[[1023, 27, 5]] magic-state factory, T0·T1·T2·T3·T4·T5·T6·T7·T8·T9·T10·T11...

The circuit

The 47\times1023 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 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860 870 880 890 900 910 920 930 940 950 960 970 980 990 1000 1010 1020 \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \| ' \|
out 0 (509)	1·····1·111··1·111·1·11··1··111··1··111···1·1···111··1·1·11111·1···11·11·11111·11·11······1·1··111·1·1111·11····1·····11···11·1·1·····1·111··1·111·1·11··1··111··1··111···1·1···111··1·1·11111··111··1··1·····1··1··111111·1·11···1·1····1··1111·11111··111··1111·11······1·1··1···11·11·11111·1·11111··111··1····1·1····1··111111·1·11··1··111·1·····1·111··1·1···11·1·1·····111·11···111·1·1·11·11······1·1··1···11·11·11111·1·11111··111··1····1·1····1··11····1·1··11·11···1·11111·1···11···111··111·1·1111··1··1···111·111·1··111··11111·1111··1····1·1·····1·1······11·11·11111·11·11···11·····1·1·11···111·1·111···11·11111··1··11·1·111·1··111·1·····11·1··111··11111·1111··1····1·1·····1·1······11·11·11111·11·11·····11111·1·1··111···1·1···111··1·1···11·11··1111·11·11·······1·11·11·1·111···11·111·····1·1·11···11·11···1·11111·1···11·11··1·1··1111··1····1·1··1·1··1111·11·11·11·····11·1·111·111·11·1·1··11·1·11·1·111···111·11··1·1111·1··1·11·11··1···11111··1··111·1·11·1·····11··111·1·1·11··1····1·1···1·····11···1··1·1··1··1···1·······
out 1 (513)	·1111···11··11·1··1·11·11··11··1·1·1·1·····111111111111·1·11·1·1·1··1·1············11111·1·1·1·11··11··1··1·11·1··11··111····111··1·11·11··11··11····111··11··1········1·1··1·11·1·1·1·····1111····11111·1·1·1··1·11·1·11111111·11··11···1111··11··11··1··1·111····11111·1·1·1··1·11·1·111111111··11··111····11··11··11·11·1··11··1·11·11··11··11····111··11··111111111·1·11·1··1·1·1·11111···11·1··1·1············11111·1·1·1···11··11·11·1··1·11··11···1111·1··1111···11··11·1··1·11·11··11·1·1·1·1··111····1··11····1111·1·1·1·11·1·111111111111·····1·1·1·111··11··1··1·11·1··11··111····11··1111···11··11·1··1·11·11··11···1·1·1·11111············1·1··1··1111·····1·1·1·11·1··1·1·········11··11···1111··11··11··1··1·1111··1·11·11··11··11····111··11···11111111·1··1111·······111··111··11·1··1··11··11··1111···11··11·11111111·1·11·1··1·1·1·11111···1····11111·1·1·11·1·11·11111·1111·11··1···1···1·1·11··11111·11···11···11111···1···11·1·1···11·1···1·1·1··1···1······11111···1····1·11·111·111···1···111111·····1·1··1·1····1·1····11·1···········
out 2 (479)	1···1··11·111·1···1···11···1······1···11···1····1···1··11·111·11·111·1111·111·1···1···1·111·111111·111·1···1····1···1····1···1··1111······1111·11·1··1·1·11·1····1·11·1·1··1·111····111111····11····111···1111·11·1··1··1··1·1111·1··1··1··1·111····111···11111··1···1··1···1···111·111···1···1·111·111···1···1··1···1··1···1····1···1·1·111·111···1······1···1·111·111111·111·11·111·1·1···1·1···1111·1····1111·11·1····1·11·1·1··1·1111·1··1·111····1·1111··1···1111··1111····1··1·11··1·1··1·1··1·11··1·11······11·1···111111····111111····1··1·11·1·1··1·11··1·11·1·1··1·111····111111····11····111···1111·11·1··1··1··1·11··1·11·11·11·1···1111···111·····1·111·11··1···1·111·111··111·111···1···11···1····1···1··11·111··1·111·1111·111·1···1···1·111·11····1···1·11····11·1·111·1111·1·····1111·1····1111·11·1····1·11·11·11·1····1·11·1···1111·1·····11111····11····1·1···1··111··11···1·11···1···1·1··111··111···11·1··1·111·1·1111····11··1·1·1·1····1··111··11······1·····1·11·111··11··11····1111·1·11111······1····11·1·1···1···1··1··1···········
out 3 (475)	·11····1111··11·11··1·11·1··11·1111··11··11····1·1··11··11··1·1·11··1·1·1·11··1··11········11···1·11··1·11··1·1····11····11·····11··1·1·1·11··1··11········11··1·1··11·1··11·1·1111··1111··111111··1111····11··1··11·1··1·11··11111··11··11····1·1··11··11··1··1111··1111··11111·1··11·1··11·1···11········11···11··1·1·1·11··1·1·11··11··11·1·····11··11··1111·11··1·11·1··11···11····1111··1··1·11··11··11·1·····11··11··11111··11·1··1·11··111··1111····11·1····11····11·····1·11··1·11····1··11········11·1·111·11·11·····1······1111·······1·1·11·1··1·1·1··111111111111···11·1·1·1·1·1··11·1·1··11··1·1·1111111··11·······11·1·1··1·1·11···111111······1··1·1·11··11·1·1·······11··111111·11·1·1··1·1·11···111111······1·······1111·······1·1·11·1··1·1··11·········1·1·1···1·11····1·11···111111······11·11·1·1··1·1·11·······11··111111·1·1·1·1···111111·111···11·111··1·1·1······11·1···1·1··111·1·1·11··111·1·111··1·1111·1111111·11111···1···11·1··11·1·11·1·1··1·111·11·1·······11···1·11·1·111···1··1···1·1·······1·111···1·1·1···1···············
out 4 (511)	1··1······1··1··111·1··11·1···1·1111·11··1····1·1···111111···1·111·11·11·11·11111·1···1·111·1····1····1·1111·11···111·11·111······111·11·111···11·1111·1····1····1·111·1···1·11111·11·11·11·111·1···111111···1·1····1··11·1111·1···1·11··1·111··1··1······1··111·111······111·11····1··11·1111·1···1·11··1·111·1·11·111111·11·1111···1··1···11111·1111·1····1····1·111·1···1·11···1··1··1··1··1111·11·11·11·111··1·111·1···1·1111·1111·1····1·····111·11·111··1·1··1······1··1·1···1·1···1·1·111····1··11·11111·1·1·11··1···1··11·1···1·111·1··111·11·11·11·111111···1··1···11111·1111·1····1··1···1·11··1·111·1·11·111111·11·1·1···111111···1··1111·11··1······1111·11··1····11·111······111·1·1··1······1··1·1···1·11··1·111111·1111·1····1·····111·11·111·1····1··1··1··11··1··1···1·1··11····1····1·1111·11···111·11·111·····111111·1·11·11111·1·111····1111·1·····1111111111·11·1·111····11·111···1·1·11··1··1·11·1·1···1·11·····11·1·11·1·1··1111·11··11·1·111····11·1111·111·····1·1·11·11·····1·11··11··········11··11··11111···11······11·1···········
out 5 (481)	11··11·11····1111····111··11··1·1·11·1·················1·1··1·1····1111·1·1·1·11·1·1·1·····1111··11··111··1·11··11·1··1··11··1111··11··1··1·11·1··1·11···11··11····11111·1·1·1·1·1·1·1·1111·····1·11·1·11111111·········1·11·1·1··11··111····11··1111··1··11···1·1·1·1·1111········11111·1·1·1·1··1·11···11··1111··11··1··1·11···1111··1··11··11··11··111····11·········1·11·1··1·11·1·1111111·········1·1··1·1·1·11·1·········11····111··11··1·11··11·11····1··11·1··1··11··11··11··1·1··1··111·1·1·1·····111····1···1······111111····1·1·1·1·1·1·1·1·····111111··11···11·1··1·11·1··1··11··111··11··1··1111··11····111··11··11·1··1·111111111········1·1··1···1·11·1·11111111111111111·1··1·11··11··111····1111····11·11··11111··11··1··1·11··11·1··111··111·····11111·1·111····11·1···111·····1111··1···1·1··1·1······1···111·111··111·1·1·1·111···11··1·1··111···111·····11111·1··111·11···11·1·1·1·1111111·1·1···1·11··11···1··11··11··1····1···111·111·11·1····1111·1······1·1·1··1·1····1111111···111·······111·11··11···1·1··1···1·········1···1·······
out 6 (553)	··1·111·111111··111111····1·111·1··11·111·11·1111·11·11·1··11·1···1·111·111111·1······1111·1···1·11··1···1··1··11·11·11·1··11·1··1·1·111·1111·11·1111·1··1·1·111···111·111··111111··1111···111···1·1·111·1111·1·1····1·11·1·1···111···1···11···111··1111···1111···11···1···111··111···1111··1111·1111·111·1·1····1·1·11·1····1·111··111·111···1·111···1111··1111·1111·111·1·1··11·1·1··1·1111····1··1···1··11·11·11··1·11·11·11·111111·111·1······1·1111·······11·11·111·11··1·1·11··1111·111·1·111111·11111···111·11·111·1111···1··1···1··11·1·1··11·1··1··1··1······1···1·111···1·1111······1··1··1···1··11·11·11··1·11·11·11·111111·111·1······1·1111·······111··111·111···1·111···1111··1111·1111·111·1·1··11·1·1··1·1111··111··111·111···111··111·····1·1·1111·1····1·11·1·11111111·11·11·1···1·1111111·····111·111·1··1····1·11·11111··1·1·11·1111111·1····1·1··11·11·11·1···1·····11····1·········111··1··1111111·1·111·11·111·11···1···1··1·1·1111····11·11·111··1···1111·11····1·1111·111·111·1··111111111·1··1····11·11·1111·····1····11·1···1·······
out 7 (521)	··1111··1···1···1···1·····1111····1111··1···1··1·111·11111····1··1···1·1····111·1111···11·111·1··1···1·1····1111····111··1···1··111·11111·1··1···1·11·11···1····111·11111·1··1·11·1··1··111·111·1··1·11···1···1···1···1·1··1·11·1··1·11···1···1111·111·1·11·1·111·111·11····1111····11111·111·111·111·11····111·1111·····1···1····1111·1·111·11·1···1··111····1···1111·1·111·111·111·11···111111·11·1·····1···1111·111··1··1·111·11·1·····1···1···1···11·11·1·1·111·111··1·11·1··1·11···111···1·111·111··11111·111111111·1·1··11···1···11·1··1···1·11·1·111·111·111·111··1·11·1··1·11·1·111·111·1··1·11111·111·111·111··1··1·111·11·1·····1···1111·111··1··1·1····1111·1·111·111·111·11···1111·111····1·1···1··1·111·11···111··1·11······11··111·111···1···11·1··111·····1···11··1······11··11·11··111·11···1·····11·111·111·1···11111····111·1···11·111·····11111·11·1·11·1·11·····1··1111··11111···11·111··1····11111·11·····1··1·1·11·111·1··111111·11·1·11···1···111·11···1·1··111·1··1··1·1111··1·1·11·····1·1····1···111···11·11··11·1·1·1···1···1·······
out 8 (493)	11·11·······1·11··1··1111111·1·1·1·111111···11··1·1······111··1··111··11·1·1111··111··11·1·1111·····1·11··1··11·····1·11··1··11··11·11··1·1111111··1··11·1·····1111·1·11··111······1·1··11···111··111······1·1·1··111······1·1·1·1·······11·11·1·1·······11·111··11·11··1·1111111··1··11·1·····1111·1·11··111······1·1··11···111··111······1·1·1··111······1·1·1·1·······11·11·1·1·······11·111·11·11·······1·11··1··1111111·1·1·1·111111···11··1·1······111·····111··11·1·1111··111···1·1·1··1·····1·11········1·····111·11·111··111··1111·1·1·11···11····1·1··1·11111··11·11·1·1·····11··1··111··1··1·1·1111111··1··1·1·111111111·1·1·11···111111·1·1·11···1···111··1·1·1····11···11·1·1·111111111111·1·1·11··111···1···1··11·1·1··1···········11·1·111·1···1··11··11111·1·11··11·11··1···11·11·111··1·1·1·1·111··1·1·11····111·1·1·11·11·1····1·111·1111111·1·1111···1·1···11111····1···1···11······1···11···11111···1·11·1·1······1·1···111·111·11····11111·1··11···1·111··11·1··1··1·11···11··111···1··1111·1··11·1···1·1·1··1111·1·1·1····1··1···1·······
out 9 (505)	11··1·1····11··11·······1·1·11·111111···11·1·1·1·1··11·11··11111·1··11···11··········11·11·1·1···111111·1·1·11··11··1·11111··11111111···11·1·1··1·11··1··11·····11··1·1····11····1111111·1·1··1··111111·1·1·11·1··11·1·····11··1·1··11···11····111111··1··1·1···1·11··1··11····111111···11·1·1·11·······1·1·11·1··11·1·1111··11·11··1·11111··1111······1·1·1··1111111··1··1·1·11·1··11···11···111·······1·1·11··11··1·1····11···1·11··1··11··········111··1·1··111111··1··1·1·1·1·11···11··1··1·11··1·11·11·11··1·1··1111··1·1···111111·1·1·11··11··1·11111··11·1·11··111··1111111111··1··1·1·1111111···11·1·1·1·1··11·11··11111··11·1·1111··11··1111111·1·1····1·11·11·1·1111···1111·111··1·11111·11······1···1··1·1·11·11111111····1111···11·1··1···1····11··1111·1·11·11··11··111····1·1·1··1······1·1···1·1·111······1111·1111··1··1·1·1·1··11····1·····111·1··1·111··11·11···11111·11······11···1··1·1··11·1111111··11········1111·1·1··11··1·1·1··1111·1····1·111··11····11·1·11·111······1··1·11·1···11·····11···11···1······11·111·1·1·1·1·············
out 10 (473)	··1···1···1111·1···1···1····1111···1····1111······1···1111····1·1111···1···1······1111·111·111·111····1111·111·1····1111···1·····1···1·11·1··1··1···1··1·11·1···1···1···1··1·11··1···1···1·11·11·11·1··1·111·11··1·11·1··1···1·11·1··1···1···1··1··1·111·111·1····1···1···1111·1···1···1····111·111·1111····111111·111····1111··1111···1···1······1111·111·111····1111····1···1·1111····111·11···1···1·11·1··1··1···1··1·11·1··1·111·111·11·1··11·111·111·1··111·11·1··1·111·11··1·1111··1··111··1·11·111··11·11······111·1·1····1·11·1··1···1·1·11·1··1·111·11·1··1·111·111·1111·1··1···1···1··1···1··1·11·1····1···1·11·1··1···1···1···11·····11··111111···1·····1··1·11·11·1·1·111111·1···111·1·111·11·1·11······1·····1·····11··1·1···11··1·······11···111··11·11···11····1·1···11··1·11·1··11111·1·1·1·······1··11111·1·1··1··11··111·1·1·11111··1··1·1111111·11·······111·····11·1·1·11·11111··1···1··111·11·11111····1··11·1·······11111·11·11··111··1···11·1·1··11···11·11···111·1··11·1···1···1·11··11···1··1·111··11·1····1··111······1··1···········
out 11 (517)	1···111·1··1···1·11·111·1···111·1111·111···1·11·111·1···1111·1111·1···111·1111·11·1111···1·111·111·11·1···111·1···111·1···1··1·11·1···111·1111·11·1111···1·111····1··1·111···1·111···1·111·11·11·111···1·11·111·1··1···1·111····1111·111···1·11·111·1···1111·1····111·1···1··1·111·11·1···111·1··1····111·1···1··1·111···1····11···1·111····1··1····1···111·1··1·11·111·1···111·1···111·1··1··11···1·111····1··1····1···111·1···1··1···1·111···1·111···1·11·11·111···1·111·11·1···1····111··111··1····1·1·1·111···1·1··11·1·111·1···1111·11·1111·11·1111·111···1····1··1···1·111···1·11·1111·11··1·111·11··111·1····1··11·1111·11··111·1·1111·1·1·11··1·11·1·11··111·1··1·111···111··1··1··1·1······1···1····11·111···111·1111·1111·······1··11······111······1··111···1·1111111·1········111···11·11111·1·11·1111·1·1·1111···1··111···1·1·111···11···111··11·1·1·····11·111··1111111·11·11·11····11··11·11·1··1111··1·11·11·1···111111·111·11··1111·11·········1··111··11111··1·1··1··11·1····1111·1···1···1·1·111··111·1··1··1····11··11···1·1·1·1···········
out 12 (499)	··1··1··1111·11·1111·11···1··1··1···111··1·111·11·1···11·111···1····1·····1··1····1··1·1····1····1·111·1·111····1···11111·1···1·111·1··111···1·111···1··111·1····1····11·11·111·1··1···11·1111·111···1·1···1·111···1·11111···1··1··1·····1····111·1111·1·11·11··111·1·····111·1111···1·1···1·11··1····1·1··1····1··1·····1····1···111·11···1·11·111·1··111···1·1·11·111··1····1··1····11·11·11·111·11·1·1111·111····1·····1··1·1·111·····1·111···1·111·1·111··11····1··111·11·1···1·1·1·1111·11··1·111·11·····1··1·11·1·111·111··1·111·1·111···1·111·····1·111··1111·11111··1·11·111··111·111·1·111··1·11·111111·11·11111··11·11111·1·11··11·111·111·111·1··11···11111·111···1·1·1·1·11·1··11··········1···1·1·11111··11·11·1·1·11·1·1·1·1·1·1···111111·1···1····11111·11111····1·1111·11····1·11····1·1··1··11··111···1111··1···11·111·111·1·1·11·1·1·111·11·1··1··111····1··1·1····1··1··1·111··111·111··11111···111····111··1·····1·1·1·1·1·1·1111··1·1···11·1111·········1··1111····1··1···1·1·1111···1···11···1·1······11····1··1··11·1·1·1·······1·······
out 13 (509)	·111··1····1·1··1·1····1··111····111··11111·1·11·1·11111··111···1·1·····11···11··111··11111·1·1·1·1····1··111··11···11·1111·1·111···11·····1·1··1·1·····11···11··111··1····1·1··1·1····1··111··1·1·1111·11···11··111··1····1·1··1·1·····11···11··111··11111·1··11111·1···11·11··11·11···1·1111111111·1·11··1··11··1··11·1·111111··1··11·1·11111·····1·1··11·11·1··1··111·1·····11111·1···11·11111111·1·11··1··11··1··11·1·11111·····1·111··1··11··1··111·1····11··1··111·1·····111111·1··11·11··11·11·····1·1·111···1·1····1··1·1·111111··11·1·1111·1111··1··11·1111··1·····11·1··1·1··1··1··1111111····1···111··1··1111·111···11·11···111··11···11··1···1·11··11··1··1·1·11··1···1·1··1·1·11·1111·11·1···111111·1··11·1···111···1·1·1·11··1111·1···1·1·111·1··1··1··11·1·111111···1·11··111····111111·111·1·1···111·11·······1··1111··1·1·11···11·111·11··11···1··11···1··11111··1·1···1111·1·111·1·1·······111·····111·········11·1111·1·11·1····11······11··1··11···1111·11111·11····11111··1111······11·1·1·11·1111··1···1·1111····1·1·1···1·1·1···········
out 14 (509)	·111·1·1111·11·1111·11·11···1·1·1·1··11·11·····1··11111·1·1··1111···1·11111·11·1111·11···111·1··1·1··111··11111·11······1·1··11··111·1·1111·11·1111·11·11···1·11·1·11··1··11111·11·····1·1·11····111·1·····1··1····1··111···1·1·1·1··111··11111·11······1·1··1·1··111111·1·11··1·1·11···11·····1111·11···111·1·11···1·11111·11·1··11111·1·1··11·1·1··11·11·········1··1··111·1·11···1·1····1···1··111111·1·11··1·1·11···11·········1··111···1·1··111·1·····1····11·····1·1111·1··1··1·1111111····1·1·111·1····11·1··11···11·····11··11111··111·1·1··11·1····1····11·11·1·····11··11·11·1·1111··1····1····1·11··11···1111··11····11··11111·111·11····1·1·1··1·11·1·1111·1···1··11·1·11·11··1······11·1······11·1111·1···11···1·111·11····1·1··1··1111··11·1·11·1·1111··1·11·····1·111·····1·111·1·1111111··1·111·111····1·1·11·1··11·1···1111·111·1····1·1·1·1····111·11·11111···11111··1··1·111··11·1··1·11·111··1··1··1111··1·1·1··1·1·11··1·1·1·1·1··111··1·1···11···1111···11··11111···11·1·1··11·11·1·1····1111·111·11··1··1··11···1·····1·111·1···1·······
out 15 (473)	·1·11·11···1···1·11·1··111·111·1···1·····1·11·1111·111·1·11·1·····1111··1···1···1111···11·111·11·111·11111····1··1···1·1····1111····111··1···1····1111··1···1····1···1·1····111·1···1·····1111·1·11·1··111·111·11·1··1··111·111···1···1·1··1·111···1·····1·11···1···1·····1111·11·111·1·1111···111····11·111·111····111··1···1··111·11111·1··1····1···1·1··1·1111·1··1··111·111·1··1·11···1·······1···1·1··1·111···1·····1·11·11·11·11·11··1··111·······111··1·11······11·1···11·1·1···1····111·111·1···1111········1111····1111·1·1·11·····111·111··1111···1·1···1·1········111··1·1·11·11··1···········111··11···1··11···1·11111111·1·1·1··1··111·11·1·11··1··111111···111···1111··1··1··1··1··11·1·111·····1·1·111·······1·11···1···1·1·1···1·111111··1··1····11··1··11··1··1·11·11···········1·1·1·111·11······11··1·1111··1·11·111111··1·11111··11·11111·1·1·1····1·1·····1·11·111····11··1··111·1·11··111··1111···111·11·1·1··1·11····1···11····11·11·1·11·11···11·11·11·111·1111·111····11··1·····1···1·1·1·····11····1·1111·····11·1·1·1·1·············
out 16 (547)	111···1···1·1111·1111·111·11·1111·1·1···1··11·1111··111·111111··1····1·11·11·11·111···1111·1······11····111111·11·1·1··1·11··1··111111·111··111·1··11·111·1·1····1··1···1····1·111·1···1···111··1··11·1··1·1·111······1111··111111·1····111···111·11·11·1····1111·11·11·1····1····1·1111···111··111111····11····1··11·1··1·1·11111·1···1···111·11·11·111·1111·11·11··1···1·1·11·111111·111··11···1····111·1111111111··1·11··1···11·11111111·11111···11·11·1111·111··11··11··1··1····1·1·1···1··1·1·111·1···111·111·1···1···111·1111·111··11··111·1··11·1·11·11······1111··111··1·11·1····111111·1···11·11111···11111·111··1·1··111·11111·1111··111····1·11·1·1·11···111·1111··1··111·1···1·1·····1·1·1·11···1·11·11111·1·11··1111111·11111·1·11111···1······1·1··11····1···11··1·11·11···1111··1·1··1·111·11··1··1111···1···111······11·1··11111·1·11·11·1·111··1··11····111·1·1·1·1111·11111··11·1·11··1··111111·11·1·1·111···111··1·1····11111····1···11··11111111·1·1·1··1··11·····1··111····11111·1·1111·1··1····1·1····11··1··1·1···1···1··1··1···1·······
out 17 (515)	·1111··1·1··1·11··11··111111111··11··11·1·1·1·11··1·11·····11111·1··1·111····1111111111·11··11··1·1·1·111··11······1111·11·1··11··1·11·····111111··11··1·1·1·1·1··11··11111111111····11·1·11·1·1111····1··1·11··1·1·1·111··11··········1··11··11·1··1·111····1·11····11·1·11·1··11··11···········11··11·1·1·1·11··1·11·····11111·1··1·111····1111111111·11··11·111··11·11····111·11···111111·1··1·1·11···11·1·1·11·1·····111···11111···1·111111·111·1·11·1··1·11·111····11·111·····11·11··1·1···1··1·11111·1·1···1····1·1··1···111·11·11·1··1···11··11·11·111·1·1111·111·1······1·1·1·1···1111·····1·11·11·11··11111··1·11····11·11111·1·11··1·····11·1····11·11·1·11·1·1·111··1····1·1·1·1·11111·1·1·1·1·1·111111··11··11···11·1·111····1·111··1·11·111·1···111···1········1·1···111·1·111·1····1·11·1··1····11·11·1·1·1··111····1··1··1·1·11···1·11···111·111···111··1111·11··1···1··1111··11··111·1·11111···11·111···111111········11·11···1·1·11·11·11···111111·1·11·1·1··11·1·····1··11····111·111··111···11···1···11·1····1·11·1··1········1·1···········
out 18 (483)	···111111··11····1111··············111111··11··11····11111111111··1·11··1·1·1·11·1··1·11··11··11··1·11··1·1·1·1·1·11·1··11··11·1·1·1·1·1··1·11··11··11·1·1··1·1·1·1·1·1·11·1··1·11··11·1·1··1·111··11··1111············11····11··11··11····1111········11····1···········1111····11··111111··············1111··11··11······111··11·····11·11···1·1····1··111··11111·1···1·1111·····111·1·1·1··1·1··1·1··111·1··11·1111···1·11·11111·11··1··1111·1·11·1··11111·1···1·1·1··1·11···111···1·1····11··11···111·111·11··1···1·1··1·111······1···11111·1··111····1·1···1111··111111·11111····11111·1···1·1·1·1······1·1··11·1··111·1·1··11·1·111······1·1111··111111·····1··1··1·1····1·11·11·1·····11··1111·1·1··1·11·11····1·1··11··11····1111··11·11··11···1·11··1·1·····1·11·11111····11·1···1111·····1··1··11·11····11··1·1·1··1111··11·11·1··1··11·1·1·1··1111····1··1··1··1·1·1···11·11·11·1··1·1·11·1··1·1111·11·····11·1··1···1111·111·····1111·11·1···111··111111···11·1··11··11111·1··11·1·1··1111·11··1···1·1111··11····1·1··1····111·····11······1·······
out 19 (495)	11·11···11···11·····1·1····1·1·1··111···11·11··1111·1·1·····1·1·11···11·11·11··1111·1·111111·1··11·11··1··111··11111·1·····1·1·····1·1······1·1·11···11·11·11·······1·11111·1·1·11·11··1··111·······1·1····1·1·1··1··111··111··1111·1·1·····1·1·11···111··1···11111·1·1·····1·11··111···11·11···········1···1·11··11111·11··1···1·11··11·11·11·1·11·111····11···1111111·1·11·1111111·11··11·1··111····1·11··1·1··11····11·111···1···1·1·1··1····11·11·11··11··111·····1·11··1·1··1····11····11111·111·11··1·111·1·1··1111···1·111·1·111···11····1··11····1··11·1·1·11111·11··111···1··11··1··1·1111··1111·1·1111··1··1·11···1··11·11·1·1·1······1·1·1·1·111····111111·1··11·1·····1111··11·1·····1·111111·1··111·1·111····1·1···11··11·1··1·1··1··1·1·1···1··111·1·1·1·1··11··1·1··1···11··1·····1·····1·1111111···111·11·1·11··11111·11111·1··1·11·11·11·1·11····11·1111··11·1111·1··1·1···1·1·1·1····11111····11·11···11·111··1·1111·····1·111·11···········111·1···11···1111111··111···1111·11···1·1·1·1··1···111·······111····111··1·1···1·1·1·····1·······
out 20 (495)	111111·111··1111···111····1·111·1····1···1··1···1··11·1··1·1·1111·1·1··1·11··1···1··1···1····1····1·1111···111····11···1······1··1·1·111·11··1·11·11·11·1····1····1·111·111···1···11····111111·1······1111··111·111···1···1·111·1····1·11·11·11·1··11·111·1··11111·1···1···1·111·1····1·1·1··1··1·1·111·1··1···111111··1··111···11···11·11·111·1·1111·11·11·11·1·11·111111111··111···111··1111···1·1··1111111··1··11····11···1··1···1·1··1·11··111·······11·1·1·1·1·11·1····111·11·1··1111··111·1··11111··1·11111·1··1111···1·111····1·1··1·1·1111··1·····1111111···1·11·11·····111····1······1··1·1···1··1·11111····1·11··1·11·1····1·1·······11·111·1··1······1·1·1·1···1·1·····1111··1111·····1·111111·1··111·1·111····1·1···11··11·1··1·1··1··1·1·1···1··111·1·1·1·1··11··1·1··1····1··1·····1·····1·1111111···111·11·1·11··11111·11111·1··1·11·11·11·1·11····11·1111··11·1111·1··1·1···1·1·1·1····11111····11·11···11·111··1·1111·····1·111··1···········1·1·11··1····1111111··111···1111·11··11·111·1··1·1·111·······111·1··111··1·1···1·1·1·····1·······
out 21 (285)	·11·1·1·····11···11·1·111111··11·1·11···11·····1·1·11··1··11111··11·1·111111··1··11·1·1·····11·1·1·11··1··111111·1·11···11·········1··1··111·1·····1··111···1·11··1·····1·111··1··1····1·1···11····1··111···1·1····1··1··111·1·1··1····1·11··1··11···111·11····1·1·11·111··11·1·11111·····1·11··1··11·1111·1·1·11·····1···11·11···1····1·1111·1111111111111··1·1·11·1··11··11·1·1·111·111·1·11····11··1·1····1·1·11···1···111···11··11···11·1·1·1·1·11·1···11··1··1·111··1·11··1··11···1·111···1·11·····························11··1·11··1111····1····1··11·11···111·····1···11··111····1······1···1····1·11·1·1············1·11·1·1··········1··11····1········1·1········1····························1···························1·················································································································································································1························11·····1···············1·······1···············1···1···························································
out 22 (309)	11··11··11·1··1····1111111111111·1··1·11·1·1·1·11··11····1111···11·1··11··11··1111111111111·····1·1·1·11·1··1·111····1111··11····1111····11··111·1·1·1··1·11·1·············11111··1·11··11··11···11··1111·1···1···11·1·····1··111·1·1··1·111·1···1·1·····111······1····1····1111···11111·111·11·1··1···111·1··1·1··1······11··111··11··1111111·1··11··1·1···1111·1·1···1·11·1·11·1··1·11·1·11··11111··11·11··1·····11·1·1·1111·1··1··11·1·1·1·1··1·11··1111·11·11·11·11·11·1···11·11······11·····111·1·········1·················1111111111111··1··1···1··11····1·11·11········11···111···1·11···11·1··1··········1··1······11·11···1··1··········11···········11·······11·11··1·························1···························1·················································································································································································1·······················1·1·············111·····1·······1···············11······························································
out 23 (503)	1··111····1·1····1·1····111··1···1··1111·····1·1·11111····11·111·····1·11·11······11·11·1·····1111·1·11·1··111·1···11·1··1·1·····1··111·11111·11·11111·111··1···1··111·111·1·11··1·1···1···11·1···1·1···1·111····11··1··111·1···1·11··1·111··111·1··11······1111·1·······11·1··1·1··111····1·1··1·1··1·1111111·1·····11·11···1··1111··11···11111··1·1111·1······11·11···1····1·1111·1·11·····1···11···1···111111·11··111·1·1··1111··1111··11··11·11···11·1··1·1111111···1111·1···1·1··1··1··111··111··11··11111·1·1··1111···1·11·1111·1·1·11·1·1·1·1··1····1·11111·1111·1·1···11·1·11·111··111·····1111·1·1·1··11··1·1·11··1··1·····11·1·1······1·111·1··11······11·1·1·11111··1··1111··1111·····1·11111111··111·1·111····1·1···11··11·1··1·1··1··1·1·1···1··111·1·1·1·1··11··1·1··1···11··1·····1·····1·1111111···111·11·1·11··11111·11111·1··1·11·11·11·1·11····11·1111··11·1111·1··1·1···1·1·1·1····11111····11·11···11·111··1·1111·····1·111111····1······1···1···11···1111111··111···1111··1··11·1·1·1··1·1·111·······111·1··111··1·1···1·1·1·····1·······
out 24 (343)	1·11111·····1·111111·1··1·111111··1··1111··1··111··1··1·11·11·1·1·11111·····1·111111·1··1·111111··1··1111··1··111··1··1·11·11··1·1·1111····1·1·1111·1·11·111111···111·111··11·1·111·1·1·11·111·1···1····1·1·1111111·1·1111···1111·111··1·1·1·1·11·11·1·11·······1·111·····1·1·11···11···1111····11111··1·11·1·1·1··1····1·1····11·11·11·1··111··111·11·····1111··11111111··11··1·11·1·1·1··111·1·······1·1·11··1··1···111·11·1·11··11····11·11·1111·11···111···11·1··1·11111···11111····1111···1111·11·····1···1················11······11·1···11·1·1·1···1·1·111111·1····1·1·111111··11·11···1·1·11··1·1···11··1·1··1·····1·1111·111··········1··1·····1·1····111·1····11················1··············1···························1·················································1·························································································································································1··············1··1···1························11·1···1·······1···············1·······························
out 25 (315)	·11··11111111111··1·11·1·1··1·1··11··1111111111·11·1··1·1·11·1111··11··111111111··1·11··1·11·1···11··11········1··1·11··1·111111·1111··11111·11·111··1·11111····1·1·1·11·111··11·1··11·1··1·1·1·1·11111·1···11·1···1··1·1·1···1·11··1·····11·111·111111·11·1···11·1·····1···1··1····111··1·1111·111···1·11··11·1·1·11··1····1··1111·1·11·····1··11··1·1·111··111·1·1·1···11····1··1·1111··1·11·111·1··11········11··111···111·1111···111·1···11··1·11····1·1·1···11·1··1·1·11············1·1···1·11111·····1····················1······1·11·1·1····11···11········1··11111··11·1111··11·11·11··11··········1·11·1··1·1·····1·1·11·111··1·1········1················1·····1··1·············1··········································1·················································1·······················································································································································111·1···1········1··1···1·······················1·1·····1·······1···············································
out 26 (315)	···11········1111······11··1111·11·1·1··11··1·1·1·11··1·1·1·111·1·1·11··1·11··11··11·1·1··1·1·····111·11··1·1···1111·11111·1·11·1···1·1111111·1··1·111·111111··1··11···1····1·11·······1··1···11··1·111·1··1·1·11111··1·11·1·1111111·11·1····111···1·11···1······11111111··1·1111···1·111··1·1·1·11·1·1·11··11·1111·1·····1·1····1111····1·11111···11111·····1·111·1·11··11·11····111111·11111·111···1··111···11111·1····1·1··11·1·1·11··1········1111·1·1··1··11·1111·····1··11·11····11111···1···11··························1···11·1··111·····11·1····111·111·1·1···111··11·111111··11111·1···11····1·1···1··1·11·1·····1·1111··1···········1··1············1·1·········11··1··········1··············1·············································································1···························································································································································1···········1·1·····1·······················1···1···1·······1···············································
check 27 (512)	1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1
check 28 (512)	·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··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··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··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 29 (512)	···1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111····1111
check 30 (512)	·······11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111········11111111
check 31 (512)	···············1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111················1111111111111111
check 32 (512)	·······························11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111································11111111111111111111111111111111
check 33 (512)	·······························································1111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111
check 34 (512)	·······························································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111································································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111································································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111································································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 35 (512)	·······························································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111································································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 36 (512)	·······························································································································································································································································································································································································································································································································11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
check 37 (480)	1·1·1·1·1·1·1·1·1·11·1·1·1··1·1····················11111111·····1·11·1··1·11·1··1·1·1·11·1·1·1·1111····1111····11111111·········1·1·1·11·1·1·1··1·11·1··1·11·1·11111111········1111····1111····1·1··1·1·1·11·1·1·1·1·1·1·1·1·1·1111········111111111111111111111·1·1·1·1·1·1·1··1·11·1·1·1··1·11111111111111111····11111111·····1·11·1··1·11·1·1·1·1·1··1·1·1·11111····1111············111111111·1·1·1··1·1·1·1·1·11·1··1·11·1·········111111111111····1111····1·1··1·1·1·11·1··1·1·1·1·1·1·1·11111········1111·················1·11·1··1·11·1·1·1·1·1··1·1·1·1····1111····111111111111········1·1·1·1·1·1·1·1··1·11·1·1·1··1·1················1111········1111·1·11·1·1·1··1·11·1·1·1·1·1·1·1·1111········1111·················1·1·1·11·1·1·1·1·1··1·11·1··1·1········111111111111····1111····1·1··1·11·1··1·11·1·1·1··1·1·1·11111····1111····11111111········1·1·1·1·1·1·1·1·1·1··1·1·1·11·1·····················11111111····1·1··1·1·1·11·1·1·1·1·1·1·1·1·1·····11111111·····················1·1·1·11·1·1·1··1·11·1··1·11·1·········11111111····1111····1111
check 38 (528)	··1···1···1···1···1···1111·111···1···1·11·111·1··1···1···1···1·111·111·111·111·111·111····1···111·111·1··1···1·11·111·111·111·1111····1111····1···1111·111····111·1··1···1·11·1··1·11·1··1·11·1···1111····1111·111····1···1111···1·11·111·1··1·11·1··1·11·1··1····1111····1111····1111·111····1··1·11·111·1··1···1·11·1··1·11·1111····1111····1111····1···1111·11·1··1···1·11·111·1··1·11·1··1·111·111·111·111····1···1111·111·11·111·1··1···1···1···1···1···1····1···1···1···1111·111····1···1··1···1·11·111·111·111·111·111·1·111·1111···1····111·111·111·111·1···1···1···1···1···1··1·111·11·111·1111···1····111·111·111·111·1···1···1···1···1···1··1·111·11·1111···1····1111····1111····111·1··1·11·1··1·111·11·1···1··1·11·1111···1····1111····1111····111·1··1·11·1··1·111·11·1···1··1·111····111·1111···1····1111····1111·11·1··1·11·1··1·11·1···1··1·111····111·1111···1····1111····1111·11·1··1·11·1··1·11·1···1··1·111···1····111·111·111·111·111·1111·111·111·111·11·1···1··1·111·111···1····111·111·111·111·111·1111·111·111·111·11·1···1··1·111·11
check 39 (528)	··1·1·····1·1··111·1·11111·1·11···11·11···11·11111··1··111··1···1·····11·11111·1·11111··1·····1·1··111·1·11···11·11···1·1··111····1·1·····1·1··111·1·11111·1·11111··1··111··1·····11·11···11·111·11111··1·····1·1·····11·11111··1··111·1·11···11·11···1·1··111····11·11111··1··111··1·····11·11···1·1··111·1·11111·1·11···1·1··1·11···11·11···1·1··111··1··111·1·11111·1·11111··1·····1·1·····1111··1·····11·11···11·11111··1·····1·1··111·1·11111·1·11···1·1··1·11···11·11···1·1··111··1··111··1·····1·1·····11·11111·1·11111···1··111··1··111··1··111··1··11111·1·11111·1·11111·1·11111·1·111·111··1·1···11·1·111··1·1···11·11·····1··11111·11·····1··11111·1··1··111··1··111··1··111··1··111··1·1·····1·1·····1·1·····1·1···1···11·1·111··1·1···11·1·111··1·1·····1··11111·11·····1··11111·111·1·111··1·1···11·1·111··1·1·····1··11111·11·····1··11111·11····11111·1·11111·1·11111·1·11111·11···11·11···11·11···11·11···11·1··1·1···11·1·111··1·1···11·1·111··1··11111·11·····1··11111·11····11111·1·11111·1·11111·1·11111·1·111··1··111··1··111··1··111··1·
check 40 (528)	·11··11·11··11···1111··1··1·11··11··11·11··11··1··1·11·11····11····1111·1·11·1·········1·1·1·1·1·1··1·1····1111·1·1·1·1··········11··11·11··11···1111··1··1·11·1··11··1··11··11·11·1··1··1111······1111·1·11·1·········1·1·1·1··1·11·1·1111····1·1·1·1·1111111111··11··1··11··111····11·11·1··11··11··1··11··11·11·1··1··1111··1111····1·1··1·111111111·1·1·1·1·1·11·1·1111····1·1·1·1·11111111··11··11·11··11···1111··1··1·11·1··11··1··11··11·11·1··1··1111······1111·1·11·1·········1·1·1·1··1·11·1·1111····1·1·1·1·1111111111····111··1·11···11··111··11··1·11·1··111····11·11··11···11··11·········1·1·1·11111·····1·11·1··1·1·1·111111111·1·11·1·····1111··1111···11·1··111··11···11··11··11·1··111····11·11··11···11··11111111111·1·1·1·····11111·1··1·1·1·1·1·111111111·1·11·1·····1111··1111···11·1··111··11···11··11·1··1·11···1111··1··11··111··11··111111111·1·1·1·····11111·1··1·11·1·1·1·········1·1··1·11111······1111···11·1··111··11···11··11··11·1··111····11·11··11···11··11111111111·1·1·1·····11111·1··1·1·1·1·1·111111111·1·11·1·····1111
check 41 (480)	····11······11··1·1··111·1·11····11·1·111··1·1·1··111111··111111111·11·1111·11··1·111··1·1···1111···1·1··111·1·1··1····1··1·····1·111···1·111··1111·11·····1··1·11·11111··1······111·1···111·1·1·1·11··1·1·11··11111··1·····11·1··11111·11·······11·1·1··11·1·11111·11·····1··11·1···111·1···11··111·1···111·1·1··1·····11·1111·····11·11111··11·1·11··1·1·11··11··1·1·11··1·1·1··11111·11·····1·1·11···1·1··11·····11······11··11······11·······11·1·111··1·1··1·111··1·1···11····1··1····1··11··1····1··1······111·1·11···1·1·11······11·······11·1·111··1·1··1·1··111·1·11··11111··111111··1·11·1111·11·111111···1·1··111·1··1·111··1·1···11····1··1····1··111···1·111···1·1·11·11111··1····1111·11·····1··11·1···111·1···1111··1·1·11··1·1·1··11111·11·····11111··1·····11··1·1··11·1·1··11·11·11111··1······111·1···111·1·1·1···111·1···11····1··11111·11··11·····1··1111111··1·1·11··1·1·1·1·11··1·1·11··11111··1·····11·11··1·1···11·1·1·11······11··········11······11··1·1··111·1·11··11···1·1··111·1·1··1····1··1········1··1····1··11·1···11·1·111··
check 42 (528)	·····11··11····111111··11··11111·1··11·1··1·1·1·1·11··1·11·1·1··1·1·11··11··1·11·1·1··11··11·1·1111··1111··········11····111111··11··········11··11··········11·11·1·1··1·11··1·11·1·1··1·11··11··11·1·1·1·1··11··11·1·1·1·1··111······1111··1111······1111··11····11··11······1111··11··1111111·1·1··1·11··1·1·1·1·11·1··11·1··1·11··11··1·1·11·1··11··11·1·1·111111····11··········1111··1111··1111111111··11··1111111111··11·11··1·11·1·1··1·11··1·11·1·1··11··1·1·1·1·11··11··1·1·1·1·11··111··1111······1111··1111······11··11····111111··11··1111······11·11·1·1·1·1··11·1··1·1·1·1·11··1·11··1·11·1·1··11··11·1··1·1·11···1111111111··1111··········11··111111····11····111111····11·····1·11··11··1·1·1·1·11··11··1·1·1·1·1·11·1··11·1··1·1·11·1··11·1·1111··11··1111111111··11··111111··111111····11··11······1111··11·11··1·1·1·1·11·1··11·1·1·1·1··1·11·1·1··1·11··11··1·1·11·1··11···11··········1111··1111111111··1111··1111······1111··1111·······1·1·11··11··1·1·1·1·11··11··1·1·1·11··1·11·1·1··1·11··1·11·1·1·111111··11··1111111111··11··1111
check 43 (528)	···1111·1·11·1···1111···11·1··1····11111·1··1·111····11·11·1··1·11·1··1··1111··1·1··1·11111····1··1·11···1111··1·1··1·1····1111········1·1·1·1···11··111··11··1·········1·1·1·111··11··1··11··11··11··1··11··11·1·1·1·111111111·11··11···11··11·1·1·1·1·········1·11·1·····1111·11·1··1··1111···1·11·1·1111····1··1·11···1111··11····111··1·11·····1111·1·11·1···1111··1··1·11·····11111·1··1·1·1·1·1·111111111·11··11·11··11···1·1·1·1········1··11··111··11····11··111··11··111111111·1·1·1·111··11··1··11··1111111111·1·1·1·1111····1·1··1·111····111··1·11·1111·····1·11·1···1111··1··1·11·1··1·11·11····11·1·11·1·····1111·11·1··111····11·1·11·1·1111····11111111·1·1·1·111··11···11··11·111111111·1·1·1···11··11·11··11··11··11·11··11··1·1·1·1·········1··11··111··11··1·1·1·1·11111111·1·11·1·····1111·11·1··1··1111···1·11·1·1111····1··1·11···1111··11····111··1·11·····1111·1·11·1···1111··1··1·11·····11111·1··1·1·1·1·1·111111111·11··11·11··11···1·1·1·1········1··11··111··11····11··111··11··111111111·1·1·1·111··11··1··11··1111111111·1·1·1·
check 44 (480)	·········1111············1111····11··11····111111··11··1111········1111··11··111111····11··11··11····111111111111····111111111111111111··1111··11111111··1111····11··111111····11··11······11111111······11··11····111111··11··11····11········11····11··········11··111111······11··111111····11111111··1111··········11····11··1111··1111111111····11············111111··11······111111··11··11··11··1111····11··11··1111····1111111111····11··········1111··11····1111111111··1111··············1111··11··11····1111··11··1111111111··1111··········11····1111··11······111111··11······1111····111111··11······111111··11··11····11··········1111··11111111··········1111··1111111111····1111··11··1111····11··11··1111····1111····11··11··1111····11··11··11····1111111111··1111··········11··11··1111······11··11····1111··········1111············1111····1111············1111··············1111··11··111111····11··11····11··111111····11··11······1111········11····11········11····1111····11········11····11············111111··11··1111······11··11
check 45 (528)	···········1111·1·11·1··1·1·1·1111111111111····1·1··1·11·1·1·1·11··11····1111··1··1·11··11··11···11··1111····11·11·1··11··11··1··11··11··1111···11·1··1·11··11·11··11··11····111··1·11·1··11··111111111····11111·1··1·1·1·1·1·1········1111·····1·11·1·1·1·1·1··1·11·1··1·1·1·1············1111·1·11·1··1·1·1·1············1111·11·1··11··11··1··11··1111····11·11·1··11··11··1··11··1111····111··1·11·1··11··111··11··11····111··1·11·1··11··111··11··11····111·1··1·1·1·1·1·111111111····11111·1··1·1·1·1·1·111111111····1111·1·1·1·11·1··1·11111············1·1·1·1··1·11·1·····1111111111111··11··11··1·11···1111····11··11·11··11··11·1··111····1111··11···11··11·1··1·11·11····11··11··111··11··1·11·1··1··1111··11··11··1·1·1·1·1·1··1·1····1111·········1·1·1·1·1·11·1·1111····11111111····1111111111111·1·1·1··1·11·1·····1111111111111·1·1·1··1·11·1···1111····11··111··11··11··1·11···1111····11··111··11··11··1·11·11····11··11··11·11··11·1··1·11·11····11··11··11·11··11·1··1·11·1111····11111111·1·1·1·1·1·11·1·1111····11111111·1·1·1·1·1·11·1·
check 46 (528)	·······11111111··11··1111··11······11111111······1111··11····11········1111111111··11····11··111111········1111··1111··11····11··1111··11····11····11111111····11··11····11··1111111111········11····11··1111······11111111····11··11····11··11········11111111·1·1·1·1·1·1·1·11··11··11··11··1·1·11·1··1·11·1·1··1·11·1··1·11··1·1·1·1·1·1·1·1·11··11··11··11·1·1··1·11·1··1·11··1·11·1··1·11·1··1·11·1··1·11··1·11·1··1·11·1··11··11··11··11·1·1·1·1·1·1·1·1··11·1··1·11·1··1·1·11·1··1·11·1··11··11··11··11··1·1·1·1·1·1·1·1·11··11·1··11··1·1·1·1·11·1·1·1··11·1··11··1·11··1·11·1·1·1··1·1·11··11·1··11··11·1·1·1··1·1·1·11··1·11··11·1··1·1·11·1·1·1··1·11·1··1·1·1·11·1·1··1·11··11·1··1·1·1·1·11·1·1·1··11··11·1··11··1·1·11·1·1·1··1·11··1·11··11·1··1·1·1·1·11·1·1·1·1··11··1·11··11···11··11··11··111111111111111111··1111····1111··1111····1111······11··11··11··11················11····1111····111111····1111········1111····111111····1111····111111111111111111··11··11··11··111111····1111····11····1111····11111111111111111111··11··11··11··

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 n1023Noisy T states per run.

outputs k27

distance d5Exact, proved and witnessed here.

error coefficient A_{5}8,866,408Faults of weight 5 in the circuit shown that pass every check and damage the output. The output error is A_{5}\,p^{5} to leading order.

wires N47

checks r20

V_{\mathrm{ex}}27T states per run. CCZ counts as two.

\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log d2.2583Overhead per extractable T state. Lower is better.

\gamma = \log(n/k)/\log d2.2583Overhead 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 width27Rank of the output rows modulo the check rows.

Output gate

27 T0 CS0 CCZon 27 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}

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 (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 20 single-wire gates and 448 \mathrm{CZ} gates: \mathrm{Z} on output 0, \mathrm{S} on output 2, \mathrm{S}^\dagger on output 3, \mathrm{S} on output 4, \mathrm{Z} on output 8, \mathrm{Z} on output 11, \mathrm{S}^\dagger on output 12, \mathrm{Z} on output 13, \mathrm{Z} on output 14, \mathrm{S}^\dagger on output 16, \mathrm{S}^\dagger on output 17, \mathrm{S}^\dagger on output 18, \mathrm{S} on output 19, \mathrm{S} on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{S} on output 23, \mathrm{S} on output 24, \mathrm{S}^\dagger on output 25, \mathrm{S}^\dagger on output 26, \mathrm{CZ} on output 0, output 1, \mathrm{CZ} on output 0, output 3, \mathrm{CZ} on output 0, output 4, \mathrm{CZ} on output 0, output 5 and 444 more (listed below). The circuit's action is then exactly the gate above, and an error-free run passes every check with certainty.

All 468 correction gates

\mathrm{Z} on output 0, \mathrm{S} on output 2, \mathrm{S}^\dagger on output 3, \mathrm{S} on output 4, \mathrm{Z} on output 8, \mathrm{Z} on output 11, \mathrm{S}^\dagger on output 12, \mathrm{Z} on output 13, \mathrm{Z} on output 14, \mathrm{S}^\dagger on output 16, \mathrm{S}^\dagger on output 17, \mathrm{S}^\dagger on output 18, \mathrm{S} on output 19, \mathrm{S} on output 20, \mathrm{Z} on output 21, \mathrm{Z} on output 22, \mathrm{S} on output 23, \mathrm{S} on output 24, \mathrm{S}^\dagger on output 25, \mathrm{S}^\dagger on output 26, \mathrm{CZ} on output 0, output 1, \mathrm{CZ} on output 0, output 3, \mathrm{CZ} on output 0, output 4, \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 10, \mathrm{CZ} on output 0, output 11, \mathrm{CZ} on output 0, output 12, \mathrm{CZ} on output 0, output 13, \mathrm{CZ} on output 0, output 14, \mathrm{CZ} on output 0, output 15, \mathrm{CZ} on output 0, output 17, \mathrm{CZ} on output 0, output 19, \mathrm{CZ} on output 0, output 20, \mathrm{CZ} on output 0, output 22, \mathrm{CZ} on output 0, output 24, \mathrm{CZ} on output 0, output 25, \mathrm{CZ} on output 0, output 26, \mathrm{CZ} on output 0, check 29, \mathrm{CZ} on output 0, check 30, \mathrm{CZ} on output 0, check 31, \mathrm{CZ} on output 0, check 33, \mathrm{CZ} on output 0, check 34, \mathrm{CZ} on output 0, check 37, \mathrm{CZ} on output 0, check 39, \mathrm{CZ} on output 0, check 40, \mathrm{CZ} on output 0, check 41, \mathrm{CZ} on output 0, check 42, \mathrm{CZ} on output 0, check 43, \mathrm{CZ} on output 1, output 4, \mathrm{CZ} on output 1, output 5, \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, output 13, \mathrm{CZ} on output 1, output 15, \mathrm{CZ} on output 1, output 17, \mathrm{CZ} on output 1, output 18, \mathrm{CZ} on output 1, output 21, \mathrm{CZ} on output 1, output 25, \mathrm{CZ} on output 1, check 27, \mathrm{CZ} on output 1, check 28, \mathrm{CZ} on output 1, check 29, \mathrm{CZ} on output 1, check 31, \mathrm{CZ} on output 1, check 35, \mathrm{CZ} on output 1, check 36, \mathrm{CZ} on output 1, check 37, \mathrm{CZ} on output 1, check 38, \mathrm{CZ} on output 1, check 39, \mathrm{CZ} on output 1, check 43, \mathrm{CZ} on output 1, check 44, \mathrm{CZ} on output 1, check 46, \mathrm{CZ} on output 2, output 4, \mathrm{CZ} on output 2, output 9, \mathrm{CZ} on output 2, output 14, \mathrm{CZ} on output 2, output 15, \mathrm{CZ} on output 2, output 16, \mathrm{CZ} on output 2, output 18, \mathrm{CZ} on output 2, output 19, \mathrm{CZ} on output 2, output 20, \mathrm{CZ} on output 2, output 21, \mathrm{CZ} on output 2, output 24, \mathrm{CZ} on output 2, output 26, \mathrm{CZ} on output 2, check 28, \mathrm{CZ} on output 2, check 30, \mathrm{CZ} on output 2, check 32, \mathrm{CZ} on output 2, check 35, \mathrm{CZ} on output 2, check 36, \mathrm{CZ} on output 2, check 37, \mathrm{CZ} on output 2, check 38, \mathrm{CZ} on output 2, check 39, \mathrm{CZ} on output 2, check 43, \mathrm{CZ} on output 2, check 45, \mathrm{CZ} on output 2, check 46, \mathrm{CZ} on output 3, output 4, \mathrm{CZ} on output 3, output 5, \mathrm{CZ} on output 3, output 8, \mathrm{CZ} on output 3, output 9, \mathrm{CZ} on output 3, output 12, \mathrm{CZ} on output 3, output 14, \mathrm{CZ} on output 3, output 18, \mathrm{CZ} on output 3, output 19, \mathrm{CZ} on output 3, output 20, \mathrm{CZ} on output 3, output 25, \mathrm{CZ} on output 3, check 27, \mathrm{CZ} on output 3, check 30, \mathrm{CZ} on output 3, check 31, \mathrm{CZ} on output 3, check 32, \mathrm{CZ} on output 3, check 33, \mathrm{CZ} on output 3, check 38, \mathrm{CZ} on output 3, check 39, \mathrm{CZ} on output 3, check 40, \mathrm{CZ} on output 3, check 41, \mathrm{CZ} on output 3, check 43, \mathrm{CZ} on output 4, output 5, \mathrm{CZ} on output 4, output 6, \mathrm{CZ} on output 4, output 8, \mathrm{CZ} on output 4, output 13, \mathrm{CZ} on output 4, output 14, \mathrm{CZ} on output 4, output 15, \mathrm{CZ} on output 4, output 16, \mathrm{CZ} on output 4, check 27, \mathrm{CZ} on output 4, check 30, \mathrm{CZ} on output 4, check 33, \mathrm{CZ} on output 4, check 35, \mathrm{CZ} on output 4, check 36, \mathrm{CZ} on output 4, check 37, \mathrm{CZ} on output 4, check 40, \mathrm{CZ} on output 4, check 41, \mathrm{CZ} on output 4, check 42, \mathrm{CZ} on output 4, check 45, \mathrm{CZ} on output 4, check 46, \mathrm{CZ} on output 5, output 7, \mathrm{CZ} on output 5, output 9, \mathrm{CZ} on output 5, output 11, \mathrm{CZ} on output 5, output 13, \mathrm{CZ} on output 5, output 14, \mathrm{CZ} on output 5, output 17, \mathrm{CZ} on output 5, output 19, \mathrm{CZ} on output 5, output 20, \mathrm{CZ} on output 5, output 21, \mathrm{CZ} on output 5, output 24, \mathrm{CZ} on output 5, check 27, \mathrm{CZ} on output 5, check 29, \mathrm{CZ} on output 5, check 30, \mathrm{CZ} on output 5, check 31, \mathrm{CZ} on output 5, check 33, \mathrm{CZ} on output 5, check 34, \mathrm{CZ} on output 5, check 35, \mathrm{CZ} on output 5, check 36, \mathrm{CZ} on output 5, check 37, \mathrm{CZ} on output 5, check 40, \mathrm{CZ} on output 5, check 41, \mathrm{CZ} on output 5, check 42, \mathrm{CZ} on output 5, check 44, \mathrm{CZ} on output 6, output 8, \mathrm{CZ} on output 6, output 10, \mathrm{CZ} on output 6, output 13, \mathrm{CZ} on output 6, output 14, \mathrm{CZ} on output 6, output 16, \mathrm{CZ} on output 6, output 17, \mathrm{CZ} on output 6, output 20, \mathrm{CZ} on output 6, output 21, \mathrm{CZ} on output 6, output 22, \mathrm{CZ} on output 6, output 25, \mathrm{CZ} on output 6, output 26, \mathrm{CZ} on output 6, check 27, \mathrm{CZ} on output 6, check 31, \mathrm{CZ} on output 6, check 32, \mathrm{CZ} on output 6, check 34, \mathrm{CZ} on output 6, check 36, \mathrm{CZ} on output 6, check 37, \mathrm{CZ} on output 6, check 43, \mathrm{CZ} on output 6, check 46, \mathrm{CZ} on output 7, output 8, \mathrm{CZ} on output 7, output 10, \mathrm{CZ} on output 7, output 11, \mathrm{CZ} on output 7, output 14, \mathrm{CZ} on output 7, output 17, \mathrm{CZ} on output 7, output 19, \mathrm{CZ} on output 7, output 20, \mathrm{CZ} on output 7, output 22, \mathrm{CZ} on output 7, output 23, \mathrm{CZ} on output 7, output 25, \mathrm{CZ} on output 7, output 26, \mathrm{CZ} on output 7, check 27, \mathrm{CZ} on output 7, check 29, \mathrm{CZ} on output 7, check 30, \mathrm{CZ} on output 7, check 31, \mathrm{CZ} on output 7, check 33, \mathrm{CZ} on output 7, check 34, \mathrm{CZ} on output 7, check 36, \mathrm{CZ} on output 7, check 38, \mathrm{CZ} on output 7, check 42, \mathrm{CZ} on output 7, check 44, \mathrm{CZ} on output 8, output 9, \mathrm{CZ} on output 8, output 10, \mathrm{CZ} on output 8, output 11, \mathrm{CZ} on output 8, output 12, \mathrm{CZ} on output 8, output 17, \mathrm{CZ} on output 8, output 18, \mathrm{CZ} on output 8, output 22, \mathrm{CZ} on output 8, output 24, \mathrm{CZ} on output 8, output 25, \mathrm{CZ} on output 8, output 26, \mathrm{CZ} on output 8, check 28, \mathrm{CZ} on output 8, check 29, \mathrm{CZ} on output 8, check 30, \mathrm{CZ} on output 8, check 32, \mathrm{CZ} on output 8, check 35, \mathrm{CZ} on output 8, check 37, \mathrm{CZ} on output 8, check 38, \mathrm{CZ} on output 8, check 39, \mathrm{CZ} on output 8, check 40, \mathrm{CZ} on output 8, check 41, \mathrm{CZ} on output 8, check 43, \mathrm{CZ} on output 8, check 45, \mathrm{CZ} on output 9, output 13, \mathrm{CZ} on output 9, output 14, \mathrm{CZ} on output 9, output 15, \mathrm{CZ} on output 9, output 16, \mathrm{CZ} on output 9, output 17, \mathrm{CZ} on output 9, output 20, \mathrm{CZ} on output 9, output 21, \mathrm{CZ} on output 9, output 22, \mathrm{CZ} on output 9, output 23, \mathrm{CZ} on output 9, output 25, \mathrm{CZ} on output 9, check 28, \mathrm{CZ} on output 9, check 31, \mathrm{CZ} on output 9, check 32, \mathrm{CZ} on output 9, check 34, \mathrm{CZ} on output 9, check 41, \mathrm{CZ} on output 9, check 42, \mathrm{CZ} on output 9, check 43, \mathrm{CZ} on output 10, output 12, \mathrm{CZ} on output 10, output 13, \mathrm{CZ} on output 10, output 15, \mathrm{CZ} on output 10, output 16, \mathrm{CZ} on output 10, output 17, \mathrm{CZ} on output 10, output 18, \mathrm{CZ} on output 10, output 19, \mathrm{CZ} on output 10, output 24, \mathrm{CZ} on output 10, check 28, \mathrm{CZ} on output 10, check 29, \mathrm{CZ} on output 10, check 30, \mathrm{CZ} on output 10, check 34, \mathrm{CZ} on output 10, check 35, \mathrm{CZ} on output 10, check 37, \mathrm{CZ} on output 10, check 38, \mathrm{CZ} on output 10, check 42, \mathrm{CZ} on output 10, check 45, \mathrm{CZ} on output 11, output 12, \mathrm{CZ} on output 11, output 13, \mathrm{CZ} on output 11, output 14, \mathrm{CZ} on output 11, output 16, \mathrm{CZ} on output 11, output 22, \mathrm{CZ} on output 11, output 24, \mathrm{CZ} on output 11, output 25, \mathrm{CZ} on output 11, output 26, \mathrm{CZ} on output 11, check 27, \mathrm{CZ} on output 11, check 28, \mathrm{CZ} on output 11, check 29, \mathrm{CZ} on output 11, check 34, \mathrm{CZ} on output 11, check 35, \mathrm{CZ} on output 11, check 36, \mathrm{CZ} on output 11, check 37, \mathrm{CZ} on output 11, check 39, \mathrm{CZ} on output 11, check 44, \mathrm{CZ} on output 12, output 13, \mathrm{CZ} on output 12, output 14, \mathrm{CZ} on output 12, output 19, \mathrm{CZ} on output 12, output 21, \mathrm{CZ} on output 12, check 28, \mathrm{CZ} on output 12, check 31, \mathrm{CZ} on output 12, check 34, \mathrm{CZ} on output 12, check 35, \mathrm{CZ} on output 12, check 36, \mathrm{CZ} on output 12, check 37, \mathrm{CZ} on output 12, check 40, \mathrm{CZ} on output 12, check 41, \mathrm{CZ} on output 12, check 44, \mathrm{CZ} on output 13, output 16, \mathrm{CZ} on output 13, output 20, \mathrm{CZ} on output 13, output 22, \mathrm{CZ} on output 13, output 23, \mathrm{CZ} on output 13, output 24, \mathrm{CZ} on output 13, output 25, \mathrm{CZ} on output 13, output 26, \mathrm{CZ} on output 13, check 27, \mathrm{CZ} on output 13, check 28, \mathrm{CZ} on output 13, check 29, \mathrm{CZ} on output 13, check 30, \mathrm{CZ} on output 13, check 31, \mathrm{CZ} on output 13, check 36, \mathrm{CZ} on output 13, check 37, \mathrm{CZ} on output 13, check 38, \mathrm{CZ} on output 13, check 41, \mathrm{CZ} on output 13, check 42, \mathrm{CZ} on output 13, check 44, \mathrm{CZ} on output 13, check 45, \mathrm{CZ} on output 13, check 46, \mathrm{CZ} on output 14, output 15, \mathrm{CZ} on output 14, output 18, \mathrm{CZ} on output 14, output 19, \mathrm{CZ} on output 14, output 20, \mathrm{CZ} on output 14, output 22, \mathrm{CZ} on output 14, output 24, \mathrm{CZ} on output 14, output 26, \mathrm{CZ} on output 14, check 28, \mathrm{CZ} on output 14, check 29, \mathrm{CZ} on output 14, check 31, \mathrm{CZ} on output 14, check 32, \mathrm{CZ} on output 14, check 33, \mathrm{CZ} on output 14, check 35, \mathrm{CZ} on output 14, check 36, \mathrm{CZ} on output 14, check 37, \mathrm{CZ} on output 14, check 38, \mathrm{CZ} on output 14, check 42, \mathrm{CZ} on output 14, check 43, \mathrm{CZ} on output 14, check 45, \mathrm{CZ} on output 14, check 46, \mathrm{CZ} on output 15, output 16, \mathrm{CZ} on output 15, output 18, \mathrm{CZ} on output 15, output 20, \mathrm{CZ} on output 15, output 25, \mathrm{CZ} on output 15, check 29, \mathrm{CZ} on output 15, check 31, \mathrm{CZ} on output 15, check 32, \mathrm{CZ} on output 15, check 34, \mathrm{CZ} on output 15, check 37, \mathrm{CZ} on output 15, check 39, \mathrm{CZ} on output 15, check 40, \mathrm{CZ} on output 15, check 45, \mathrm{CZ} on output 15, check 46, \mathrm{CZ} on output 16, output 17, \mathrm{CZ} on output 16, output 19, \mathrm{CZ} on output 16, output 20, \mathrm{CZ} on output 16, output 21, \mathrm{CZ} on output 16, output 22, \mathrm{CZ} on output 16, output 23, \mathrm{CZ} on output 16, output 25, \mathrm{CZ} on output 16, check 29, \mathrm{CZ} on output 16, check 30, \mathrm{CZ} on output 16, check 33, \mathrm{CZ} on output 16, check 34, \mathrm{CZ} on output 16, check 37, \mathrm{CZ} on output 16, check 38, \mathrm{CZ} on output 16, check 39, \mathrm{CZ} on output 16, check 41, \mathrm{CZ} on output 16, check 42, \mathrm{CZ} on output 16, check 44, \mathrm{CZ} on output 16, check 45, \mathrm{CZ} on output 16, check 46, \mathrm{CZ} on output 17, output 18, \mathrm{CZ} on output 17, output 19, \mathrm{CZ} on output 17, output 21, \mathrm{CZ} on output 17, output 23, \mathrm{CZ} on output 17, check 27, \mathrm{CZ} on output 17, check 28, \mathrm{CZ} on output 17, check 29, \mathrm{CZ} on output 17, check 33, \mathrm{CZ} on output 17, check 34, \mathrm{CZ} on output 17, check 36, \mathrm{CZ} on output 17, check 40, \mathrm{CZ} on output 17, check 42, \mathrm{CZ} on output 17, check 44, \mathrm{CZ} on output 18, output 20, \mathrm{CZ} on output 18, output 22, \mathrm{CZ} on output 18, output 25, \mathrm{CZ} on output 18, output 26, \mathrm{CZ} on output 18, check 27, \mathrm{CZ} on output 18, check 29, \mathrm{CZ} on output 18, check 33, \mathrm{CZ} on output 18, check 34, \mathrm{CZ} on output 18, check 38, \mathrm{CZ} on output 18, check 43, \mathrm{CZ} on output 18, check 44, \mathrm{CZ} on output 18, check 45, \mathrm{CZ} on output 18, check 46, \mathrm{CZ} on output 19, output 20, \mathrm{CZ} on output 19, output 23, \mathrm{CZ} on output 19, output 24, \mathrm{CZ} on output 19, check 27, \mathrm{CZ} on output 19, check 28, \mathrm{CZ} on output 19, check 30, \mathrm{CZ} on output 19, check 31, \mathrm{CZ} on output 19, check 34, \mathrm{CZ} on output 19, check 38, \mathrm{CZ} on output 19, check 43, \mathrm{CZ} on output 20, output 23, \mathrm{CZ} on output 20, output 24, \mathrm{CZ} on output 20, output 26, \mathrm{CZ} on output 20, check 27, \mathrm{CZ} on output 20, check 33, \mathrm{CZ} on output 20, check 34, \mathrm{CZ} on output 20, check 38, \mathrm{CZ} on output 20, check 40, \mathrm{CZ} on output 20, check 44, \mathrm{CZ} on output 20, check 45, \mathrm{CZ} on output 21, output 22, \mathrm{CZ} on output 21, output 26, \mathrm{CZ} on output 21, check 31, \mathrm{CZ} on output 21, check 33, \mathrm{CZ} on output 21, check 34, \mathrm{CZ} on output 21, check 35, \mathrm{CZ} on output 21, check 36, \mathrm{CZ} on output 21, check 38, \mathrm{CZ} on output 21, check 40, \mathrm{CZ} on output 21, check 41, \mathrm{CZ} on output 21, check 43, \mathrm{CZ} on output 22, output 23, \mathrm{CZ} on output 22, output 24, \mathrm{CZ} on output 22, check 31, \mathrm{CZ} on output 22, check 32, \mathrm{CZ} on output 22, check 37, \mathrm{CZ} on output 22, check 38, \mathrm{CZ} on output 22, check 39, \mathrm{CZ} on output 22, check 40, \mathrm{CZ} on output 22, check 41, \mathrm{CZ} on output 22, check 43, \mathrm{CZ} on output 22, check 44, \mathrm{CZ} on output 23, output 24, \mathrm{CZ} on output 23, output 25, \mathrm{CZ} on output 23, check 28, \mathrm{CZ} on output 23, check 29, \mathrm{CZ} on output 23, check 30, \mathrm{CZ} on output 23, check 33, \mathrm{CZ} on output 23, check 34, \mathrm{CZ} on output 23, check 37, \mathrm{CZ} on output 23, check 39, \mathrm{CZ} on output 23, check 40, \mathrm{CZ} on output 23, check 41, \mathrm{CZ} on output 23, check 44, \mathrm{CZ} on output 23, check 46, \mathrm{CZ} on output 24, output 25, \mathrm{CZ} on output 24, output 26, \mathrm{CZ} on output 24, check 27, \mathrm{CZ} on output 24, check 29, \mathrm{CZ} on output 24, check 31, \mathrm{CZ} on output 24, check 34, \mathrm{CZ} on output 24, check 36, \mathrm{CZ} on output 24, check 37, \mathrm{CZ} on output 24, check 39, \mathrm{CZ} on output 24, check 41, \mathrm{CZ} on output 24, check 42, \mathrm{CZ} on output 24, check 43, \mathrm{CZ} on output 24, check 45, \mathrm{CZ} on output 25, output 26, \mathrm{CZ} on output 25, check 27, \mathrm{CZ} on output 25, check 28, \mathrm{CZ} on output 25, check 29, \mathrm{CZ} on output 25, check 31, \mathrm{CZ} on output 25, check 32, \mathrm{CZ} on output 25, check 33, \mathrm{CZ} on output 25, check 34, \mathrm{CZ} on output 25, check 35, \mathrm{CZ} on output 25, check 39, \mathrm{CZ} on output 25, check 40, \mathrm{CZ} on output 25, check 41, \mathrm{CZ} on output 26, check 28, \mathrm{CZ} on output 26, check 30, \mathrm{CZ} on output 26, check 33, \mathrm{CZ} on output 26, check 38, \mathrm{CZ} on output 26, check 39, \mathrm{CZ} on output 26, check 41, \mathrm{CZ} on output 26, check 44, \mathrm{CZ} on output 26, check 46

These Clifford gates cannot be avoided. No choice of \mathrm{T}, \mathrm{T}^3, \mathrm{T}^5 or \mathrm{T}^\dagger for each rotation removes them; the catalogue proves this by showing that the linear system over \mathbb{Z}_4 the powers would have to solve has no solution.

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/1023.27.5.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-1023.27.5.a.txt", "w") as out:
    out.write("\n".join(lines) + "\n")

Distance

d=5, exact. No fault of weight below 5 is both undetectable and damaging. One of weight 5 is.

Exactly 8,866,408 faults of weight 5 are undetectable and damaging, so A_{5}=8{,}866{,}408. If each rotation fails independently with probability p, an accepted run has a damaged output with probability A_{5}\,p^{5}+O(p^{6}).

A damaging fault of weight 5 sits on columns [95,197,281,549,921].

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 campaign; a verified witness, not a maximum

Found by: AI search

Discovery: AI search

1 recorded source

[
 {
  "regime": "AI search",
  "file": "master_catalog/catalogue_new",
  "label": "T0.T1.T2.T3.T4.T5.T6.T7.T8.T9.T10.T11.T12.T13.T14.T15.T16.T17.T18.T19.T20.T21.T22.T23.T24.T25.T26",
  "N": 47,
  "d": 5,
  "d_is_exact": true,
  "origin": "frontier_campaign",
  "provenance": "frontier_campaign \u00b7 catalogue.jsonl:397"
 }
]

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/1023.27.5.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[1346].