd overlap gives a CS, and an odd triple overlap gives a CCZ. The circuit is a valid factory because every such parity that touches a check row is even.

Figures of merit

inputs n684Noisy T states per run.
outputs k132
distance d3Exact, proved and witnessed here.
error coefficient A_{3}5,760Faults of weight 3 in the circuit shown that pass every check and damage the output. The output error is A_{3}\,p^{3} to leading order.
wires N168
checks r36
V_{\mathrm{ex}}132T states per run. CCZ counts as two.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.4975Overhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d1.4975Overhead per output qubit.
\gamma_T = \log(n/T)/\log dnot computedOverhead per unit of T-count.
T-countnot computedMinimal T-count of the output gate. Not computable at this width.
phase-polynomial degreenot computedMinimised over changes of output basis.
effective width132Rank of the output rows modulo the check rows.

Output gate

132 T0 CS0 CCZon 132 output wires

As gates: \mathrm{T}_{0}\cdot \mathrm{T}_{1}\cdot \mathrm{T}_{2}\cdot \mathrm{T}_{3}\cdot \mathrm{T}_{4}\cdot \mathrm{T}_{5}\cdot \mathrm{T}_{6}\cdot \mathrm{T}_{7}\cdot \mathrm{T}_{8}\cdot \mathrm{T}_{9}\cdot \mathrm{T}_{10}\cdot \mathrm{T}_{11}\cdot \mathrm{T}_{12}\cdot \mathrm{T}_{13}\cdot \mathrm{T}_{14}\cdot \mathrm{T}_{15}\cdot \mathrm{T}_{16}\cdot \mathrm{T}_{17}\cdot \mathrm{T}_{18}\cdot \mathrm{T}_{19}\cdot \mathrm{T}_{20}\cdot \mathrm{T}_{21}\cdot \mathrm{T}_{22}\cdot \mathrm{T}_{23}\cdot \mathrm{T}_{24}\cdot \mathrm{T}_{25}\cdot \mathrm{T}_{26}\cdot \mathrm{T}_{27}\cdot \mathrm{T}_{28}\cdot \mathrm{T}_{29}\cdot \mathrm{T}_{30}\cdot \mathrm{T}_{31}\cdot \mathrm{T}_{32}\cdot \mathrm{T}_{33}\cdot \mathrm{T}_{34}\cdot \mathrm{T}_{35}\cdot \mathrm{T}_{36}\cdot \mathrm{T}_{37}\cdot \mathrm{T}_{38}\cdot \mathrm{T}_{39}\cdot \mathrm{T}_{40}\cdot \mathrm{T}_{41}\cdot \mathrm{T}_{42}\cdot \mathrm{T}_{43}\cdot \mathrm{T}_{44}\cdot \mathrm{T}_{45}\cdot \mathrm{T}_{46}\cdot \mathrm{T}_{47}\cdot \mathrm{T}_{48}\cdot \mathrm{T}_{49}\cdot \mathrm{T}_{50}\cdot \mathrm{T}_{51}\cdot \mathrm{T}_{52}\cdot \mathrm{T}_{53}\cdot \mathrm{T}_{54}\cdot \mathrm{T}_{55}\cdot \mathrm{T}_{56}\cdot \mathrm{T}_{57}\cdot \mathrm{T}_{58}\cdot \mathrm{T}_{59}\cdot \mathrm{T}_{60}\cdot \mathrm{T}_{61}\cdot \mathrm{T}_{62}\cdot \mathrm{T}_{63}\cdot \mathrm{T}_{64}\cdot \mathrm{T}_{65}\cdot \mathrm{T}_{66}\cdot \mathrm{T}_{67}\cdot \mathrm{T}_{68}\cdot \mathrm{T}_{69}\cdot \mathrm{T}_{70}\cdot \mathrm{T}_{71}\cdot \mathrm{T}_{72}\cdot \mathrm{T}_{73}\cdot \mathrm{T}_{74}\cdot \mathrm{T}_{75}\cdot \mathrm{T}_{76}\cdot \mathrm{T}_{77}\cdot \mathrm{T}_{78}\cdot \mathrm{T}_{79}\cdot \mathrm{T}_{80}\cdot \mathrm{T}_{81}\cdot \mathrm{T}_{82}\cdot \mathrm{T}_{83}\cdot \mathrm{T}_{84}\cdot \mathrm{T}_{85}\cdot \mathrm{T}_{86}\cdot \mathrm{T}_{87}\cdot \mathrm{T}_{88}\cdot \mathrm{T}_{89}\cdot \mathrm{T}_{90}\cdot \mathrm{T}_{91}\cdot \mathrm{T}_{92}\cdot \mathrm{T}_{93}\cdot \mathrm{T}_{94}\cdot \mathrm{T}_{95}\cdot \mathrm{T}_{96}\cdot \mathrm{T}_{97}\cdot \mathrm{T}_{98}\cdot \mathrm{T}_{99}\cdot \mathrm{T}_{100}\cdot \mathrm{T}_{101}\cdot \mathrm{T}_{102}\cdot \mathrm{T}_{103}\cdot \mathrm{T}_{104}\cdot \mathrm{T}_{105}\cdot \mathrm{T}_{106}\cdot \mathrm{T}_{107}\cdot \mathrm{T}_{108}\cdot \mathrm{T}_{109}\cdot \mathrm{T}_{110}\cdot \mathrm{T}_{111}\cdot \mathrm{T}_{112}\cdot \mathrm{T}_{113}\cdot \mathrm{T}_{114}\cdot \mathrm{T}_{115}\cdot \mathrm{T}_{116}\cdot \mathrm{T}_{117}\cdot \mathrm{T}_{118}\cdot \mathrm{T}_{119}\cdot \mathrm{T}_{120}\cdot \mathrm{T}_{121}\cdot \mathrm{T}_{122}\cdot \mathrm{T}_{123}\cdot \mathrm{T}_{124}\cdot \mathrm{T}_{125}\cdot \mathrm{T}_{126}\cdot \mathrm{T}_{127}\cdot \mathrm{T}_{128}\cdot \mathrm{T}_{129}\cdot \mathrm{T}_{130}\cdot \mathrm{T}_{131}

As monomials: 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50+51+52+53+54+55+56+57+58+59+60+61+62+63+64+65+66+67+68+69+70+71+72+73+74+75+76+77+78+79+80+81+82+83+84+85+86+87+88+89+90+91+92+93+94+95+96+97+98+99+100+101+102+103+104+105+106+107+108+109+110+111+112+113+114+115+116+117+118+119+120+121+122+123+124+125+126+127+128+129+130+131 (output wires per term, separated by +)

This row stands for every gate that a CNOT circuit and S, Z and CZ gates on the outputs can reach from this one. They all prepare the same magic state. The wires are shown in the S_k-canonical frame.

Clifford correction

With every rotation a \mathrm{T}=\mathrm{diag}(1,e^{i\pi/4}), the rotations deposit the gate above times a diagonal Clifford. Undo it after the rotations and before the checks are measured, with 120 single-wire gates and 1032 \mathrm{CZ} gates: \mathrm{S} on output 0, \mathrm{S} on output 1, \mathrm{Z} on output 2, \mathrm{S} on output 3, \mathrm{Z} on output 4, \mathrm{S}^\dagger on output 6, \mathrm{S} on output 7, \mathrm{S}^\dagger on output 8, \mathrm{Z} on output 9, \mathrm{Z} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{Z} on output 13, \mathrm{S} on output 14, \mathrm{Z} on output 15, \mathrm{S}^\dagger on output 17, \mathrm{S} on output 18, \mathrm{S}^\dagger on output 19, \mathrm{Z} on output 20, \mathrm{Z} on output 21, \mathrm{S} on output 22, \mathrm{S} on output 23, \mathrm{Z} on output 24, \mathrm{S} on output 25 and 1128 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.

All 1152 correction gates

\mathrm{S} on output 0, \mathrm{S} on output 1, \mathrm{Z} on output 2, \mathrm{S} on output 3, \mathrm{Z} on output 4, \mathrm{S}^\dagger on output 6, \mathrm{S} on output 7, \mathrm{S}^\dagger on output 8, \mathrm{Z} on output 9, \mathrm{Z} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{Z} on output 13, \mathrm{S} on output 14, \mathrm{Z} on output 15, \mathrm{S}^\dagger on output 17, \mathrm{S} on output 18, \mathrm{S}^\dagger on output 19, \mathrm{Z} on output 20, \mathrm{Z} on output 21, \mathrm{S} on output 22, \mathrm{S} on output 23, \mathrm{Z} on output 24, \mathrm{S} on output 25, \mathrm{Z} on output 26, \mathrm{S}^\dagger on output 28, \mathrm{S} on output 29, \mathrm{S}^\dagger on output 30, \mathrm{Z} on output 31, \mathrm{Z} on output 32, \mathrm{S} on output 33, \mathrm{S} on output 34, \mathrm{Z} on output 35, \mathrm{S} on output 36, \mathrm{Z} on output 37, \mathrm{S}^\dagger on output 39, \mathrm{S} on output 40, \mathrm{S}^\dagger on output 41, \mathrm{Z} on output 42, \mathrm{Z} on output 43, \mathrm{S} on output 44, \mathrm{S} on output 45, \mathrm{Z} on output 46, \mathrm{S} on output 47, \mathrm{Z} on output 48, \mathrm{S}^\dagger on output 50, \mathrm{S} on output 51, \mathrm{S}^\dagger on output 52, \mathrm{Z} on output 53, \mathrm{Z} on output 54, \mathrm{S} on output 55, \mathrm{S} on output 56, \mathrm{Z} on output 57, \mathrm{S} on output 58, \mathrm{Z} on output 59, \mathrm{S}^\dagger on output 61, \mathrm{S} on output 62, \mathrm{S}^\dagger on output 63, \mathrm{Z} on output 64, \mathrm{Z} on output 65, \mathrm{S} on output 66, \mathrm{S} on output 67, \mathrm{S} on output 68, \mathrm{S} on output 69, \mathrm{S} on output 77, \mathrm{S} on output 78, \mathrm{S} on output 79, \mathrm{S} on output 80, \mathrm{S} on output 88, \mathrm{S} on output 89, \mathrm{S} on output 90, \mathrm{S} on output 91, \mathrm{S} on output 99, \mathrm{S} on output 100, \mathrm{S} on output 101, \mathrm{S} on output 102, \mathrm{S} on output 110, \mathrm{S} on output 111, \mathrm{S} on output 112, \mathrm{S} on output 113, \mathrm{S} on output 121, \mathrm{S} on output 122, \mathrm{S} on output 123, \mathrm{S} on output 124, \mathrm{S} on check 132, \mathrm{S} on check 133, \mathrm{S} on check 134, \mathrm{S} on check 135, \mathrm{S} on check 136, \mathrm{S} on check 137, \mathrm{S} on check 138, \mathrm{S} on check 139, \mathrm{S} on check 140, \mathrm{S} on check 141, \mathrm{S} on check 142, \mathrm{S} on check 143, \mathrm{S} on check 144, \mathrm{S} on check 145, \mathrm{S} on check 146, \mathrm{S} on check 147, \mathrm{S} on check 148, \mathrm{S} on check 149, \mathrm{S} on check 150, \mathrm{S} on check 151, \mathrm{S} on check 152, \mathrm{S} on check 153, \mathrm{S} on check 154, \mathrm{S} on check 155, \mathrm{S} on check 156, \mathrm{S} on check 157, \mathrm{S} on check 158, \mathrm{S} on check 159, \mathrm{S} on check 160, \mathrm{S} on check 161, \mathrm{S} on check 162, \mathrm{S} on check 163, \mathrm{S} on check 164, \mathrm{S} on check 165, \mathrm{S} on check 166, \mathrm{S} on check 167, \mathrm{CZ} on output 0, output 5, \mathrm{CZ} on output 0, output 6, \mathrm{CZ} on output 0, output 7, \mathrm{CZ} on output 0, output 8, \mathrm{CZ} on output 0, check 133, \mathrm{CZ} on output 0, check 135, \mathrm{CZ} on output 0, check 136, \mathrm{CZ} on output 0, check 137, \mathrm{CZ} on output 1, output 2, \mathrm{CZ} on output 1, output 5, \mathrm{CZ} on output 1, output 7, \mathrm{CZ} on output 1, output 8, \mathrm{CZ} on output 1, output 9, \mathrm{CZ} on output 1, output 10, \mathrm{CZ} on output 1, check 132, \mathrm{CZ} on output 1, check 133, \mathrm{CZ} on output 1, check 134, \mathrm{CZ} on output 1, check 136, \mathrm{CZ} on output 2, output 4, \mathrm{CZ} on output 2, output 5, \mathrm{CZ} on output 2, output 6, \mathrm{CZ} on output 2, output 7, \mathrm{CZ} on output 2, output 10, \mathrm{CZ} on output 2, check 133, \mathrm{CZ} on output 2, check 134, \mathrm{CZ} on output 2, check 135, \mathrm{CZ} on output 2, check 136, \mathrm{CZ} on output 2, check 137, \mathrm{CZ} on output 4, output 5, \mathrm{CZ} on output 4, output 7, \mathrm{CZ} on output 4, output 8, \mathrm{CZ} on output 4, check 132, \mathrm{CZ} on output 4, check 133, \mathrm{CZ} on output 4, check 134, \mathrm{CZ} on output 4, check 136, \mathrm{CZ} on output 5, output 7, \mathrm{CZ} on output 5, output 8, \mathrm{CZ} on output 5, check 132, \mathrm{CZ} on output 5, check 137, \mathrm{CZ} on output 6, output 8, \mathrm{CZ} on output 6, output 9, \mathrm{CZ} on output 6, check 135, \mathrm{CZ} on output 7, output 9, \mathrm{CZ} on output 7, check 132, \mathrm{CZ} on output 7, check 135, \mathrm{CZ} on output 7, check 136, \mathrm{CZ} on output 7, check 137, \mathrm{CZ} on output 8, output 10, \mathrm{CZ} on output 8, check 133, \mathrm{CZ} on output 8, check 134, \mathrm{CZ} on output 8, check 135, \mathrm{CZ} on output 8, check 137, \mathrm{CZ} on output 9, output 10, \mathrm{CZ} on output 9, check 132, \mathrm{CZ} on output 9, check 135, \mathrm{CZ} on output 9, check 136, \mathrm{CZ} on output 10, check 134, \mathrm{CZ} on output 10, check 135, \mathrm{CZ} on output 10, check 136, \mathrm{CZ} on output 11, output 16, \mathrm{CZ} on output 11, output 17, \mathrm{CZ} on output 11, output 18, \mathrm{CZ} on output 11, output 19, \mathrm{CZ} on output 11, check 139, \mathrm{CZ} on output 11, check 141, \mathrm{CZ} on output 11, check 142, \mathrm{CZ} on output 11, check 143, \mathrm{CZ} on output 12, output 13, \mathrm{CZ} on output 12, output 16, \mathrm{CZ} on output 12, output 18, \mathrm{CZ} on output 12, output 19, \mathrm{CZ} on output 12, output 20, \mathrm{CZ} on output 12, output 21, \mathrm{CZ} on output 12, check 138, \mathrm{CZ} on output 12, check 139, \mathrm{CZ} on output 12, check 140, \mathrm{CZ} on output 12, check 142, \mathrm{CZ} on output 13, output 15, \mathrm{CZ} on output 13, output 16, \mathrm{CZ} on output 13, output 17, \mathrm{CZ} on output 13, output 18, \mathrm{CZ} on output 13, output 21, \mathrm{CZ} on output 13, check 139, \mathrm{CZ} on output 13, check 140, \mathrm{CZ} on output 13, check 141, \mathrm{CZ} on output 13, check 142, \mathrm{CZ} on output 13, check 143, \mathrm{CZ} on output 15, output 16, \mathrm{CZ} on output 15, output 18, \mathrm{CZ} on output 15, output 19, \mathrm{CZ} on output 15, check 138, \mathrm{CZ} on output 15, check 139, \mathrm{CZ} on output 15, check 140, \mathrm{CZ} on output 15, check 142, \mathrm{CZ} on output 16, output 18, \mathrm{CZ} on output 16, output 19, \mathrm{CZ} on output 16, check 138, \mathrm{CZ} on output 16, check 143, \mathrm{CZ} on output 17, output 19, \mathrm{CZ} on output 17, output 20, \mathrm{CZ} on output 17, check 141, \mathrm{CZ} on output 18, output 20, \mathrm{CZ} on output 18, check 138, \mathrm{CZ} on output 18, check 141, \mathrm{CZ} on output 18, check 142, \mathrm{CZ} on output 18, check 143, \mathrm{CZ} on output 19, output 21, \mathrm{CZ} on output 19, check 139, \mathrm{CZ} on output 19, check 140, \mathrm{CZ} on output 19, check 141, \mathrm{CZ} on output 19, check 143, \mathrm{CZ} on output 20, output 21, \mathrm{CZ} on output 20, check 138, \mathrm{CZ} on output 20, check 141, \mathrm{CZ} on output 20, check 142, \mathrm{CZ} on output 21, check 140, \mathrm{CZ} on output 21, check 141, \mathrm{CZ} on output 21, check 142, \mathrm{CZ} on output 22, output 27, \mathrm{CZ} on output 22, output 28, \mathrm{CZ} on output 22, output 29, \mathrm{CZ} on output 22, output 30, \mathrm{CZ} on output 22, check 145, \mathrm{CZ} on output 22, check 147, \mathrm{CZ} on output 22, check 148, \mathrm{CZ} on output 22, check 149, \mathrm{CZ} on output 23, output 24, \mathrm{CZ} on output 23, output 27, \mathrm{CZ} on output 23, output 29, \mathrm{CZ} on output 23, output 30, \mathrm{CZ} on output 23, output 31, \mathrm{CZ} on output 23, output 32, \mathrm{CZ} on output 23, check 144, \mathrm{CZ} on output 23, check 145, \mathrm{CZ} on output 23, check 146, \mathrm{CZ} on output 23, check 148, \mathrm{CZ} on output 24, output 26, \mathrm{CZ} on output 24, output 27, \mathrm{CZ} on output 24, output 28, \mathrm{CZ} on output 24, output 29, \mathrm{CZ} on output 24, output 32, \mathrm{CZ} on output 24, check 145, \mathrm{CZ} on output 24, check 146, \mathrm{CZ} on output 24, check 147, \mathrm{CZ} on output 24, check 148, \mathrm{CZ} on output 24, check 149, \mathrm{CZ} on output 26, output 27, \mathrm{CZ} on output 26, output 29, \mathrm{CZ} on output 26, output 30, \mathrm{CZ} on output 26, check 144, \mathrm{CZ} on output 26, check 145, \mathrm{CZ} on output 26, check 146, \mathrm{CZ} on output 26, check 148, \mathrm{CZ} on output 27, output 29, \mathrm{CZ} on output 27, output 30, \mathrm{CZ} on output 27, check 144, \mathrm{CZ} on output 27, check 149, \mathrm{CZ} on output 28, output 30, \mathrm{CZ} on output 28, output 31, \mathrm{CZ} on output 28, check 147, \mathrm{CZ} on output 29, output 31, \mathrm{CZ} on output 29, check 144, \mathrm{CZ} on output 29, check 147, \mathrm{CZ} on output 29, check 148, \mathrm{CZ} on output 29, check 149, \mathrm{CZ} on output 30, output 32, \mathrm{CZ} on output 30, check 145, \mathrm{CZ} on output 30, check 146, \mathrm{CZ} on output 30, check 147, \mathrm{CZ} on output 30, check 149, \mathrm{CZ} on output 31, output 32, \mathrm{CZ} on output 31, check 144, \mathrm{CZ} on output 31, check 147, \mathrm{CZ} on output 31, check 148, \mathrm{CZ} on output 32, check 146, \mathrm{CZ} on output 32, check 147, \mathrm{CZ} on output 32, check 148, \mathrm{CZ} on output 33, output 38, \mathrm{CZ} on output 33, output 39, \mathrm{CZ} on output 33, output 40, \mathrm{CZ} on output 33, output 41, \mathrm{CZ} on output 33, output 81, \mathrm{CZ} on output 33, output 82, \mathrm{CZ} on output 33, output 84, \mathrm{CZ} on output 33, output 87, \mathrm{CZ} on output 33, output 103, \mathrm{CZ} on output 33, output 104, \mathrm{CZ} on output 33, output 106, \mathrm{CZ} on output 33, output 109, \mathrm{CZ} on output 33, output 114, \mathrm{CZ} on output 33, output 115, \mathrm{CZ} on output 33, output 117, \mathrm{CZ} on output 33, output 120, \mathrm{CZ} on output 33, output 125, \mathrm{CZ} on output 33, output 126, \mathrm{CZ} on output 33, output 128, \mathrm{CZ} on output 33, output 131, \mathrm{CZ} on output 33, check 151, \mathrm{CZ} on output 33, check 153, \mathrm{CZ} on output 33, check 154, \mathrm{CZ} on output 33, check 155, \mathrm{CZ} on output 34, output 35, \mathrm{CZ} on output 34, output 38, \mathrm{CZ} on output 34, output 40, \mathrm{CZ} on output 34, output 41, \mathrm{CZ} on output 34, output 42, \mathrm{CZ} on output 34, output 43, \mathrm{CZ} on output 34, output 70, \mathrm{CZ} on output 34, output 71, \mathrm{CZ} on output 34, output 73, \mathrm{CZ} on output 34, output 76, \mathrm{CZ} on output 34, output 81, \mathrm{CZ} on output 34, output 82, \mathrm{CZ} on output 34, output 84, \mathrm{CZ} on output 34, output 87, \mathrm{CZ} on output 34, output 92, \mathrm{CZ} on output 34, output 93, \mathrm{CZ} on output 34, output 95, \mathrm{CZ} on output 34, output 98, \mathrm{CZ} on output 34, output 114, \mathrm{CZ} on output 34, output 115, \mathrm{CZ} on output 34, output 117, \mathrm{CZ} on output 34, output 120, \mathrm{CZ} on output 34, check 150, \mathrm{CZ} on output 34, check 151, \mathrm{CZ} on output 34, check 152, \mathrm{CZ} on output 34, check 154, \mathrm{CZ} on output 35, output 37, \mathrm{CZ} on output 35, output 38, \mathrm{CZ} on output 35, output 39, \mathrm{CZ} on output 35, output 40, \mathrm{CZ} on output 35, output 43, \mathrm{CZ} on output 35, output 81, \mathrm{CZ} on output 35, output 82, \mathrm{CZ} on output 35, output 84, \mathrm{CZ} on output 35, output 87, \mathrm{CZ} on output 35, output 92, \mathrm{CZ} on output 35, output 93, \mathrm{CZ} on output 35, output 95, \mathrm{CZ} on output 35, output 98, \mathrm{CZ} on output 35, output 103, \mathrm{CZ} on output 35, output 104, \mathrm{CZ} on output 35, output 106, \mathrm{CZ} on output 35, output 109, \mathrm{CZ} on output 35, output 114, \mathrm{CZ} on output 35, output 115, \mathrm{CZ} on output 35, output 117, \mathrm{CZ} on output 35, output 120, \mathrm{CZ} on output 35, output 125, \mathrm{CZ} on output 35, output 126, \mathrm{CZ} on output 35, output 128, \mathrm{CZ} on output 35, output 131, \mathrm{CZ} on output 35, check 151, \mathrm{CZ} on output 35, check 152, \mathrm{CZ} on output 35, check 153, \mathrm{CZ} on output 35, check 154, \mathrm{CZ} on output 35, check 155, \mathrm{CZ} on output 37, output 38, \mathrm{CZ} on output 37, output 40, \mathrm{CZ} on output 37, output 41, \mathrm{CZ} on output 37, output 70, \mathrm{CZ} on output 37, output 71, \mathrm{CZ} on output 37, output 73, \mathrm{CZ} on output 37, output 76, \mathrm{CZ} on output 37, output 81, \mathrm{CZ} on output 37, output 82, \mathrm{CZ} on output 37, output 84, \mathrm{CZ} on output 37, output 87, \mathrm{CZ} on output 37, output 92, \mathrm{CZ} on output 37, output 93, \mathrm{CZ} on output 37, output 95, \mathrm{CZ} on output 37, output 98, \mathrm{CZ} on output 37, output 103, \mathrm{CZ} on output 37, output 104, \mathrm{CZ} on output 37, output 106, \mathrm{CZ} on output 37, output 109, \mathrm{CZ} on output 37, output 114, \mathrm{CZ} on output 37, output 115, \mathrm{CZ} on output 37, output 117, \mathrm{CZ} on output 37, output 120, \mathrm{CZ} on output 37, output 125, \mathrm{CZ} on output 37, output 126, \mathrm{CZ} on output 37, output 128, \mathrm{CZ} on output 37, output 131, \mathrm{CZ} on output 37, check 150, \mathrm{CZ} on output 37, check 151, \mathrm{CZ} on output 37, check 152, \mathrm{CZ} on output 37, check 154, \mathrm{CZ} on output 38, output 40, \mathrm{CZ} on output 38, output 41, \mathrm{CZ} on output 38, output 70, \mathrm{CZ} on output 38, output 71, \mathrm{CZ} on output 38, output 73, \mathrm{CZ} on output 38, output 76, \mathrm{CZ} on output 38, output 103, \mathrm{CZ} on output 38, output 104, \mathrm{CZ} on output 38, output 106, \mathrm{CZ} on output 38, output 109, \mathrm{CZ} on output 38, output 114, \mathrm{CZ} on output 38, output 115, \mathrm{CZ} on output 38, output 117, \mathrm{CZ} on output 38, output 120, \mathrm{CZ} on output 38, output 125, \mathrm{CZ} on output 38, output 126, \mathrm{CZ} on output 38, output 128, \mathrm{CZ} on output 38, output 131, \mathrm{CZ} on output 38, check 150, \mathrm{CZ} on output 38, check 155, \mathrm{CZ} on output 39, output 41, \mathrm{CZ} on output 39, output 42, \mathrm{CZ} on output 39, output 103, \mathrm{CZ} on output 39, output 104, \mathrm{CZ} on output 39, output 106, \mathrm{CZ} on output 39, output 109, \mathrm{CZ} on output 39, output 114, \mathrm{CZ} on output 39, output 115, \mathrm{CZ} on output 39, output 117, \mathrm{CZ} on output 39, output 120, \mathrm{CZ} on output 39, output 125, \mathrm{CZ} on output 39, output 126, \mathrm{CZ} on output 39, output 128, \mathrm{CZ} on output 39, output 131, \mathrm{CZ} on output 39, check 153, \mathrm{CZ} on output 40, output 42, \mathrm{CZ} on output 40, output 70, \mathrm{CZ} on output 40, output 71, \mathrm{CZ} on output 40, output 73, \mathrm{CZ} on output 40, output 76, \mathrm{CZ} on output 40, check 150, \mathrm{CZ} on output 40, check 153, \mathrm{CZ} on output 40, check 154, \mathrm{CZ} on output 40, check 155, \mathrm{CZ} on output 41, output 43, \mathrm{CZ} on output 41, output 81, \mathrm{CZ} on output 41, output 82, \mathrm{CZ} on output 41, output 84, \mathrm{CZ} on output 41, output 87, \mathrm{CZ} on output 41, output 92, \mathrm{CZ} on output 41, output 93, \mathrm{CZ} on output 41, output 95, \mathrm{CZ} on output 41, output 98, \mathrm{CZ} on output 41, output 103, \mathrm{CZ} on output 41, output 104, \mathrm{CZ} on output 41, output 106, \mathrm{CZ} on output 41, output 109, \mathrm{CZ} on output 41, output 114, \mathrm{CZ} on output 41, output 115, \mathrm{CZ} on output 41, output 117, \mathrm{CZ} on output 41, output 120, \mathrm{CZ} on output 41, output 125, \mathrm{CZ} on output 41, output 126, \mathrm{CZ} on output 41, output 128, \mathrm{CZ} on output 41, output 131, \mathrm{CZ} on output 41, check 151, \mathrm{CZ} on output 41, check 152, \mathrm{CZ} on output 41, check 153, \mathrm{CZ} on output 41, check 155, \mathrm{CZ} on output 42, output 43, \mathrm{CZ} on output 42, output 70, \mathrm{CZ} on output 42, output 71, \mathrm{CZ} on output 42, output 73, \mathrm{CZ} on output 42, output 76, \mathrm{CZ} on output 42, output 103, \mathrm{CZ} on output 42, output 104, \mathrm{CZ} on output 42, output 106, \mathrm{CZ} on output 42, output 109, \mathrm{CZ} on output 42, output 114, \mathrm{CZ} on output 42, output 115, \mathrm{CZ} on output 42, output 117, \mathrm{CZ} on output 42, output 120, \mathrm{CZ} on output 42, output 125, \mathrm{CZ} on output 42, output 126, \mathrm{CZ} on output 42, output 128, \mathrm{CZ} on output 42, output 131, \mathrm{CZ} on output 42, check 150, \mathrm{CZ} on output 42, check 153, \mathrm{CZ} on output 42, check 154, \mathrm{CZ} on output 43, output 92, \mathrm{CZ} on output 43, output 93, \mathrm{CZ} on output 43, output 95, \mathrm{CZ} on output 43, output 98, \mathrm{CZ} on output 43, output 114, \mathrm{CZ} on output 43, output 115, \mathrm{CZ} on output 43, output 117, \mathrm{CZ} on output 43, output 120, \mathrm{CZ} on output 43, check 152, \mathrm{CZ} on output 43, check 153, \mathrm{CZ} on output 43, check 154, \mathrm{CZ} on output 44, output 49, \mathrm{CZ} on output 44, output 50, \mathrm{CZ} on output 44, output 51, \mathrm{CZ} on output 44, output 52, \mathrm{CZ} on output 44, output 82, \mathrm{CZ} on output 44, output 83, \mathrm{CZ} on output 44, output 84, \mathrm{CZ} on output 44, output 85, \mathrm{CZ} on output 44, output 104, \mathrm{CZ} on output 44, output 105, \mathrm{CZ} on output 44, output 106, \mathrm{CZ} on output 44, output 107, \mathrm{CZ} on output 44, output 115, \mathrm{CZ} on output 44, output 116, \mathrm{CZ} on output 44, output 117, \mathrm{CZ} on output 44, output 118, \mathrm{CZ} on output 44, output 126, \mathrm{CZ} on output 44, output 127, \mathrm{CZ} on output 44, output 128, \mathrm{CZ} on output 44, output 129, \mathrm{CZ} on output 44, check 157, \mathrm{CZ} on output 44, check 159, \mathrm{CZ} on output 44, check 160, \mathrm{CZ} on output 44, check 161, \mathrm{CZ} on output 45, output 46, \mathrm{CZ} on output 45, output 49, \mathrm{CZ} on output 45, output 51, \mathrm{CZ} on output 45, output 52, \mathrm{CZ} on output 45, output 53, \mathrm{CZ} on output 45, output 54, \mathrm{CZ} on output 45, output 71, \mathrm{CZ} on output 45, output 72, \mathrm{CZ} on output 45, output 73, \mathrm{CZ} on output 45, output 74, \mathrm{CZ} on output 45, output 82, \mathrm{CZ} on output 45, output 83, \mathrm{CZ} on output 45, output 84, \mathrm{CZ} on output 45, output 85, \mathrm{CZ} on output 45, output 93, \mathrm{CZ} on output 45, output 94, \mathrm{CZ} on output 45, output 95, \mathrm{CZ} on output 45, output 96, \mathrm{CZ} on output 45, output 115, \mathrm{CZ} on output 45, output 116, \mathrm{CZ} on output 45, output 117, \mathrm{CZ} on output 45, output 118, \mathrm{CZ} on output 45, check 156, \mathrm{CZ} on output 45, check 157, \mathrm{CZ} on output 45, check 158, \mathrm{CZ} on output 45, check 160, \mathrm{CZ} on output 46, output 48, \mathrm{CZ} on output 46, output 49, \mathrm{CZ} on output 46, output 50, \mathrm{CZ} on output 46, output 51, \mathrm{CZ} on output 46, output 54, \mathrm{CZ} on output 46, output 82, \mathrm{CZ} on output 46, output 83, \mathrm{CZ} on output 46, output 84, \mathrm{CZ} on output 46, output 85, \mathrm{CZ} on output 46, output 93, \mathrm{CZ} on output 46, output 94, \mathrm{CZ} on output 46, output 95, \mathrm{CZ} on output 46, output 96, \mathrm{CZ} on output 46, output 104, \mathrm{CZ} on output 46, output 105, \mathrm{CZ} on output 46, output 106, \mathrm{CZ} on output 46, output 107, \mathrm{CZ} on output 46, output 115, \mathrm{CZ} on output 46, output 116, \mathrm{CZ} on output 46, output 117, \mathrm{CZ} on output 46, output 118, \mathrm{CZ} on output 46, output 126, \mathrm{CZ} on output 46, output 127, \mathrm{CZ} on output 46, output 128, \mathrm{CZ} on output 46, output 129, \mathrm{CZ} on output 46, check 157, \mathrm{CZ} on output 46, check 158, \mathrm{CZ} on output 46, check 159, \mathrm{CZ} on output 46, check 160, \mathrm{CZ} on output 46, check 161, \mathrm{CZ} on output 48, output 49, \mathrm{CZ} on output 48, output 51, \mathrm{CZ} on output 48, output 52, \mathrm{CZ} on output 48, output 71, \mathrm{CZ} on output 48, output 72, \mathrm{CZ} on output 48, output 73, \mathrm{CZ} on output 48, output 74, \mathrm{CZ} on output 48, output 82, \mathrm{CZ} on output 48, output 83, \mathrm{CZ} on output 48, output 84, \mathrm{CZ} on output 48, output 85, \mathrm{CZ} on output 48, output 93, \mathrm{CZ} on output 48, output 94, \mathrm{CZ} on output 48, output 95, \mathrm{CZ} on output 48, output 96, \mathrm{CZ} on output 48, output 104, \mathrm{CZ} on output 48, output 105, \mathrm{CZ} on output 48, output 106, \mathrm{CZ} on output 48, output 107, \mathrm{CZ} on output 48, output 115, \mathrm{CZ} on output 48, output 116, \mathrm{CZ} on output 48, output 117, \mathrm{CZ} on output 48, output 118, \mathrm{CZ} on output 48, output 126, \mathrm{CZ} on output 48, output 127, \mathrm{CZ} on output 48, output 128, \mathrm{CZ} on output 48, output 129, \mathrm{CZ} on output 48, check 156, \mathrm{CZ} on output 48, check 157, \mathrm{CZ} on output 48, check 158, \mathrm{CZ} on output 48, check 160, \mathrm{CZ} on output 49, output 51, \mathrm{CZ} on output 49, output 52, \mathrm{CZ} on output 49, output 71, \mathrm{CZ} on output 49, output 72, \mathrm{CZ} on output 49, output 73, \mathrm{CZ} on output 49, output 74, \mathrm{CZ} on output 49, output 104, \mathrm{CZ} on output 49, output 105, \mathrm{CZ} on output 49, output 106, \mathrm{CZ} on output 49, output 107, \mathrm{CZ} on output 49, output 115, \mathrm{CZ} on output 49, output 116, \mathrm{CZ} on output 49, output 117, \mathrm{CZ} on output 49, output 118, \mathrm{CZ} on output 49, output 126, \mathrm{CZ} on output 49, output 127, \mathrm{CZ} on output 49, output 128, \mathrm{CZ} on output 49, output 129, \mathrm{CZ} on output 49, check 156, \mathrm{CZ} on output 49, check 161, \mathrm{CZ} on output 50, output 52, \mathrm{CZ} on output 50, output 53, \mathrm{CZ} on output 50, output 104, \mathrm{CZ} on output 50, output 105, \mathrm{CZ} on output 50, output 106, \mathrm{CZ} on output 50, output 107, \mathrm{CZ} on output 50, output 115, \mathrm{CZ} on output 50, output 116, \mathrm{CZ} on output 50, output 117, \mathrm{CZ} on output 50, output 118, \mathrm{CZ} on output 50, output 126, \mathrm{CZ} on output 50, output 127, \mathrm{CZ} on output 50, output 128, \mathrm{CZ} on output 50, output 129, \mathrm{CZ} on output 50, check 159, \mathrm{CZ} on output 51, output 53, \mathrm{CZ} on output 51, output 71, \mathrm{CZ} on output 51, output 72, \mathrm{CZ} on output 51, output 73, \mathrm{CZ} on output 51, output 74, \mathrm{CZ} on output 51, check 156, \mathrm{CZ} on output 51, check 159, \mathrm{CZ} on output 51, check 160, \mathrm{CZ} on output 51, check 161, \mathrm{CZ} on output 52, output 54, \mathrm{CZ} on output 52, output 82, \mathrm{CZ} on output 52, output 83, \mathrm{CZ} on output 52, output 84, \mathrm{CZ} on output 52, output 85, \mathrm{CZ} on output 52, output 93, \mathrm{CZ} on output 52, output 94, \mathrm{CZ} on output 52, output 95, \mathrm{CZ} on output 52, output 96, \mathrm{CZ} on output 52, output 104, \mathrm{CZ} on output 52, output 105, \mathrm{CZ} on output 52, output 106, \mathrm{CZ} on output 52, output 107, \mathrm{CZ} on output 52, output 115, \mathrm{CZ} on output 52, output 116, \mathrm{CZ} on output 52, output 117, \mathrm{CZ} on output 52, output 118, \mathrm{CZ} on output 52, output 126, \mathrm{CZ} on output 52, output 127, \mathrm{CZ} on output 52, output 128, \mathrm{CZ} on output 52, output 129, \mathrm{CZ} on output 52, check 157, \mathrm{CZ} on output 52, check 158, \mathrm{CZ} on output 52, check 159, \mathrm{CZ} on output 52, check 161, \mathrm{CZ} on output 53, output 54, \mathrm{CZ} on output 53, output 71, \mathrm{CZ} on output 53, output 72, \mathrm{CZ} on output 53, output 73, \mathrm{CZ} on output 53, output 74, \mathrm{CZ} on output 53, output 104, \mathrm{CZ} on output 53, output 105, \mathrm{CZ} on output 53, output 106, \mathrm{CZ} on output 53, output 107, \mathrm{CZ} on output 53, output 115, \mathrm{CZ} on output 53, output 116, \mathrm{CZ} on output 53, output 117, \mathrm{CZ} on output 53, output 118, \mathrm{CZ} on output 53, output 126, \mathrm{CZ} on output 53, output 127, \mathrm{CZ} on output 53, output 128, \mathrm{CZ} on output 53, output 129, \mathrm{CZ} on output 53, check 156, \mathrm{CZ} on output 53, check 159, \mathrm{CZ} on output 53, check 160, \mathrm{CZ} on output 54, output 93, \mathrm{CZ} on output 54, output 94, \mathrm{CZ} on output 54, output 95, \mathrm{CZ} on output 54, output 96, \mathrm{CZ} on output 54, output 115, \mathrm{CZ} on output 54, output 116, \mathrm{CZ} on output 54, output 117, \mathrm{CZ} on output 54, output 118, \mathrm{CZ} on output 54, check 158, \mathrm{CZ} on output 54, check 159, \mathrm{CZ} on output 54, check 160, \mathrm{CZ} on output 55, output 60, \mathrm{CZ} on output 55, output 61, \mathrm{CZ} on output 55, output 62, \mathrm{CZ} on output 55, output 63, \mathrm{CZ} on output 55, output 81, \mathrm{CZ} on output 55, output 83, \mathrm{CZ} on output 55, output 84, \mathrm{CZ} on output 55, output 86, \mathrm{CZ} on output 55, output 103, \mathrm{CZ} on output 55, output 105, \mathrm{CZ} on output 55, output 106, \mathrm{CZ} on output 55, output 108, \mathrm{CZ} on output 55, output 114, \mathrm{CZ} on output 55, output 116, \mathrm{CZ} on output 55, output 117, \mathrm{CZ} on output 55, output 119, \mathrm{CZ} on output 55, output 125, \mathrm{CZ} on output 55, output 127, \mathrm{CZ} on output 55, output 128, \mathrm{CZ} on output 55, output 130, \mathrm{CZ} on output 55, check 163, \mathrm{CZ} on output 55, check 165, \mathrm{CZ} on output 55, check 166, \mathrm{CZ} on output 55, check 167, \mathrm{CZ} on output 56, output 57, \mathrm{CZ} on output 56, output 60, \mathrm{CZ} on output 56, output 62, \mathrm{CZ} on output 56, output 63, \mathrm{CZ} on output 56, output 64, \mathrm{CZ} on output 56, output 65, \mathrm{CZ} on output 56, output 70, \mathrm{CZ} on output 56, output 72, \mathrm{CZ} on output 56, output 73, \mathrm{CZ} on output 56, output 75, \mathrm{CZ} on output 56, output 81, \mathrm{CZ} on output 56, output 83, \mathrm{CZ} on output 56, output 84, \mathrm{CZ} on output 56, output 86, \mathrm{CZ} on output 56, output 92, \mathrm{CZ} on output 56, output 94, \mathrm{CZ} on output 56, output 95, \mathrm{CZ} on output 56, output 97, \mathrm{CZ} on output 56, output 114, \mathrm{CZ} on output 56, output 116, \mathrm{CZ} on output 56, output 117, \mathrm{CZ} on output 56, output 119, \mathrm{CZ} on output 56, check 162, \mathrm{CZ} on output 56, check 163, \mathrm{CZ} on output 56, check 164, \mathrm{CZ} on output 56, check 166, \mathrm{CZ} on output 57, output 59, \mathrm{CZ} on output 57, output 60, \mathrm{CZ} on output 57, output 61, \mathrm{CZ} on output 57, output 62, \mathrm{CZ} on output 57, output 65, \mathrm{CZ} on output 57, output 81, \mathrm{CZ} on output 57, output 83, \mathrm{CZ} on output 57, output 84, \mathrm{CZ} on output 57, output 86, \mathrm{CZ} on output 57, output 92, \mathrm{CZ} on output 57, output 94, \mathrm{CZ} on output 57, output 95, \mathrm{CZ} on output 57, output 97, \mathrm{CZ} on output 57, output 103, \mathrm{CZ} on output 57, output 105, \mathrm{CZ} on output 57, output 106, \mathrm{CZ} on output 57, output 108, \mathrm{CZ} on output 57, output 114, \mathrm{CZ} on output 57, output 116, \mathrm{CZ} on output 57, output 117, \mathrm{CZ} on output 57, output 119, \mathrm{CZ} on output 57, output 125, \mathrm{CZ} on output 57, output 127, \mathrm{CZ} on output 57, output 128, \mathrm{CZ} on output 57, output 130, \mathrm{CZ} on output 57, check 163, \mathrm{CZ} on output 57, check 164, \mathrm{CZ} on output 57, check 165, \mathrm{CZ} on output 57, check 166, \mathrm{CZ} on output 57, check 167, \mathrm{CZ} on output 59, output 60, \mathrm{CZ} on output 59, output 62, \mathrm{CZ} on output 59, output 63, \mathrm{CZ} on output 59, output 70, \mathrm{CZ} on output 59, output 72, \mathrm{CZ} on output 59, output 73, \mathrm{CZ} on output 59, output 75, \mathrm{CZ} on output 59, output 81, \mathrm{CZ} on output 59, output 83, \mathrm{CZ} on output 59, output 84, \mathrm{CZ} on output 59, output 86, \mathrm{CZ} on output 59, output 92, \mathrm{CZ} on output 59, output 94, \mathrm{CZ} on output 59, output 95, \mathrm{CZ} on output 59, output 97, \mathrm{CZ} on output 59, output 103, \mathrm{CZ} on output 59, output 105, \mathrm{CZ} on output 59, output 106, \mathrm{CZ} on output 59, output 108, \mathrm{CZ} on output 59, output 114, \mathrm{CZ} on output 59, output 116, \mathrm{CZ} on output 59, output 117, \mathrm{CZ} on output 59, output 119, \mathrm{CZ} on output 59, output 125, \mathrm{CZ} on output 59, output 127, \mathrm{CZ} on output 59, output 128, \mathrm{CZ} on output 59, output 130, \mathrm{CZ} on output 59, check 162, \mathrm{CZ} on output 59, check 163, \mathrm{CZ} on output 59, check 164, \mathrm{CZ} on output 59, check 166, \mathrm{CZ} on output 60, output 62, \mathrm{CZ} on output 60, output 63, \mathrm{CZ} on output 60, output 70, \mathrm{CZ} on output 60, output 72, \mathrm{CZ} on output 60, output 73, \mathrm{CZ} on output 60, output 75, \mathrm{CZ} on output 60, output 103, \mathrm{CZ} on output 60, output 105, \mathrm{CZ} on output 60, output 106, \mathrm{CZ} on output 60, output 108, \mathrm{CZ} on output 60, output 114, \mathrm{CZ} on output 60, output 116, \mathrm{CZ} on output 60, output 117, \mathrm{CZ} on output 60, output 119, \mathrm{CZ} on output 60, output 125, \mathrm{CZ} on output 60, output 127, \mathrm{CZ} on output 60, output 128, \mathrm{CZ} on output 60, output 130, \mathrm{CZ} on output 60, check 162, \mathrm{CZ} on output 60, check 167, \mathrm{CZ} on output 61, output 63, \mathrm{CZ} on output 61, output 64, \mathrm{CZ} on output 61, output 103, \mathrm{CZ} on output 61, output 105, \mathrm{CZ} on output 61, output 106, \mathrm{CZ} on output 61, output 108, \mathrm{CZ} on output 61, output 114, \mathrm{CZ} on output 61, output 116, \mathrm{CZ} on output 61, output 117, \mathrm{CZ} on output 61, output 119, \mathrm{CZ} on output 61, output 125, \mathrm{CZ} on output 61, output 127, \mathrm{CZ} on output 61, output 128, \mathrm{CZ} on output 61, output 130, \mathrm{CZ} on output 61, check 165, \mathrm{CZ} on output 62, output 64, \mathrm{CZ} on output 62, output 70, \mathrm{CZ} on output 62, output 72, \mathrm{CZ} on output 62, output 73, \mathrm{CZ} on output 62, output 75, \mathrm{CZ} on output 62, check 162, \mathrm{CZ} on output 62, check 165, \mathrm{CZ} on output 62, check 166, \mathrm{CZ} on output 62, check 167, \mathrm{CZ} on output 63, output 65, \mathrm{CZ} on output 63, output 81, \mathrm{CZ} on output 63, output 83, \mathrm{CZ} on output 63, output 84, \mathrm{CZ} on output 63, output 86, \mathrm{CZ} on output 63, output 92, \mathrm{CZ} on output 63, output 94, \mathrm{CZ} on output 63, output 95, \mathrm{CZ} on output 63, output 97, \mathrm{CZ} on output 63, output 103, \mathrm{CZ} on output 63, output 105, \mathrm{CZ} on output 63, output 106, \mathrm{CZ} on output 63, output 108, \mathrm{CZ} on output 63, output 114, \mathrm{CZ} on output 63, output 116, \mathrm{CZ} on output 63, output 117, \mathrm{CZ} on output 63, output 119, \mathrm{CZ} on output 63, output 125, \mathrm{CZ} on output 63, output 127, \mathrm{CZ} on output 63, output 128, \mathrm{CZ} on output 63, output 130, \mathrm{CZ} on output 63, check 163, \mathrm{CZ} on output 63, check 164, \mathrm{CZ} on output 63, check 165, \mathrm{CZ} on output 63, check 167, \mathrm{CZ} on output 64, output 65, \mathrm{CZ} on output 64, output 70, \mathrm{CZ} on output 64, output 72, \mathrm{CZ} on output 64, output 73, \mathrm{CZ} on output 64, output 75, \mathrm{CZ} on output 64, output 103, \mathrm{CZ} on output 64, output 105, \mathrm{CZ} on output 64, output 106, \mathrm{CZ} on output 64, output 108, \mathrm{CZ} on output 64, output 114, \mathrm{CZ} on output 64, output 116, \mathrm{CZ} on output 64, output 117, \mathrm{CZ} on output 64, output 119, \mathrm{CZ} on output 64, output 125, \mathrm{CZ} on output 64, output 127, \mathrm{CZ} on output 64, output 128, \mathrm{CZ} on output 64, output 130, \mathrm{CZ} on output 64, check 162, \mathrm{CZ} on output 64, check 165, \mathrm{CZ} on output 64, check 166, \mathrm{CZ} on output 65, output 92, \mathrm{CZ} on output 65, output 94, \mathrm{CZ} on output 65, output 95, \mathrm{CZ} on output 65, output 97, \mathrm{CZ} on output 65, output 114, \mathrm{CZ} on output 65, output 116, \mathrm{CZ} on output 65, output 117, \mathrm{CZ} on output 65, output 119, \mathrm{CZ} on output 65, check 164, \mathrm{CZ} on output 65, check 165, \mathrm{CZ} on output 65, check 166, \mathrm{CZ} on output 67, output 73, \mathrm{CZ} on output 67, output 74, \mathrm{CZ} on output 67, output 75, \mathrm{CZ} on output 67, output 76, \mathrm{CZ} on output 70, output 71, \mathrm{CZ} on output 70, output 72, \mathrm{CZ} on output 70, output 73, \mathrm{CZ} on output 70, output 74, \mathrm{CZ} on output 70, output 75, \mathrm{CZ} on output 70, output 76, \mathrm{CZ} on output 70, check 150, \mathrm{CZ} on output 70, check 162, \mathrm{CZ} on output 71, output 72, \mathrm{CZ} on output 71, output 73, \mathrm{CZ} on output 71, output 74, \mathrm{CZ} on output 71, output 75, \mathrm{CZ} on output 71, output 76, \mathrm{CZ} on output 71, check 150, \mathrm{CZ} on output 71, check 156, \mathrm{CZ} on output 72, output 73, \mathrm{CZ} on output 72, output 74, \mathrm{CZ} on output 72, output 75, \mathrm{CZ} on output 72, output 76, \mathrm{CZ} on output 72, check 156, \mathrm{CZ} on output 72, check 162, \mathrm{CZ} on output 73, output 74, \mathrm{CZ} on output 73, output 75, \mathrm{CZ} on output 73, output 76, \mathrm{CZ} on output 73, check 150, \mathrm{CZ} on output 73, check 156, \mathrm{CZ} on output 73, check 162, \mathrm{CZ} on output 74, output 75, \mathrm{CZ} on output 74, output 76, \mathrm{CZ} on output 74, check 156, \mathrm{CZ} on output 75, output 76, \mathrm{CZ} on output 75, check 162, \mathrm{CZ} on output 76, check 150, \mathrm{CZ} on output 78, output 84, \mathrm{CZ} on output 78, output 85, \mathrm{CZ} on output 78, output 86, \mathrm{CZ} on output 78, output 87, \mathrm{CZ} on output 81, output 82, \mathrm{CZ} on output 81, output 83, \mathrm{CZ} on output 81, output 84, \mathrm{CZ} on output 81, output 85, \mathrm{CZ} on output 81, output 86, \mathrm{CZ} on output 81, output 87, \mathrm{CZ} on output 81, check 151, \mathrm{CZ} on output 81, check 163, \mathrm{CZ} on output 82, output 83, \mathrm{CZ} on output 82, output 84, \mathrm{CZ} on output 82, output 85, \mathrm{CZ} on output 82, output 86, \mathrm{CZ} on output 82, output 87, \mathrm{CZ} on output 82, check 151, \mathrm{CZ} on output 82, check 157, \mathrm{CZ} on output 83, output 84, \mathrm{CZ} on output 83, output 85, \mathrm{CZ} on output 83, output 86, \mathrm{CZ} on output 83, output 87, \mathrm{CZ} on output 83, check 157, \mathrm{CZ} on output 83, check 163, \mathrm{CZ} on output 84, output 85, \mathrm{CZ} on output 84, output 86, \mathrm{CZ} on output 84, output 87, \mathrm{CZ} on output 84, check 151, \mathrm{CZ} on output 84, check 157, \mathrm{CZ} on output 84, check 163, \mathrm{CZ} on output 85, output 86, \mathrm{CZ} on output 85, output 87, \mathrm{CZ} on output 85, check 157, \mathrm{CZ} on output 86, output 87, \mathrm{CZ} on output 86, check 163, \mathrm{CZ} on output 87, check 151, \mathrm{CZ} on output 89, output 95, \mathrm{CZ} on output 89, output 96, \mathrm{CZ} on output 89, output 97, \mathrm{CZ} on output 89, output 98, \mathrm{CZ} on output 92, output 93, \mathrm{CZ} on output 92, output 94, \mathrm{CZ} on output 92, output 95, \mathrm{CZ} on output 92, output 96, \mathrm{CZ} on output 92, output 97, \mathrm{CZ} on output 92, output 98, \mathrm{CZ} on output 92, check 152, \mathrm{CZ} on output 92, check 164, \mathrm{CZ} on output 93, output 94, \mathrm{CZ} on output 93, output 95, \mathrm{CZ} on output 93, output 96, \mathrm{CZ} on output 93, output 97, \mathrm{CZ} on output 93, output 98, \mathrm{CZ} on output 93, check 152, \mathrm{CZ} on output 93, check 158, \mathrm{CZ} on output 94, output 95, \mathrm{CZ} on output 94, output 96, \mathrm{CZ} on output 94, output 97, \mathrm{CZ} on output 94, output 98, \mathrm{CZ} on output 94, check 158, \mathrm{CZ} on output 94, check 164, \mathrm{CZ} on output 95, output 96, \mathrm{CZ} on output 95, output 97, \mathrm{CZ} on output 95, output 98, \mathrm{CZ} on output 95, check 152, \mathrm{CZ} on output 95, check 158, \mathrm{CZ} on output 95, check 164, \mathrm{CZ} on output 96, output 97, \mathrm{CZ} on output 96, output 98, \mathrm{CZ} on output 96, check 158, \mathrm{CZ} on output 97, output 98, \mathrm{CZ} on output 97, check 164, \mathrm{CZ} on output 98, check 152, \mathrm{CZ} on output 100, output 106, \mathrm{CZ} on output 100, output 107, \mathrm{CZ} on output 100, output 108, \mathrm{CZ} on output 100, output 109, \mathrm{CZ} on output 103, output 104, \mathrm{CZ} on output 103, output 105, \mathrm{CZ} on output 103, output 106, \mathrm{CZ} on output 103, output 107, \mathrm{CZ} on output 103, output 108, \mathrm{CZ} on output 103, output 109, \mathrm{CZ} on output 103, check 153, \mathrm{CZ} on output 103, check 165, \mathrm{CZ} on output 104, output 105, \mathrm{CZ} on output 104, output 106, \mathrm{CZ} on output 104, output 107, \mathrm{CZ} on output 104, output 108, \mathrm{CZ} on output 104, output 109, \mathrm{CZ} on output 104, check 153, \mathrm{CZ} on output 104, check 159, \mathrm{CZ} on output 105, output 106, \mathrm{CZ} on output 105, output 107, \mathrm{CZ} on output 105, output 108, \mathrm{CZ} on output 105, output 109, \mathrm{CZ} on output 105, check 159, \mathrm{CZ} on output 105, check 165, \mathrm{CZ} on output 106, output 107, \mathrm{CZ} on output 106, output 108, \mathrm{CZ} on output 106, output 109, \mathrm{CZ} on output 106, check 153, \mathrm{CZ} on output 106, check 159, \mathrm{CZ} on output 106, check 165, \mathrm{CZ} on output 107, output 108, \mathrm{CZ} on output 107, output 109, \mathrm{CZ} on output 107, check 159, \mathrm{CZ} on output 108, output 109, \mathrm{CZ} on output 108, check 165, \mathrm{CZ} on output 109, check 153, \mathrm{CZ} on output 111, output 117, \mathrm{CZ} on output 111, output 118, \mathrm{CZ} on output 111, output 119, \mathrm{CZ} on output 111, output 120, \mathrm{CZ} on output 114, output 115, \mathrm{CZ} on output 114, output 116, \mathrm{CZ} on output 114, output 117, \mathrm{CZ} on output 114, output 118, \mathrm{CZ} on output 114, output 119, \mathrm{CZ} on output 114, output 120, \mathrm{CZ} on output 114, check 154, \mathrm{CZ} on output 114, check 166, \mathrm{CZ} on output 115, output 116, \mathrm{CZ} on output 115, output 117, \mathrm{CZ} on output 115, output 118, \mathrm{CZ} on output 115, output 119, \mathrm{CZ} on output 115, output 120, \mathrm{CZ} on output 115, check 154, \mathrm{CZ} on output 115, check 160, \mathrm{CZ} on output 116, output 117, \mathrm{CZ} on output 116, output 118, \mathrm{CZ} on output 116, output 119, \mathrm{CZ} on output 116, output 120, \mathrm{CZ} on output 116, check 160, \mathrm{CZ} on output 116, check 166, \mathrm{CZ} on output 117, output 118, \mathrm{CZ} on output 117, output 119, \mathrm{CZ} on output 117, output 120, \mathrm{CZ} on output 117, check 154, \mathrm{CZ} on output 117, check 160, \mathrm{CZ} on output 117, check 166, \mathrm{CZ} on output 118, output 119, \mathrm{CZ} on output 118, output 120, \mathrm{CZ} on output 118, check 160, \mathrm{CZ} on output 119, output 120, \mathrm{CZ} on output 119, check 166, \mathrm{CZ} on output 120, check 154, \mathrm{CZ} on output 122, output 128, \mathrm{CZ} on output 122, output 129, \mathrm{CZ} on output 122, output 130, \mathrm{CZ} on output 122, output 131, \mathrm{CZ} on output 125, output 126, \mathrm{CZ} on output 125, output 127, \mathrm{CZ} on output 125, output 128, \mathrm{CZ} on output 125, output 129, \mathrm{CZ} on output 125, output 130, \mathrm{CZ} on output 125, output 131, \mathrm{CZ} on output 125, check 155, \mathrm{CZ} on output 125, check 167, \mathrm{CZ} on output 126, output 127, \mathrm{CZ} on output 126, output 128, \mathrm{CZ} on output 126, output 129, \mathrm{CZ} on output 126, output 130, \mathrm{CZ} on output 126, output 131, \mathrm{CZ} on output 126, check 155, \mathrm{CZ} on output 126, check 161, \mathrm{CZ} on output 127, output 128, \mathrm{CZ} on output 127, output 129, \mathrm{CZ} on output 127, output 130, \mathrm{CZ} on output 127, output 131, \mathrm{CZ} on output 127, check 161, \mathrm{CZ} on output 127, check 167, \mathrm{CZ} on output 128, output 129, \mathrm{CZ} on output 128, output 130, \mathrm{CZ} on output 128, output 131, \mathrm{CZ} on output 128, check 155, \mathrm{CZ} on output 128, check 161, \mathrm{CZ} on output 128, check 167, \mathrm{CZ} on output 129, output 130, \mathrm{CZ} on output 129, output 131, \mathrm{CZ} on output 129, check 161, \mathrm{CZ} on output 130, output 131, \mathrm{CZ} on output 130, check 167, \mathrm{CZ} on output 131, check 155

Or no Clifford gate at all: run \mathrm{T}^3 on rotations 1, 7, 14, 16, 23, 25, 30, 36, 38, 39, 40, 42, 44, 45, 47, 51, 57, 58, 64, 71, 73, 80, 82, 87 and 260 more (listed below); \mathrm{T}^5 on rotations 3, 8, 9, 10, 27, 60, 65, 67, 84, 117, 122, 124, 141, 174, 179, 180, 181, 198, 231, 236, 237, 238, 255, 288 and 16 more (listed below); \mathrm{T}^\dagger on rotations 0, 2, 4, 5, 6, 13, 15, 59, 61, 62, 63, 70, 72, 116, 118, 119, 120, 127, 129, 171, 173, 175, 176, 177 and 40 more (listed below), and \mathrm{T} on the rest. A power of \mathrm{T} costs one magic state, like \mathrm{T} itself. For a code this is a transversal \mathrm{T} gate, \mathrm{T}^j on each qubit.

All 284 rotations at T³

1, 7, 14, 16, 23, 25, 30, 36, 38, 39, 40, 42, 44, 45, 47, 51, 57, 58, 64, 71, 73, 80, 82, 87, 93, 95, 96, 97, 99, 101, 102, 104, 108, 114, 115, 121, 128, 130, 137, 139, 144, 150, 152, 153, 154, 156, 158, 159, 161, 165, 172, 178, 185, 187, 194, 196, 201, 207, 209, 210, 211, 213, 215, 216, 218, 222, 229, 235, 242, 244, 251, 253, 258, 264, 266, 267, 268, 270, 272, 273, 275, 279, 286, 292, 299, 301, 308, 310, 315, 321, 323, 324, 325, 327, 329, 330, 332, 336, 344, 347, 350, 354, 357, 358, 359, 360, 363, 365, 366, 371, 373, 377, 378, 379, 380, 381, 382, 384, 385, 386, 387, 390, 391, 392, 394, 395, 397, 398, 401, 404, 407, 411, 414, 415, 416, 417, 420, 422, 423, 428, 430, 434, 435, 436, 437, 438, 439, 441, 442, 443, 444, 447, 448, 449, 451, 452, 454, 455, 456, 458, 461, 462, 465, 468, 469, 471, 472, 474, 476, 477, 478, 480, 482, 486, 490, 491, 493, 495, 497, 498, 499, 500, 502, 503, 504, 507, 508, 509, 511, 512, 513, 515, 518, 519, 522, 525, 526, 528, 529, 531, 533, 534, 535, 537, 539, 543, 547, 548, 550, 552, 554, 555, 556, 557, 559, 560, 561, 564, 565, 566, 568, 569, 572, 575, 578, 582, 585, 586, 587, 588, 591, 593, 594, 599, 601, 605, 606, 607, 608, 609, 610, 612, 613, 614, 615, 618, 619, 620, 622, 623, 625, 626, 627, 629, 632, 633, 636, 639, 640, 642, 643, 645, 647, 648, 649, 651, 653, 657, 661, 662, 664, 666, 668, 669, 670, 671, 673, 674, 675, 678, 679, 680, 682, 683

All 40 rotations at T⁵

3, 8, 9, 10, 27, 60, 65, 67, 84, 117, 122, 124, 141, 174, 179, 180, 181, 198, 231, 236, 237, 238, 255, 288, 293, 294, 295, 312, 343, 356, 400, 413, 457, 460, 514, 517, 571, 584, 628, 631

All 64 rotations at T†

0, 2, 4, 5, 6, 13, 15, 59, 61, 62, 63, 70, 72, 116, 118, 119, 120, 127, 129, 171, 173, 175, 176, 177, 184, 186, 228, 230, 232, 233, 234, 241, 243, 285, 287, 289, 290, 291, 298, 300, 345, 346, 349, 352, 402, 403, 406, 409, 459, 463, 466, 470, 516, 520, 523, 527, 573, 574, 577, 580, 630, 634, 637, 641

Rotations are numbered by matrix column, from 0. The correction comes from the columns by the weight expansion of Bravyi and Haah (2012). verify_catalog.py re-derives it, checks the corrected circuit's phase input by input against the gate, and on small circuits simulates it gate by gate.

Convert the output with CNOT and S

A CNOT circuit on the outputs, followed by S, Z and CZ gates, turns this factory's gate into other gates that prepare the same magic state. Type a target gate to check whether it is reachable. If it is, you get the circuit, checked on every basis state.

Or list every gate it reaches. The list is built in your browser and saved as a text file, one gate per line.

Python code that writes the same list 
import json, urllib.request

NAMES = {1: "T", 2: "CS", 3: "CCZ"}


def equivalent_gates(k, terms, limit=1_000_000):
    """Every gate a CNOT circuit and S, Z, CZ gates reach from this one.

    A gate is its set of terms mod Clifford: {a} is T, {a,b} is CS and
    {a,b,c} is CCZ on those outputs. CNOT c->t sends x_t to
    x_c + x_t - 2 x_c x_t, so a term on t but not c adds the term with t
    replaced by c, and, below CCZ, the term with c added.
    """
    start = frozenset(frozenset(m) for m in terms)
    seen, queue = {start}, [start]
    for gate in queue:
        for c in range(k):
            for t in range(k):
                if c == t:
                    continue
                new = set(gate)
                for m in gate:
                    if t in m and c not in m:
                        new ^= {(m - {t}) | {c}}
                        if len(m) < 3:
                            new ^= {m | {c}}
                new = frozenset(new)
                if new not in seen:
                    seen.add(new)
                    queue.append(new)
                    if len(seen) > limit:
                        raise RuntimeError(f"more than {limit} equivalent gates")
    return seen


def name(gate, k):
    sep = "," if k > 10 else ""
    terms = sorted((sorted(m) for m in gate), key=lambda m: (len(m), m))
    return "·".join(NAMES[len(m)] + sep.join(map(str, m)) for m in terms) or "I"


url = "https://shubhamj810.github.io/magic-state-factory-repo/data/factories/684.132.3.a.json"
record = json.load(urllib.request.urlopen(url))
k = record["parameters"]["k"]
gates = equivalent_gates(k, record["gate"]["monomials"])
lines = sorted(name(g, k) for g in gates)
print(len(lines), "equivalent gates")
with open("equivalent-gates-684.132.3.a.txt", "w") as out:
    out.write("\n".join(lines) + "\n")

Distance

d=3, exact. No fault of weight below 3 is both undetectable and damaging. One of weight 3 is.

Exactly 5,760 faults of weight 3 are undetectable and damaging, so A_{3}=5{,}760. If each rotation fails independently with probability p, an accepted run has a damaged output with probability A_{3}\,p^{3}+O(p^{4}).

A damaging fault of weight 3 sits on columns [0,1,38].

A fault is a set of faulty columns. It is undetectable when their check parts cancel, and damaging when their output parts do not.

Original source

S. P. Jain, A. Wills, and S. Singh, "Symmetry and AI-assisted discovery of magic-state factories," arXiv:2610.06535 (2026). arxiv.org/abs/2610.06535

Provenance

found by an AI search that glues catalogued small factories along a graph of paired-column contractions; exact distance verified from columns; a verified witness, not a maximum

Found by: AI search: graph gluing

Discovery: AI search

1 recorded source
[
 {
  "regime": "AI search: graph gluing",
  "file": "master_catalog/imports/2026-09-18_graph_gluing_d3/factories.json",
  "label": "graph gluing [[684,132,3]]",
  "N": 168,
  "d": 3,
  "d_is_exact": true,
  "origin": null,
  "provenance": "AI search: graph gluing -- twelve [[63,11,3]] glued along K6,6 by 36 paired-column contraction(s) (independent ports); construction and witness in master_catalog/imports/2026-09-18_graph_gluing_d3/witnesses/graph_bipartite_n684_k132_d3.json",
  "notes": "Exact A3=5760 independently counted; details in master_catalog/imports/2026-09-18_graph_gluing_d3/README.md. General gluing has prior art; publication novelty is not asserted."
 }
]

Use it in code

Load this factory and re-derive every number from its circuit with the catalogue's own verifier.

# git clone https://github.com/shubhamj810/magic-state-factory-repo
# cd magic-state-factory-repo/master_catalog
import json, urllib.request
import verify_catalog as VC

url = "https://shubhamj810.github.io/magic-state-factory-repo/data/factories/684.132.3.a.json"
record = json.load(urllib.request.urlopen(url))
columns = record["circuit"]["columns"]
k, N = record["parameters"]["k"], record["parameters"]["N"]

facts, problems = VC.derive(columns, k, N)    # gate, T-count, degree, ...
distance = VC.measure_distance(columns, k, N)  # exhaustive fault search
print(facts["gate_human"], distance["d_exact"] or distance["d_at_least"],
      problems or "verified")

Raw record

Show the JSON this page is built from

    
Source: master_catalog.json, factories[1175].