[[496, 16, 6]] magic-state factory, T0·T1·T2·T3·T4·T5·T6·T7·T8·T9·T10·T11...

The circuit

The 78\times496 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 \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| '
out 0 (95)	···1···········1·····1·····1·1·1···1···········1·····1·····1·1·1···1··········1·····1·····1·1·1···1··········1·····1·····1·1·1···1···········1·····1·····11·1···1··········1····1·····1·1·1···1···········1·····1····1·1·1···1··········1·····1·····1·1·1···1···········1·····1····1·1·1···1···········1·····1·····1·1·1···1···········1····1·····1·1·1···1···········1·····1·····1·1·1···1··········1·····1·····1·1·1···1··········1····1·····1·1·1···1··········1·····1·····1·1·1···1···········1····1·····1·1
out 1 (159)	1·····1·1·1·····1····1··1·1··11···1·1·······1·1···1·111·····11··1······1·1·····1····1··1·1··11···1·1······1·1···1·111·····11··1·····1·1·1·····1····1··1·1·11···1·1······1·1··1·111·····11··1·····1·1·1·····1····1·1·1··11···1·1······1·1···1·111·····11··1·····1·1·1·····1····1··11··11···1·1·······1·1···1·111·····11··1·····1·1·1·····1···1··1·1··11···1·1·······1·1···1·111·····11··1····1·1·1·····1····1··1·1··11···1·1······1·1···1111·····11··1·····1·1·1····1····1··1·1··11···1·1·······1·1··1·111·····11
out 2 (127)	···1·1······1·1·····1·1····1·1·····1·1······1·1·····1·1····1·1·····1·1·····1·1·····1·1····1·1·····1·······1·1·····1·1····1·1·····1·1······1·1·····1·1····11·····1·1·····1·1····1·1····1·1·····1·1······1·1·····1·1···1·1·····1·1·····1·1·····1·1····1·1·····1·1······1·1·····1·1···1·1·····1·1······1·1·····1·1····1·1·····1·1······1·1····1·1····1·1·····1·1······1·1·····1·1····1·1·····11······1·1·····1·1····1·1·····1·1·····1·1····1·1····1·1·····1·1······11·····1·1····1·1·····1·1······1·1····1·1····1·1
out 3 (63)	····················11······11······················11······11·····················11······11·····················11······11······················11······1····················11······11······················11·····11·····················11······11······················11·····11······················11······11·····················11······11······················11······11·····················11······11····················11······11·····················11······11·····················11······11
out 4 (191)	1··1····1·11··1·1····1··1·1··11···111·1····11·····1·111·····11··1··1···1·11··1·1····1··1·1··11···1111····11·····1·111·····11··1··1····1·11··1·1····1··1·1·11···111·1····1····1·111·····11··1··1····1·11··1·1····1·1·1··11···111·1···11·····1·111·····11··1··1····1·11··1·1····1··11··11···111·1····11·····1·111·····11··1··1····1·11··1·1···1··1·1··11···111·1····11·····1·111·····11··1··1···1·11··1·1····1··1·1··11···111·1···11·····1111·····11··1··1····1·11·1·1····1··1·1··11···111·1····11····1·111·····11
out 5 (159)	········1·1·1·1·····11··1·1··11·1·1·1·1·········1·1··11·····11·········1·1·1·1·····11··1·1··11·1·1·11·········1·1··11·····11··········1·1·1·1·····11··1·1·11·1·1·1·1·········1··11·····11··········1·1·1·1·····11·1·1··11·1·1·1·1········1·1··11·····11··········1·1·1·1·····11··11··11·1·1·1·1·········1·1··11·····11··········1·1·1·1····11··1·1··11·1·1·1·1·········1·1··11·····11·········1·1·1·1·····11··1·1··11·1·1·1·1········1·1·11·····11··········1·1·11·····11··1·1··11·1·1·1·1·········11··11·····11
out 6 (223)	1··1···11·1···1·1····1·11·11·11···111·11····1·····1·1111···111··1··1··11·1···1·1····1·11·11·11···11111····1·····1·1111···111··1··1···11·1···1·1····1·11·1111···111·11···1····1·1111···111··1··1···11·1···1·1····1·1·11·11···111·11···1·····1·1111···111··1··1···11·1···1·1····1·1111·11···111·11····1·····1·1111···111··1··1···11·1···1·1···1·11·11·11···111·11····1·····1·1111···111··1··1··11·1···1·1····1·11·11·11···111·11···1·····11111···111··1··1···11·1··1·1····1·11·11·11···111·11····1····1·1111···111
out 7 (95)	··········1···1······11···1··1············1···1······11···1··1···········1···1······11···1··1···········1···1······11···1··1············1···1······11···1·1············1··1·····11···1··1············1···1······11··1··1···············1······11···1··1············1···1······11··1··1············1···1······11···1··1············1···1·····11···1··1············1···1······11···1··1···········1···1······11···1··1···········1···1·····11···1··1············1··1······11···1··1············1···1·····11···1··1
out 8 (223)	1··1····111·1···1···111·1111·11···111·1··1····1···1··1···1·111··1··1···111·1···1···111·1111·11···1111··1····1···1··1···1·111··1··1····111·1···1···111·111111···111·1··1···1··1··1···1·111··1··1····111·1···1···1111111·11···111·1··1···1···1··1···1·111··1··1····111·1···1···111·111·11···111·1··1····1···1··1···1·111··1··1····111·1···1··111·1111·11···111·1··1····1···1··1···1·111··1··1···111·1···1···111·1111·11···111·1·1····1···1·1···1·111··1··1····111·1··1···111·1111·11···111·1··1····1··1··1···1·111
out 9 (159)	1·1·····1·1·····1·1··11·1·1··11·····1·1·····1·1·····11······11··1·1····1·1·····1·1··11·1·1··11·····11·····1·1·····11······11··1·1·····1·1·····1·1··11·1·1·11·····1·1····1·1····11······11··1·1·····1·1·····1·1··111·1··11·····1·1····1·1·····11······11··1·1·····1·1·····1·1··11·11··11·····1·1·····1·1·····11······11··1·1·····1·1·····1···11·1·1··11·····1·1·····1·1·····11······11··1·1····1·1·····1·1··11·1·1··11·····1·1····1·1····11······11··1·1·····1·1····1·1··11·1·1··11·····1·1·····1·1····11······11
out 10 (159)	1···1···1·1·1·1·1····1··1·1··11···1···1···········1·111·····11··1···1··1·1·1·1·1····1··1·1··11···1··1···········1·111·····11··1···1···1·1·1·1·1····1··1·1·11···1···1·········1·111·····11··1···1···1·1·1·1·1····1·1·1··11···1···1··········1·111·····11··1···1···1·1·1·1·1····1··11··11···1···1···········1·111·····11··1···1···1·1·1·1·1···1··1·1··11···1···1···········1·111·····11··1······1·1·1·1·1····1··1·1··11···1···1··········1111·····11··1···1···1·1·11·1····1··1·1··11···1···1··········1·111·····11
out 11 (95)	········1···1·······11··1····1··········1···1·······11··1····1·········1···1·······11··1····1·········1···1·······11··1····1··········1···1·······11··1···1··········1··1······11··1····1··········1···1·······11·1····1··········1··1·······11··1····1··········1···1·······11··1···1··········1···1·······11··1····1··········1···1······11··1····1··········1···1·······11··1····1·········1···1·······11··1····1·············1······11··1····1··········1···1······11··1····1··········1···1······11··1····1
out 12 (63)	···················1·1·····1·1·····················1·1·····1·1····················1·1·····1·1····················1·1·····1·1·····················1·1·····11···················1·1·····1·1·····················1·1····1·1····················1·1·····1·1·····················1·1····1·1·····················1·1·····1·1····················1·1·····1·1·····················1·1·····1·1····················1·1·····1·1·····················1·····1·1····················1·1·····1·1····················1·1·····1·1
out 13 (191)	1··1····1·1·11··1···111·1·11··1···111·1······11···1··1·····11···1··1···1·1·11··1···111·1·11··1···1111······11···1··1·····11···1··1····1·1·11··1···111·1·11·1···111·1·····11··1··1·····11···1··1····1·1·11··1···1111·11··1···111·1·····11···1··1·····11···1··1····1·1·11··1···111·111··1···111·1······11···1··1·····11···1··1····1·1·11··1··111·1·11··1···111·1······11···1··1·····11···1··1···1·1·11··1···111·1·11··1···111·1·····11···1·1·····11···1··1····1·1·1··1···111·1·11··1···111·1······11··1··1·····11·
out 14 (159)	·1·1········1·1··1··111····1·1···1·1········1·1··1··111····1·1···1·1·······1·1··1··111····1·1···1·1·······1·1··1··111····1·1···1·1········1·1··1··111····11···1·1·······1·1·1··111····1·1···1·1········1·1··1··111···1·1···1·1·······1·1··1··111····1·1···1·1········1·1··1··111···1·1···1·1········1·1··1··111····1·1···1·1········1·1··1·111····1·1···1·1········1·1··1··111····1·1···1·1·······1·1··1··111····1·1···1·1·······1·1··1·111····1·1···1·1········11··1··111····1·1···1·1········1·1····111····1·1
out 15 (63)	·····················11······11······················11······11·····················11······11·····················11······11······················11·····11····················11······11······················11·····11·····················11······11······················11·····11······················11······11·····················11······11······················11······11·····················11······11····················11······11·····················11······11·····················11······1
check 16 (256)	1111···1·1··1·11····111·1·11·1··1111···1·1··1·11····111·1·11·1··1111··1·1··1·11····111·1·11·1··1111··1·1··1·11····111·1·11·1··1111···1·1··1·11····111·1·111··1111···1·1·1·11···111·1·11·1··1111···1·1··1·11····1111·11·1··1111···1·1·1·11····111·1·11·1··1111···1·1··1·11····111·111·1··1111···1·1··1·11····111·1·11·1··1111···1·1··1·11···111·1·11·1··1111···1·1··1·11····111·1·11·1··1111··1·1··1·11····111·1·11·1··1111···11··1·11···111·1·11·1··1111···1·1··111····111·1·11·1··1111···1·1··1·11···111·1·11·1
check 17 (128)	·11······1····1······11···1··1···11······1····1······11···1··1···11·····1····1······11···1··1···11·····1····1······11···1··1···11······1····1······11···1·1···11······1···1·····11···1··1···11······1····1······11··1··1···11······1···1······11···1··1···11······1····1······11··1··1···11······1····1······11···1··1···11······1····1·····11···1··1···11······1····1······11···1··1···11·····1····1······11···1··1···11·····1····1·····11···1··1···11······1···1······11···1··1···11······1····1·····11···1··1
check 18 (128)	·······1·1··1·1·········1·11·1·········1·1··1·1·········1·11·1········1·1··1·1·········1·11·1········1·1··1·1·········1·11·1·········1·1··1·1·········1·111·········1·1·1·1········1·11·1·········1·1··1·1········1·11·1·········1·1·1·1·········1·11·1·········1·1··1·1·········111·1·········1·1··1·1·········1·11·1·········1·1··1·1········1·11·1·········1·1··1·1·········1·11·1········1·1··1·1·········1·11·1·········11··1·1········1·11·1·········1·1··11·········1·11·1·········1·1··1·1········1·11·1
check 19 (256)	11·1·1··1·11··1·11·1·1··1·11··11··1·1·11·1··11·1··1·1·11·1··11··11·1·1·1·11··1·11·1·1··1·11··11··1·111·1··11·1··1·1·11·1··11··11·1·1··1·11··1·11·1·1··1·11·11··1·1·11·1·11·1·1·1·11·1··11··11·1·1··1·11··1·11·1·1·1·11··11··1·1·11·1·11·1··1·1·11·1··11··11·1·1··1·11··1·11·1·1··111··11··1·1·11·1··11·1··1·1·11·1··11··11·1·1··1·11··1·111·1··1·11··11··1·1·11·1··11·1··1·1·11·1··11··11·11··1·11··1·11·1·1··1·11··11··1·1·111··11·1··11·11·1··11··11·1·1··1·11·1·11·1·1··1·11··11··1·1·11·1··11·1·1·1·11·1··11
check 20 (128)	1·1·········1·1·····1·1·1·1·····1·1·········1·1·····1·1·1·1·····1·1········1·1·····1·1·1·1·····1·1········1·1·····1·1·1·1·····1·1·········1·1·····1·1·1·1····1·1········1·1····1·1·1·1·····1·1·········1·1·····1·11·1·····1·1········1·1·····1·1·1·1·····1·1·········1·1·····1·1·11·····1·1·········1·1·····1·1·1·1·····1·1·········1·1····1·1·1·1·····1·1·········1·1·····1·1·1·1·····1·1········1·1·····1·1·1·1·····1·1········1·1····1·1·1·1·····1·1·········11·····1·1·1·1·····1·1·········1·1····1·1·1·1···
check 21 (128)	·1···1····1···1··1···1····1···1···1···1··1···1····1···1··1···1···1···1···1···1··1···1····1···1···1··1··1···1····1···1··1···1···1···1····1···1··1···1····1··1···1···1··1··1···1···1··1···1···1···1····1···1··1···1···1···1···1···1··1··1····1···1··1···1···1···1····1···1··1···1···1···1···1···1··1···1····1···1··1···1···1···1····1···1··1··1····1···1···1···1··1···1····1···1··1···1···1··1····1···1··1···1····1···1···1···1·1···1····1··1··1···1···1···1····1··1··1···1····1···1···1···1··1···1···1···1··1···1
check 22 (64)	··········1···1···········1···1···1···1···········1···1··················1···1···········1···1···1··1···········1···1···················1···1···········1··1···1···1·········1···1···················1···1··········1···1···1···1··········1···1···················1···1··········1···1···1···1···········1···1···················1···1··········1···1···1···1···········1···1··················1···1···········1···1···1···1··········1··1···················1··1···········1···1···1···1··········1···1·······
check 23 (160)	1····1··1·111···1··111··1·1·······11········11····1·1······1·1··1····1·1·111···1··111··1·1·······11·······11····1·1······1·1··1····1··1·111···1··111··1·1······11·······11···1·1······1·1··1····1··1·111···1··111·1·1·······11·······11····1·1······1·1··1····1··1·111···1··111··11·······11········11····1·1······1·1··1····1··1·111···1·111··1·1·······11········11····1·1······1·1··1···1··1·111···1··111··1·1·······11·······11····11······1·1··1····1··1·111··1··111··1·1·······11········11···1·1······1·1
check 24 (96)	·····················11······11·····1·1·····1·1·····11······11······················11······11·····11·····1·1·····11······11·······················11·····11·····1·1····1·1····11······11·······················11·····11·····1·1····1·1·····11······11·······················11·····11·····1·1·····1·1·····11······11······················11······11·····1·1·····1·1·····11······11······················11······11·····1·1····1·1····11······11······················11······11·····1·1·····1·1····11······11
check 25 (128)	···1·1······1·1·····11·····1··1····1··1·····11······1·1····1·1·····1·1·····1·1·····11·····1··1····1·1·····11······1·1····1·1·····1·1······1·1·····11·····1·1····1··1····11·····1·1····1·1·····1·1······1·1·····11····1··1····1··1····11······1·1····1·1·····1·1······1·1·····11····1··1····1··1·····11······1·1····1·1·····1·1······1·1····11·····1··1····1··1·····11······1·1····1·1·····11······1·1·····11·····1··1····1··1····11·····1·1····1·1·····1·1······11·····11·····1··1····1··1·····11·····1·1····1·1
check 26 (160)	1··1·······11···1···1·············111·11·1··11····1···11·1·1·1··1··1······11···1···1·············11111·1··11····1···11·1·1·1··1··1·······11···1···1············111·11·1·11···1···11·1·1·1··1··1·······11···1···1············111·11·1·11····1···11·1·1·1··1··1·······11···1···1············111·11·1··11····1···11·1·1·1··1··1·······11···1··1·············111·11·1··11····1···11·1·1·1··1··1······11···1···1·············111·111··11····1··11·1·1·1··1··1·······11··1···1·············111·11·1··11···1···11·1·1·1
check 27 (112)	········1·1·1·1·····11··1·1··11·····················11······11·········1·1·1·1·····11··1·1··11····················11······11··········1·1·1·1·····11··1·1·11···················11······11··········1·1·1·1·····11·1·1··11····················11······11··········1·1·1·1·····11··11··11·····················11······11··········1·1·1·1····11··1·1··11·····················11······11·········1·1·1·1·····11··1·1··11···················11······11··········1·1·11·····11··1·1··11····················11······11
check 28 (160)	1··1····1·11··1·1·····1·1·1·······111·1······11···1·1······1·1··1··1···1·11··1·1·····1·1·1·······1111······11···1·1······1·1··1··1····1·11··1·1·····1·1·1······111·1·····11··1·1······1·1··1··1····1·11··1·1·····11·1·······111·1·····11···1·1······1·1··1··1····1·11··1·1·····1·11·······111·1······11···1·1······1·1··1··1····1·11··1·1····1·1·1·······111·1······11···1·1······1·1··1··1···1·11··1·1·····1·1·1·······111·1·····11···11······1·1··1··1····1·11·1·1·····1·1·1·······111·1······11··1·1······1·1
check 29 (192)	·1·1····1·1······1·1····1·1·····11111·1·····1·11·····1·11111·1···1·1···1·1······1·1····1·1·····111111·····1·11·····1·11111·1···1·1····1·1······1·1····1·1····11111·1····1·11····1·11111·1···1·1····1·1······1·1···1·1·····11111·1····1·11·····1·11111·1···1·1····1·1······1·1····11·····11111·1·····1·11·····1·11111·1···1·1····1·1······11····1·1·····11111·1·····1·11·····1·11111·1···1·1···1·1······1·1····1·1·····11111·1····1·11····1·11111·1···1·1····1·1·····1·1····1·1·····11111·1·····1·11····1·11111·1
check 30 (128)	········1·1·1·1·····1·1·1·1·····1·1·1·1·············1·1·1·1············1·1·1·1·····1·1·1·1·····1·1·11·············1·1·1·1·············1·1·1·1·····1·1·1·1····1·1·1·1···········1·1·1·1·············1·1·1·1·····1·11·1·····1·1·1·1············1·1·1·1·············1·1·1·1·····1·1·11·····1·1·1·1·············1·1·1·1·············1·1·1·1····1·1·1·1·····1·1·1·1·············1·1·1·1············1·1·1·1·····1·1·1·1·····1·1·1·1···········1·1·1·1·············1·1·11·····1·1·1·1·····1·1·1·1············1·1·1·1···
check 31 (96)	·····················11······11······················11111111·······················11······11·····················11111111························11·····11····················11111111························11·····11·····················11111111························11·····11······················11111111·······················11······11······················11111111·······················11······11····················11111111·······················11······11·····················11111111·
check 32 (256)	·11··111··1·11···11·11·1··1··11··11··111··1·11···11·11·1··1··1111··11··11·1··111··1··1·11·11··11··11··11·1··111··1··1·11·11····11··111··1·11···11·11·1··1·11··11··111··111··11·11·1··1··1111··11···11·1··111··1··111·11··11··11···111··111··1··1·11·11····11··111··1·11···11·11·1·1··11··11··111··1·11···11·11·1··1··1111··11···11·1··111·1··1·11·11··11··11···11·1··111··1··1·11·11····11·111··1·11···11·11·1··1··11··11··111·1·11···1111·1··1··1111··11···11·1·111··1··1·11·11··11··11···11·1··111·1··1·11·11·
check 33 (128)	··1···1···1···1···1···1···1···1···1···1···1···1···1···1···1···1·1···1··1···1···1···1···1···1···1···1··1···1···1···1···1···1·····1···1···1···1···1···1···1··1···1···1···1··1··1···1···1···1·1···1···1···1···1···1··1···1···1···1···1··1···1···1···1···1·····1···1···1···1···1···1··1···1···1···1···1···1···1···1···1···1·1···1···1···1···1··1···1···1···1···1···1···1···1···1···1···1·····1··1···1···1···1···1···1···1···1···1··1···1···1··1···1···1·1···1···1···1··1···1···1···1···1···1···1···1···1··1···1···1·
check 34 (224)	1111·11·1···111·111·1···1··1·····1·111····1··1···1····1···111·1·1··1···111·1···1···111·1111·11···1111··1····1···1··1···1·111··1111·11·1···111·111·1···1··1····1·111····1·1··1····1···111·1·1··1····111·1···1···1111111·11···111·1··1···1···1··1···1·111··1111·11·1···111·111·1···1·1·····1·111····1··1···1····1···111·1·1··1····111·1···1··111·1111·11···111·1··1····1···1··1···1·111··111111·1···111·111·1···1··1·····1·111···1··1···1···1···111·1·1··1····111·1··1···111·1111·11···111·1··1····1··1··1···1·111
check 35 (64)	··1···1···1···1···1···1···1···1···1···1···1···1···1···1···1···1·································································1···1···1···1···1···1···1··1···1···1···1··1··1···1···1···1·································································1···1···1···1···1···1··1···1···1···1···1···1···1···1···1···1··································································1··1···1···1···1···1···1···1···1···1··1···1···1··1···1···1·····························································
check 36 (128)	·····11······11······11······11······11······11······11······11····11·····11······11······11······11·····11······11······11········11······11······11·····11······11·····11·····11······11····11······11······11·····11······11·····11······11······11········11······11······11·····11······11······11······11······11····11······11·····11······11······11······11······11······11·······11······11······11······11······11·····11·····11······11····11······11·····11······11······11······11·····11······11·
check 37 (128)	1·····1·1·1·····1·····1·1·1·······1·1·······1·1···1·1·······1·1·1···1··1·1·1·1·1···1···1·1·1·1···1··1···········1···1·········1·····1·1·1·····1·····1·1·1······1·1······1·1··1·1·······1·1·1···1···1·1·1·1·1···1··1·1·1·1···1···1··········1···1·········1·····1·1·1·····1·····1·11·······1·1·······1·1···1·1·······1·1·1···1···1·1·1·1·1··1···1·1·1·1···1···1···········1···1·········1····1·1·1·····1·····1·1·1·······1·1······1·1···11·······1·1·1···1···1·1·11·1···1···1·1·1·1···1···1··········1···1·······
check 38 (160)	·······1··1·11······1·11··1··11········1··1·11······1·11··1··11········11·1··1·····1·1·11·11··········11·1··1·····1·1·11·11··········1··1·11······1·11··1·11········1··111·····1·11··1··11·········11·1··1·····1·111·11···········111··1·····1·1·11·11··········1··1·11······1·11·1··11········1··1·11······1·11··1··11·········11·1··1····1·1·11·11···········11·1··1·····1·1·11·11·········1··1·11······1·11··1··11········1·1·11·····1·11··1··11·········11·1·1·····1·1·11·11···········11·1··1····1·1·11·11·
check 39 (64)	··········1···1···········1···1···········1···1···········1···1········1···1···········1···1··········1···1···········1···1·············1···1···········1··1···········1··1··········1···1·········1···1··········1···1···········1··1···········1···1·············1···1··········1···1···········1···1···········1···1·········1···1··········1···1···········1···1···········1···1············1···1···········1···1··········1···1··········1···1·········1···1··········1···1···········1···1··········1···1·
check 40 (208)	1··1····1···111·1···111·1··1······111·1···1··1····1··1····111·1·1··1···111·1···1···111·1111·11···1111··1····1···1··1···1·111··1··1····1···111·1···111·1··1·····111·1···1·1···1··1····111·1·1··1····111·1···1···1111111·11···111·1··1···1···1··1···1·111··1··1····1···111·1···111·1·1······111·1···1··1····1··1····111·1·1··1····111·1···1··111·1111·11···111·1··1····1···1··1···1·111··1··1···1···111·1···111·1··1······111·1··1··1····1·1····111·1·1··1····111·1··1···111·1111·11···111·1··1····1··1··1···1·111
check 41 (192)	·11····1····1····11·1·11······1··11····1····1····11·1·11······1··11···1····1··11··1·1··111111···11···1····1··11··1·1··111111···11····1····1····11·1·11·····1··11····1···1···11·1·11······1··11····1····1··11··1·1·111111···11····1···1··11··1·1··111111···11····1····1····11·1·11·····1··11····1····1····11·1·11······1··11····1····1··11·1·1··111111···11····1····1··11··1·1··111111···11···1····1····11·1·11······1··11····1···1····111·11······1··11····1····1·11··1·1··111111···11····1····1··11·1·1··111111
check 42 (192)	1··1···11·1···1·1·····111·11······111·11····1·····1·1··1···11·1·1··1··11·1···1·1·····1··1··111···11111····1·····1·1···111··1··1··1···11·1···1·1·····111·11·····111·11···1····1·1··1···11·1·1··1···11·1···1·1·····1·1··111···111·11···1·····1·1···111··1··1··1···11·1···1·1·····11111······111·11····1·····1·1··1···11·1·1··1···11·1···1·1····1··1··111···111·11····1·····1·1···111··1··1··1··11·1···1·1·····111·11······111·11···1·····11··1···11·1·1··1···11·1··1·1·····1··1··111···111·11····1····1·1···111··1
check 43 (192)	·1···1····1···1··1···1····1···1··1···1····1···1··1···1····1···1··1···1···1···1··1···1····1···111·1111111·111·11·111·1111·111···1···1····1···1··1···1····1··1··1···1····1··1·1···1····1···1··1···1····1···1··1···1···1···111·111·1111111·11·111·1111·111···1···1····1···1··1···1···1···1··1···1····1···1··1···1····1···1··1···1····1···1··1··1····1···111·111·1111·111·11·111·1111·111···1··1····1···1··1···1····1···1··1···1···1···1··1··1····1···1··1···1····1··1··1···1····1···111·111·1111·111·11111·1111·111
check 44 (128)	···1·1······1·1·····11·····1··1····1·1······1·1·····11·····1··1····1·1·····1·1·····11·····1··1·····11····1·1·····1··1·····11·····1·1······1·1·····11·····1·1····1·1·····1·1····11·····1··1····1·1······1·1·····11····1··1·····1·1···1·1·····1··1·····11·····1·1······1·1·····11····1··1····1·1······1·1·····11·····1··1····1·1······1·1····11·····1··1·····1·1····1·1·····1··1·····11·····11······1·1·····11·····1··1····1·1·····1·1····11·····1··1····1·1······11·····11·····1··1·····1·1····1·1····1··1·····11
check 45 (96)	··········1···1···········1···1···········1···1···········1···1··········1···1···········1···1·······111·111·········111·111············1···1···········1··1···········1··1··········1···1···········1···1··········1···1········111111·········111·111············1···1··········1···1···········1···1···········1···1···········1···1··········1···1········111·111·········111·111···········1···1···········1···1··········1···1··········1···1···········1··1···········1···1········111·111········111·111
check 46 (256)	·1··1··1···111···1·111·1····1···111···111·11·11·1111·1111·1···1··1··1·1···111···1·111·1····1···111··111·11·11·1111·1111·1···111·11·11·111···111·1···1·1111111···111···1·1··1···1····1·111·11·11·11·111···111·1···11111·111···111···1·1··1····1····1·111···1··1··1···111···1·111·1···1···111···111·11·11·1111·1111·1···1··1··1··1···111···1111·1····1···111···111·11·11·1111·1111·1···111·1111·111···111·1···1·1111·111···111··1··1··1···1····1·111·11·11·11·111··111·1···1·1111·111···111···1··1··1···1····1·111
check 47 (128)	1···1···1·1·1·1·1···1···1·1·1·1·1···1···1·1·1·1·1···1···1·1·1·1·1···1··1·1·1·1·1···1···1·1·1·1·1···1··1·1·1·1·1···1···1·1·1·1···1···1···········1···1··········1···1·········1···1···········1···1···········1···1··········1···1··········1···1·········1···1···1·1·1·1·1···1···11·1·1·1···1···1·1·1·1·1···1···1·1·1·1·1···1···1·1·1·1·1··1···1·1·1·1·1···1···1·1·1·1·1···1···1·1·1·1···1··1···········1···1···········1···1··········1··1···········1···1··········1···1···········1···1··········1···1·······
check 48 (192)	11······1····1··11······1····1···11·1·1···1·111··11·1·1···1·111·11·····1····1··11······1····1···11·11···1·111··11·1·1···1·111·1·1··11·111···1·1·1··11·111··1·····11···1·1······11···1··1···1·1··11·111···1·1·1··11111···1·····11···1·1·······11···1··1···11······1····1··11······1···1···11·1·1···1·111··11·1·1···1·111·11······1····1··11·····1····1···11·1·1···1·111··11·1·1···1·111·1·1·11·111···1·1·1··11·111···1·····11··1··1······11···1··1···1·1··11·111··1·1·1··11·111···1·····11···1··1······11···1··1·
check 49 (192)	1···1···1·11·1··1··1····1·1·11····1···1····1111···111·1······11·1···1··1·11·1··1··1····1·1·11····1··1····1111···111·1······11·1··1·11·1·1·1·1·1···111·1·11·1···1111··········1··1·····11···1··1·11·1·1·1·1·1···1111·11··1···1111···········1··1·····11···1···1···1·11·1··1··1····11·11····1···1····1111···111·1······11·1···1···1·11·1··1·1····1·1·11····1···1····1111···111·1······11·1··111·1·1·1·1·1···111·1·11··1···1111···········1·1·····11···1··1·11·1·1·11·1···111·1·11··1···1111···········1··1·····11·
check 50 (192)	1··1····1·1·11··1···1···1·11·1····111·1······11···1···1····1111·1··1···1·1·11··1···1···1·11·1····1111······11···1···1····1111·1··1·11·1·1·1·1·1···111·1·11·1···1111··········1··1·····11···1··1·11·1·1·1·1·1···1111·11··1···1111···········1··1·····11···1··1····1·1·11··1···1···111·1····111·1······11···1···1····1111·1··1····1·1·11··1··1···1·11·1····111·1······11···1···1····1111·1··111·1·1·1·1·1···111·1·11··1···1111···········1·1·····11···1··1·11·1·1·11·1···111·1·11··1···1111···········1··1·····11·
check 51 (224)	1··1···1···1·11·1···1111····1·····111·111·1111····1··1·11·1···1·1··1··1···1·11·1···1111····1·····111111·1111····1··1·11·1···1·1··1····111·1···1···111·111111···111·1··1···1··1··1···1·111··1··1····111·1···1···1111111·11···111·1··1···1···1··1···1·111··1··1···1···1·11·1···1111···1·····111·111·1111····1··1·11·1···1·1··1···1···1·11·1··1111····1·····111·111·1111····1··1·11·1···1·1··1···111·1···1···111·1111·11···111·1·1····1···1·1···1·111··1··1····111·1··1···111·1111·11···111·1··1····1··1··1···1·111
check 52 (64)	···········1111············1111············1111············1111···········1111············1111···········1111············1111·······································································································································1111···········1111············1111············1111············1111···········1111············1111············1111··························································································································
check 53 (192)	11·····1······1·11·11··1···11·1·11·····1······1·11·11··1···11·1·11····1······1·11·11··1···11·1·11····1······1·11·11··1···11·1·11·····1······11··1··11·111·1··11·····1·····11·1··11·111··1··11·····1······11··1··11111··1··11·····1·····11··1··11·111··1··11·····1······1·11·11··1··11·1·11·····1······1·11·11··1···11·1·11·····1······1·1111··1···11·1·11·····1······1·11·11··1···11·1·11····1······11··1··11·111··1··11·····1·····11··1·11·111··1··11·····1·····11··1··11·111··1··11·····1······11·1··11·111··1
check 54 (160)	········1·1·1·1······11·1·1·11··1·1·1·1·········1·1·11·······11········1·1·1·1······11·1·1·11··1·1·11·········1·1·11·······11·········1·1·1·1·1·1·11······11·1·1·1·1············11·1·1·11··········1·1·1·1·1·1·11······11·1·1·1·1·············11·1·1·11··········1·1·1·1······11·11·11··1·1·1·1·········1·1·11·······11·········1·1·1·1·····11·1·1·11··1·1·1·1·········1·1·11·······11········1·1·1·1·1·1·11·······11·1·1·1·1············11·1·1·11··········1·1·11·1·1·11·······11·1·1·1·1·············11·1·1·11
check 55 (256)	11······1·111···11·1111·1·1··11·11······1·111···11·1111·1·1··11·11·····1·111···11·1111·1·1··11·11·····1·111···11·1111·1·1··11·11······1·111···11·1111·1·1·111··111111·1··111·1····1·1·11···11······1·111···11·11111·1··111··111111·1··111··1····1·1·11···11······1·111···11·1111·11··11·11······1·111···11·1111·1·1··11·11······1·111···111111·1·1··11·11······1·111···11·1111·1·1··11·11·····1·111···11·1111·1·1··111··1111111···111··1···1·1·11···11······1·111··11·1111·1·1··111··111111·1···111·1····1·1·11·
check 56 (64)	································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1································1·1·11·1·1·1·1·1·1·1·1·1·1·1·1···························································································································································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1································1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1··························································································································
check 57 (224)	·1·1···1··1··11··1···1·1··11··1··1·1···1··1··11··1···1·1··11··1··1·1··1··1··11··1···1·1··11··1··1·1··1··1··11··1···1·1··11··1··1·1···1··1··11··1···1·1··11·1··1·1···1··1·11·1···1·1··11··111·1·111·11·11··11·111·111··11·11·1·111·1111··11·111·1·11··11···1·1···1··1··11··1···1·1·11··1··1·1···1··1··11··1···1·1··11··1··1·1···1··1··11··1··1·1··11··1··1·1···1··1··11··1···1·1··11··1··1·1··1··1··11··1···1·1··11··1··1·1···1·1··11··1··1·1··11··111·1·111·11·11·11·111·1·11··11·11·1·111·11·11··11111·1·11··11
check 58 (208)	·1·1······1·1····1··111···11·11··1·1······1·1····1··111···11·11··1·1·····1·1····1··111···11·11··1·1·····1·1····1··111···11·11··1·1······1·1····1··111···1111··1·1······11···1··111···11·11··1·1······1·1····1··111··11·1111·1·1111111·1111·11···111··1····1·1······1·1····1··111··11·11··1·1······1·1····1··111···11·11··1·1······1·1····1·111···11·11··1·1······1·1····1··111···11·11··1·1·····1·1····1··111···11·11··1·1·····1·1····1·111···11·11··1·1······1·1···1··111···11·1111·1·111111·1·111111···111··1·
check 59 (256)	·1111···11··11···111··1·11···11··1111···11··11···111··1·11···11··1111··11··11···111··1·11···11··1111··11··11···111··1·11···11··1111···11··11···111··1·11··11··1111···11·11··111··1·11···11··1111···11··11···111··111···11··1111···11·11···111··1·11···1111····111··11··111···11·1·111··11····111··11··111···11·1··111··11····111··11··111··11·1··111··11····111··11··111···11·1··111··11···111··11··111···11·1··111··11····111·11··111··11·1··111··11····111··11·111···11·1··111··11····111··11··111··11·1··111·
check 60 (128)	··1·1···1·····1···1·1···1·····1···1·1···1·····1···1·1···1·····1···1·1··1·····1···1·1···1·····1···1·1··1·····1···1·1···1·····1···1·1···1·····1···1·1···1····1···1·1···1····1··1·1···1·····1···1·1···1·····1···1·1··1·····1···1·1···1····1···1·1···1·····1·1·····1···1·1···1·····1··1·1···1·····1···1·1···1·····1···1·1···1·····1···1·1···1····1···1·1···1·····1···1·1···1·····1···1·1···1····1···1·1···1·····1···1·1···1·····1··1·1···1····1···1·1···1·····1···1·1··1·····1···1·1···1·····1···1·1···1····1···1·1·
check 61 (224)	1111····111·111·111·111·1111·····1·11·1··1···1···1···1···1·11·1·1111···111·111·111·111·1111·····1·111··1···1···1···1···1·11·1·1111····111·111·111·111·1111····1·11·1··1··1··1···1···1·11·1·1111····111·111·111·1111111·····1·11·1··1··1···1···1···1·11·1·1··1·11·1···1···1···1···1·1·11···1111····1···1···1···1···1111··1··1·11·1···1···1··1···1··1·11···1111····1···1···1···1···1111··1··111·1···1···1···1···1··1·11···1111···1···1···1··1···1111··1··1·11·1···1··1···1···1··1·11···1111····1···1··1···1···1111
check 62 (128)	1·1·····1·1·····1·1·····1·1·········1·1·····1·1·····1·1·····1·1·1·1····1·1·····1·1·····1·1·········11·····1·1·····1·1·····1·1·1·1·····1·1·····1·1·····1·1········1·1····1·1····1·1·····1·1·1·1·····1·1·····1·1····1·1·········1·1····1·1·····1·1·····1·1·1·····1·1·····1·1·····1·1····1···1·1·····1·1·····1·1·····1·1···1·····1·1·····1·1····1·1·····1···1·1·····1·1·····1·1·····1·1···1····1·1·····1·1·····1·1·····1···1·1····1·1·····11·····1·1···1·····1·1····1·1·····1·1·····1···1·1·····1·1····1·1·····1·1·
check 63 (128)	···11········11····11········11····11········11····11········11····11·······11····11········11····11·······11····11········11····11········11····11·······11····11·······11···11········11····11········11····11·······11····11·······11····11········11······11····11········11···11········11····11········11····11········11····11·······11····11········11····11········11····11·······11····11········11····11········11···11·······11····11········11····11·······11····11········11····11·······11····11·
check 64 (128)	1···1···1·1·1·1·1·····1·1·1·······1···1···········1·1·······1·1·1···1··1·1·1·1·1·····1·1·1·······1··1···········1·1·······1·1·1···1···1·1·1·1·1·····1·1·1······1···1·········1·1·······1·1·1···1···1·1·1·1·1·····11·1·······1···1··········1·1·······1·1·1·····1·1·1·····1···1···11·1·1···1·1·······1·1···1···1·········1·····1·1·1·····1··1···1·1·1·1···1·1·······1·1···1···1·········1····1·1·1·····1···1···1·1·1·1···1·1······1·1···1··1·········1·····1·1·1····1···1···1·1·1·1···1·1·······1·1··1···1·······
check 65 (160)	········11··11······1·1·11···11·········11··11······1·1·11···11········11··11······1·1·11···11········11··11······1·1·11···11·········11··11······1·1·11··11·········11·11·····1·1·11···11·········11··11······1·111···11·········11·11······1·1·11···11········1··11··1·····1·11·111··········1··11··1·····1·11··111··········1··11··1····1·11··111··········1··11··1·····1·11··111·········1··11··1·····1·11··111··········1·11··1····1·11··111··········1··11·1·····1·11··111··········1··11··1····1·11··111·
check 66 (176)	1··1····1·1·11··1···1···1·11·1····111·1······11···1···1····1111·1··1···1·1·11··1···1···1·11·1····1111······11···1···1····1111·1··1····1·1·11··1···1···1·111····111·1·····11··1···1····1111·1··1····1·1·11··1···1··1·11·1····111·1·····11···1···1····1111·1··1····1·11··1·1···1···11·1·1···111·1····11·····1···1·········1··1····1·11··1·1··1···1·1·1·1···111·1····11·····1···1·········1··1···1·11··1·1···1···1·1·1·1···111·1···11·····1··1·········1··1····1·11·1·1···1···1·1·1·1···111·1····11····1···1·······
check 67 (192)	·11······1····1··111·1···1·1·11··11······1····1··111·1···1·1·11··11·····1····1··111·1···1·1·11··11·····1····1··111·1···1·1·11··11······1····1··111·1···1·111··11······1···1·111·1···1·1·11··11······1····1··111·1··1·1·11··11······1···1··111·1···1·1·11··11······1····111···1·1111·1····11······1····111···1·111·1·1····11······1····111··1·111·1·1····11······1····111···1·111·1·1····11·····1····111···1·111·1·1····11·····1····111··1·111·1·1····11······1···111···1·111·1·1····11······1····111··1·111·1·1·
check 68 (128)	·11······1····1··11······1····1··11······1····1··11······1····1··11·····1····1··11······1····1··11·····1····1··11······1····1··11······1····1··11······1···1··11······1···1·11······1····1··11······1····1··11·····1····1··11······1···1··11······1····1··11······1····1······11··1··1···11······1····1······11···1··1···11······1····1·····11···1··1···11······1····1······11···1··1···11·····1····1······11···1··1···11·····1····1·····11···1··1···11······1···1······11···1··1···11······1····1·····11···1··1
check 69 (192)	1··1····111·1···1···1···1111······111·1··1····1···1···1··1·11·1·1··1···111·1···1···1···1111······1111··1····1···1···1··1·11·1·1··1····111·1···1···1···1111·····111·1··1···1··1···1··1·11·1·1··1····111·1···1···1··1111······111·1··1···1···1···1··1·11·1·1··1····111·1···1···1··1···111···111·1··1····1···1···111·1··1··1··1····111·1···1··1··1····111···111·1··1····1···1···111·1··1··1··1···111·1···1···1··1····111···111·1·1····1···1··111·1··1··1··1····111·1··1···1··1····111···111·1··1····1··1···111·1··1
check 70 (192)	·1·1····1·····1··1·1····1·····1··1·1····1·····1··1·1····1·····1··1·1···1·····1··1·1····1·····1··1·1···1·····1··1·1····1·····1··1·1····1·····1··1·1····1····1··1·1····1····1·1·1····1·····1··1·1····1·····1··1·1···1·····1··1·1····1····1··1·1····1·····1··1·1····1·····1··1·1····1····111·1·1111·11111·11·1·1111·11111···1·1····1·····1··11····1·····111·1·1111·11111·11·1·1111·11111···1·1···1·····1··1·1····1·····111·1·111111111·11·11111·11111···1·1····1····1··1·1····1·····111·1·1111·11111·111·1111·11111
check 71 (160)	·1·1········1·1··1··1······1··1··1·1········1·1··1··1······1··1··1·1·······1·1··1··1······1··1··1·1·······1·1··1··1······1··1··1·1········1·1··1··1······1·1··1·1·······1·1·1··1······1··1··1·1········1·1··1··1·····1··1··1·1·······1·1··1··1······1··1··1·1········1·1··1··1·····1··1···11·11··11·11····1·111··111·1···1·1········1·1··1·1······1··1···11·11··11·11····1·111··111·1···1·1·······1·1··1··1······1··1···11·11·11·11····1111··111·1···1·1········11··1··1······1··1···11·11··11·11···1·111··111·1
check 72 (128)	········1···1·······1·1·1·····1·········1···1·······1·1·1·····1········1···1·······1·1·1·····1········1···1·······1·1·1·····1·········1···1·······1·1·1····1·········1··1······1·1·1·····1·········1···1·······1·11·····1·········1··1·······1·1·1·····1·········1···1·······1·1·1····1········1·111·11·····1·11·11111··········1···1······1·1·1·····1········1·111·11·····1·11·11111·········1···1·······1·1·1·····1········1111·11····1·11·11111··········1···1······1·1·1·····1········1·111·11····1·11·11111
check 73 (192)	·11··········11··11··········11··11··········11··11··········11··11·········11··11··········11··11·········11··11··········11··11··········11··11·········11··11·········11·11··········11··11··········11··11·········11··11·········11··11··········11··11··········11··11·········11··11··········11··11··········1111··1111111111··11·1111111111··11··1111111111··11··1111111111····11·········11··11··········11··11·········11··11·········1111··1111111111·11··1111111111··11··1111111111··11·1111111111·
check 74 (192)	1··1····1·1·11··1···1···1·11·1····111·1······11···1···1····1111·1··1···1·1·11··1···1···1·11·1····1111······11···1···1····1111·1··1····1·1·11··1···1···1·111····111·1·····11··1···1····1111·1··1····1·1·11··1···1··1·11·1····111·1·····11···1···1····1111·1··1····1·1·11··1···1···111·1····111·1······11···1···1····1111·1···111·1·11··1·1·1·11·1·1·1·1···1··1·····11·····1111··········1··1···1·1·11··1···1···1·11·1····111·1·····11···1··1····1111·1···111·1·11·1·1··1·11·1·1·1·1···1··1·····11····1111········
check 75 (160)	·1·1········1·1··1··1······1··1··1·1········1·1··1··1······1··1··1·1·······1·1··1··1······1··1··1·1·······1·1··1··1······1··1··1·1········1·1··1··1······1·1··1·1·······1·1·1··1······1··1··1·1········1·1··1··1·····1··1··1·1·······1·1··1··1······1··1··1·1········1·1··1··1·····1··1··1·1········1·1··1··1······1··1··1·1········1·1··1·1······1··111·1·11111111·1·11·11·111111·11···1·1·······1·1··1··1······1··1··1·1·······1·1··1·1······1··1··1·1········11··1··1······1··111·1·11111111·1·1111·111111·11
check 76 (224)	·1··1···1····1···1·11·1·1··1·11··1··1···1····1···1·11·1·1··1·11··1··1··1····1···1·11·1·1··1·11··1··1··1····1···1·11·1·1··1·11··1··1···1····1···1·11·1·1··111··1··1···1···1··1·11·1·1··1·11··1··1···1····1···1·11·11··1·11··1··1···1···1···1·11·1·1··1·11··1··1···1····1···1·11·1·1·1·11··1··1···1····1···1·11·1·1··1·11··1··1···1····1···111·1·1··1·11··1··1···1····1···1·11·1·1··1·1111·11111·1111·111·1··1·1·11·1··11·11·1111111·111·1·1·1·11·1··11·11·111·1111111·1··1·1·11·1··11·11·111·1111·1111··1·1·11·1·
check 77 (208)	1··1······1··1··1····1····11······111·1·1···111···1·111·1··11·1·1··1·····1··1··1····1····11······1111·1···111···1·111·1··11·1·1··1······1··1··1····1····11·····111·1·1··111··1·111·1··11·1·1··1······1··1··1····1···11······111·1·1··111···1·111·1··11·1·1··1······1··1··1····1···11······111·1·1···111···1·111·1··11·1·1··1······1··1··1···1····11······111·1·1···111···1·111·1··11·1·1··1··111·11·1·1····1·111··111···111·11111······11111·11··1··1··1···111·111·1····1·111··111···111·11·111·····1·1111·11··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 n496Noisy T states per run.

outputs k16

distance d6Exact, proved and witnessed here.

error coefficient A_{6}not computedToo many faults to count at this size.

wires N78

checks r62

V_{\mathrm{ex}}16T states per run. CCZ counts as two.

\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d1.9165Overhead per extractable T state. Lower is better.

\gamma = \log(n/k)/\log d1.9165Overhead 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 width16Rank of the output rows modulo the check rows.

Output gate

16 T0 CS0 CCZon 16 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}

As monomials: 0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15 (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 16 single-wire gates: \mathrm{S} on output 0, \mathrm{S} on output 1, \mathrm{S} on output 2, \mathrm{S} on output 3, \mathrm{S} on output 4, \mathrm{S} on output 5, \mathrm{S} on output 6, \mathrm{S} on output 7, \mathrm{S} on output 8, \mathrm{S} on output 9, \mathrm{S} on output 10, \mathrm{S} on output 11, \mathrm{S} on output 12, \mathrm{S} on output 13, \mathrm{S} on output 14, \mathrm{S} on output 15. The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.

Or no Clifford gate at all: run every rotation as \mathrm{T}^\dagger. 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.

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/496.16.6.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-496.16.6.a.txt", "w") as out:
    out.write("\n".join(lines) + "\n")

Distance

d=6, exact. No fault of weight below 6 is both undetectable and damaging. One of weight 6 is.

The number of such faults of weight 6, A_{6}, is not computed: there are too many to count at this size.

A damaging fault of weight 6 sits on columns [253,271,355,373,396,479].

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

cap witnesses, NOT records. Each ATTAINS a proved maximum puncture count for its ambient size at d=6, making that bound exact rather than an upper bound: m=8 gives [[248,8,6]] and m=9 gives [[496,16,6]], both with n/t = 31 exactly, hence gamma = log(31)/log(6) = 1.9165 independent of m. Filed as evidence that these cells are closed, not as frontier points -- the d=6 pure-T bar is gamma 1.063146.

Found by: AI search: pure-T puncture caps

Discovery: AI search

1 recorded source

[
 {
  "regime": "AI search: pure-T puncture caps",
  "file": "magic-states-AI/campaigns/2026-09-15_m8_m9_d6/found/n496_T16_d6_CAP_WITNESS_not_a_record.json",
  "label": "n496_T16_d6_CAP_WITNESS_not_a_record",
  "N": 78,
  "d": 6,
  "d_is_exact": true,
  "origin": null,
  "provenance": "m = 9 parent, |T| = 32 triples, dim 78, no degree-4 monomials. Campaign 2026-09-15_m8_m9_d6 proves t <= 16 on that parent at d = 6 (and closes the [[447,65,6]] cell for every m = 9 parent); this ATTAINS the cap. Pure disjoint T^16, V_ex = 16, rho = n/V_ex = 31.000, gamma = log(496/16)/log 6 = 1.916545. NOT a record and not near one: the external d=6 bar is gamma 1.086033, and this is dominated many times over by direct sums of small catalogued factories (CLAUDE.md rule 6). Filed as a tightness witness for a closure, not as an improvement."
 }
]

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/496.16.6.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[1072].