The circuit
The 14\times4026 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.
| 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 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200 1210 1220 1230 1240 1250 1260 1270 1280 1290 1300 1310 1320 1330 1340 1350 1360 1370 1380 1390 1400 1410 1420 1430 1440 1450 1460 1470 1480 1490 1500 1510 1520 1530 1540 1550 1560 1570 1580 1590 1600 1610 1620 1630 1640 1650 1660 1670 1680 1690 1700 1710 1720 1730 1740 1750 1760 1770 1780 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 2110 2120 2130 2140 2150 2160 2170 2180 2190 2200 2210 2220 2230 2240 2250 2260 2270 2280 2290 2300 2310 2320 2330 2340 2350 2360 2370 2380 2390 2400 2410 2420 2430 2440 2450 2460 2470 2480 2490 2500 2510 2520 2530 2540 2550 2560 2570 2580 2590 2600 2610 2620 2630 2640 2650 2660 2670 2680 2690 2700 2710 2720 2730 2740 2750 2760 2770 2780 2790 2800 2810 2820 2830 2840 2850 2860 2870 2880 2890 2900 2910 2920 2930 2940 2950 2960 2970 2980 2990 3000 3010 3020 3030 3040 3050 3060 3070 3080 3090 3100 3110 3120 3130 3140 3150 3160 3170 3180 3190 3200 3210 3220 3230 3240 3250 3260 3270 3280 3290 3300 3310 3320 3330 3340 3350 3360 3370 3380 3390 3400 3410 3420 3430 3440 3450 3460 3470 3480 3490 3500 3510 3520 3530 3540 3550 3560 3570 3580 3590 3600 3610 3620 3630 3640 3650 3660 3670 3680 3690 3700 3710 3720 3730 3740 3750 3760 3770 3780 3790 3800 3810 3820 3830 3840 3850 3860 3870 3880 3890 3900 3910 3920 3930 3940 3950 3960 3970 3980 3990 4000 4010 4020 |
|---|---|
| out 0 (2014) | 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111···························································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································· |
| out 1 (2014) | 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111·······························································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111····························································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································································· |
| out 2 (2014) | 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111················································································································································································································································································································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111···············································································································································································································································································································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111···············································································································································································································································································································································································································································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111·············································································································································································································································································································································································································································································································································· |
| out 3 (2014) | 1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111································································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111················································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111················································································································································································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111·······························································································································································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111················································································································································································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111·······························································································································································································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111·······························································································································································································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111··············································································································································································································································································· |
| out 4 (2014) | 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111········································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111························································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111························································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111························································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111························································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111························································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111························································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111·······································································································································1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111························································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111························································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111························································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111·······································································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111························································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111·······································································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111·······································································································································111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111········································································································································ |
| check 5 (2016) | 1111111111111111111111111111111111111111111111111111111111111111·······································································111111111111111111111111111111111111111111111111111111111111111111111111································································111111111111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111························································111111111111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111························································1111111111111111111111111111111111111111111111111111111111111111························································11111111111111111111111111111111111111111111111111111111································································111111111111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111························································1111111111111111111111111111111111111111111111111111111111111111························································11111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111························································11111111111111111111111111111111111111111111111111111111································································11111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111·······································································111111111111111111111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111························································1111111111111111111111111111111111111111111111111111111111111111························································11111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111························································11111111111111111111111111111111111111111111111111111111································································11111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111·······································································1111111111111111111111111111111111111111111111111111111111111111························································11111111111111111111111111111111111111111111111111111111································································11111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111·······································································11111111111111111111111111111111111111111111111111111111································································1111111111111111111111111111111111111111111111111111111111111111·······································································1111111111111111111111111111111111111111111111111111111111111111·······································································111111111111111111111111111111111111111111111111111111111111111111111111································································ |
| check 6 (2016) | 1111111111111111111111111111····································111111111111111111111111111111111111····································111111111111111111111111111111111111···································111111111111111111111111111111111111·····························111111111111111111111111111111111111···································111111111111111111111111111111111111····························111111111111111111111111111111111111····························1111111111111111111111111111·····························111111111111111111111111111111111111···································111111111111111111111111111111111111····························111111111111111111111111111111111111····························1111111111111111111111111111····························111111111111111111111111111111111111····························1111111111111111111111111111····························1111111111111111111111111111····························1111111111111111111111111111·····································111111111111111111111111111111111111···································111111111111111111111111111111111111····························111111111111111111111111111111111111····························1111111111111111111111111111····························111111111111111111111111111111111111····························1111111111111111111111111111····························1111111111111111111111111111····························1111111111111111111111111111····································111111111111111111111111111111111111····························1111111111111111111111111111····························1111111111111111111111111111····························1111111111111111111111111111····································1111111111111111111111111111····························1111111111111111111111111111····································1111111111111111111111111111····································111111111111111111111111111111111111····································111111111111111111111111111111111111···································111111111111111111111111111111111111····························111111111111111111111111111111111111····························1111111111111111111111111111····························111111111111111111111111111111111111····························1111111111111111111111111111····························1111111111111111111111111111····························1111111111111111111111111111····································111111111111111111111111111111111111····························1111111111111111111111111111····························1111111111111111111111111111····························1111111111111111111111111111····································1111111111111111111111111111····························1111111111111111111111111111····································1111111111111111111111111111····································111111111111111111111111111111111111···································111111111111111111111111111111111111····························1111111111111111111111111111····························1111111111111111111111111111····························1111111111111111111111111111····································1111111111111111111111111111····························1111111111111111111111111111····································1111111111111111111111111111····································111111111111111111111111111111111111···································1111111111111111111111111111····························1111111111111111111111111111····································1111111111111111111111111111····································111111111111111111111111111111111111···································1111111111111111111111111111····································111111111111111111111111111111111111····································111111111111111111111111111111111111···································111111111111111111111111111111111111···························· |
| check 7 (2016) | 111111111111················1111111111111111····················1111111111111111····················11111111111111111111················1111111111111111····················11111111111111111111················11111111111111111111···············1111111111111111·············1111111111111111····················11111111111111111111················11111111111111111111···············1111111111111111·············11111111111111111111···············1111111111111111············1111111111111111············111111111111·················1111111111111111····················11111111111111111111················11111111111111111111···············1111111111111111·············11111111111111111111···············1111111111111111············1111111111111111············111111111111·················11111111111111111111···············1111111111111111············1111111111111111············111111111111················1111111111111111············111111111111················111111111111················1111111111111111·····················1111111111111111····················11111111111111111111················11111111111111111111···············1111111111111111·············11111111111111111111···············1111111111111111············1111111111111111············111111111111·················11111111111111111111···············1111111111111111············1111111111111111············111111111111················1111111111111111············111111111111················111111111111················1111111111111111·····················11111111111111111111···············1111111111111111············1111111111111111············111111111111················1111111111111111············111111111111················111111111111················1111111111111111····················1111111111111111············111111111111················111111111111················1111111111111111····················111111111111················1111111111111111····················1111111111111111····················11111111111111111111················1111111111111111····················11111111111111111111················11111111111111111111···············1111111111111111·············11111111111111111111···············1111111111111111············1111111111111111············111111111111·················11111111111111111111···············1111111111111111············1111111111111111············111111111111················1111111111111111············111111111111················111111111111················1111111111111111·····················11111111111111111111···············1111111111111111············1111111111111111············111111111111················1111111111111111············111111111111················111111111111················1111111111111111····················1111111111111111············111111111111················111111111111················1111111111111111····················111111111111················1111111111111111····················1111111111111111····················11111111111111111111················11111111111111111111···············1111111111111111············1111111111111111············111111111111················1111111111111111············111111111111················111111111111················1111111111111111····················1111111111111111············111111111111················111111111111················1111111111111111····················111111111111················1111111111111111····················1111111111111111····················11111111111111111111···············1111111111111111············111111111111················111111111111················1111111111111111····················111111111111················1111111111111111····················1111111111111111····················11111111111111111111···············111111111111················1111111111111111····················1111111111111111····················11111111111111111111················1111111111111111····················11111111111111111111················11111111111111111111···············1111111111111111············ |
| check 8 (2016) | 111111······111111··········111111··········1111111111··········111111··········1111111111··········1111111111··········1111111111······111111··········1111111111··········1111111111··········1111111111······1111111111··········1111111111······1111111111·····111111·······111111··········1111111111··········1111111111··········1111111111······1111111111··········1111111111······1111111111·····111111·······1111111111··········1111111111······1111111111·····111111·······1111111111·····111111······111111······111111···········111111··········1111111111··········1111111111··········1111111111······1111111111··········1111111111······1111111111·····111111·······1111111111··········1111111111······1111111111·····111111·······1111111111·····111111······111111······111111···········1111111111··········1111111111······1111111111·····111111·······1111111111·····111111······111111······111111···········1111111111·····111111······111111······111111··········111111······111111··········111111··········1111111111···········111111··········1111111111··········1111111111··········1111111111······1111111111··········1111111111······1111111111·····111111·······1111111111··········1111111111······1111111111·····111111·······1111111111·····111111······111111······111111···········1111111111··········1111111111······1111111111·····111111·······1111111111·····111111······111111······111111···········1111111111·····111111······111111······111111··········111111······111111··········111111··········1111111111···········1111111111··········1111111111······1111111111·····111111·······1111111111·····111111······111111······111111···········1111111111·····111111······111111······111111··········111111······111111··········111111··········1111111111···········1111111111·····111111······111111······111111··········111111······111111··········111111··········1111111111··········111111······111111··········111111··········1111111111··········111111··········1111111111··········1111111111··········1111111111······111111··········1111111111··········1111111111··········1111111111······1111111111··········1111111111······1111111111·····111111·······1111111111··········1111111111······1111111111·····111111·······1111111111·····111111······111111······111111···········1111111111··········1111111111······1111111111·····111111·······1111111111·····111111······111111······111111···········1111111111·····111111······111111······111111··········111111······111111··········111111··········1111111111···········1111111111··········1111111111······1111111111·····111111·······1111111111·····111111······111111······111111···········1111111111·····111111······111111······111111··········111111······111111··········111111··········1111111111···········1111111111·····111111······111111······111111··········111111······111111··········111111··········1111111111··········111111······111111··········111111··········1111111111··········111111··········1111111111··········1111111111··········1111111111······1111111111··········1111111111······1111111111·····111111·······1111111111·····111111······111111······111111···········1111111111·····111111······111111······111111··········111111······111111··········111111··········1111111111···········1111111111·····111111······111111······111111··········111111······111111··········111111··········1111111111··········111111······111111··········111111··········1111111111··········111111··········1111111111··········1111111111··········1111111111······1111111111·····111111······111111······111111··········111111······111111··········111111··········1111111111··········111111······111111··········111111··········1111111111··········111111··········1111111111··········1111111111··········1111111111·····111111······111111··········111111··········1111111111··········111111··········1111111111··········1111111111··········1111111111······111111··········1111111111··········1111111111··········1111111111······1111111111··········1111111111······1111111111·····111111······ |
| check 9 (2016) | ·1111·11····11····1111······11····1111······1111······111111····11····1111······1111······111111····1111······111111····111111····1111··11····1111······1111······111111····1111······111111····111111····1111··1111······111111····111111····1111··111111····1111··1111·11·····11····1111······1111······111111····1111······111111····111111····1111··1111······111111····111111····1111··111111····1111··1111·11·····1111······111111····111111····1111··111111····1111··1111·11·····111111····1111··1111·11·····1111·11····11····1111·······11····1111······1111······111111····1111······111111····111111····1111··1111······111111····111111····1111··111111····1111··1111·11·····1111······111111····111111····1111··111111····1111··1111·11·····111111····1111··1111·11·····1111·11····11····1111·······1111······111111····111111····1111··111111····1111··1111·11·····111111····1111··1111·11·····1111·11····11····1111·······111111····1111··1111·11·····1111·11····11····1111·······1111·11····11····1111······11····1111······1111······111111·····11····1111······1111······111111····1111······111111····111111····1111··1111······111111····111111····1111··111111····1111··1111·11·····1111······111111····111111····1111··111111····1111··1111·11·····111111····1111··1111·11·····1111·11····11····1111·······1111······111111····111111····1111··111111····1111··1111·11·····111111····1111··1111·11·····1111·11····11····1111·······111111····1111··1111·11·····1111·11····11····1111·······1111·11····11····1111······11····1111······1111······111111·····1111······111111····111111····1111··111111····1111··1111·11·····111111····1111··1111·11·····1111·11····11····1111·······111111····1111··1111·11·····1111·11····11····1111·······1111·11····11····1111······11····1111······1111······111111·····111111····1111··1111·11·····1111·11····11····1111·······1111·11····11····1111······11····1111······1111······111111·····1111·11····11····1111······11····1111······1111······111111····11····1111······1111······111111····1111······111111····111111····1111··11····1111······1111······111111····1111······111111····111111····1111··1111······111111····111111····1111··111111····1111··1111·11·····1111······111111····111111····1111··111111····1111··1111·11·····111111····1111··1111·11·····1111·11····11····1111·······1111······111111····111111····1111··111111····1111··1111·11·····111111····1111··1111·11·····1111·11····11····1111·······111111····1111··1111·11·····1111·11····11····1111·······1111·11····11····1111······11····1111······1111······111111·····1111······111111····111111····1111··111111····1111··1111·11·····111111····1111··1111·11·····1111·11····11····1111·······111111····1111··1111·11·····1111·11····11····1111·······1111·11····11····1111······11····1111······1111······111111·····111111····1111··1111·11·····1111·11····11····1111·······1111·11····11····1111······11····1111······1111······111111·····1111·11····11····1111······11····1111······1111······111111····11····1111······1111······111111····1111······111111····111111····1111··1111······111111····111111····1111··111111····1111··1111·11·····111111····1111··1111·11·····1111·11····11····1111·······111111····1111··1111·11·····1111·11····11····1111·······1111·11····11····1111······11····1111······1111······111111·····111111····1111··1111·11·····1111·11····11····1111·······1111·11····11····1111······11····1111······1111······111111·····1111·11····11····1111······11····1111······1111······111111····11····1111······1111······111111····1111······111111····111111····1111··111111····1111··1111·11·····1111·11····11····1111·······1111·11····11····1111······11····1111······1111······111111·····1111·11····11····1111······11····1111······1111······111111····11····1111······1111······111111····1111······111111····111111····1111··1111·11····11····1111······11····1111······1111······111111····11····1111······1111······111111····1111······111111····111111····1111··11····1111······1111······111111····1111······111111····111111····1111··1111······111111····111111····1111··111111····1111··1111·11···· |
| check 10 (2016) | ·111·1·11····11···1···111····11···1···111···1···111···111···111··11···1···111···1···111···111···111·1···111···111···111·111···111·111·1··11···1···111···1···111···111···111·1···111···111···111·111···111·111·1·1···111···111···111·111···111·111·1·111···111·111·1·111·1·11·····11···1···111···1···111···111···111·1···111···111···111·111···111·111·1·1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····111···111·111·1·111·1·11····111·1·11····11···1···111·····11···1···111···1···111···111···111·1···111···111···111·111···111·111·1·1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····111···111·111·1·111·1·11····111·1·11····11···1···111····1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····111···111·111·1·111·1·11····111·1·11····11···1···111····111···111·111·1·111·1·11····111·1·11····11···1···111····111·1·11····11···1···111····11···1···111···1···111···111···111···11···1···111···1···111···111···111·1···111···111···111·111···111·111·1·1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····111···111·111·1·111·1·11····111·1·11····11···1···111····1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····111···111·111·1·111·1·11····111·1·11····11···1···111····111···111·111·1·111·1·11····111·1·11····11···1···111····111·1·11····11···1···111····11···1···111···1···111···111···111··1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····111···111·111·1·111·1·11····111·1·11····11···1···111····111···111·111·1·111·1·11····111·1·11····11···1···111····111·1·11····11···1···111····11···1···111···1···111···111···111··111···111·111·1·111·1·11····111·1·11····11···1···111····111·1·11····11···1···111····11···1···111···1···111···111···111··111·1·11····11···1···111····11···1···111···1···111···111···111··11···1···111···1···111···111···111·1···111···111···111·111···111·111·1··11···1···111···1···111···111···111·1···111···111···111·111···111·111·1·1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····111···111·111·1·111·1·11····111·1·11····11···1···111····1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····111···111·111·1·111·1·11····111·1·11····11···1···111····111···111·111·1·111·1·11····111·1·11····11···1···111····111·1·11····11···1···111····11···1···111···1···111···111···111··1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····111···111·111·1·111·1·11····111·1·11····11···1···111····111···111·111·1·111·1·11····111·1·11····11···1···111····111·1·11····11···1···111····11···1···111···1···111···111···111··111···111·111·1·111·1·11····111·1·11····11···1···111····111·1·11····11···1···111····11···1···111···1···111···111···111··111·1·11····11···1···111····11···1···111···1···111···111···111··11···1···111···1···111···111···111·1···111···111···111·111···111·111·1·1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····111···111·111·1·111·1·11····111·1·11····11···1···111····111···111·111·1·111·1·11····111·1·11····11···1···111····111·1·11····11···1···111····11···1···111···1···111···111···111··111···111·111·1·111·1·11····111·1·11····11···1···111····111·1·11····11···1···111····11···1···111···1···111···111···111··111·1·11····11···1···111····11···1···111···1···111···111···111··11···1···111···1···111···111···111·1···111···111···111·111···111·111·1·111···111·111·1·111·1·11····111·1·11····11···1···111····111·1·11····11···1···111····11···1···111···1···111···111···111··111·1·11····11···1···111····11···1···111···1···111···111···111··11···1···111···1···111···111···111·1···111···111···111·111···111·111·1·111·1·11····11···1···111····11···1···111···1···111···111···111··11···1···111···1···111···111···111·1···111···111···111·111···111·111·1··11···1···111···1···111···111···111·1···111···111···111·111···111·111·1·1···111···111···111·111···111·111·1·111···111·111·1·111·1·11··· |
| check 11 (2016) | ·11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·1·1···1··1··11··1··1··11·1··11·11·1·1··1··11·1··11·11·11··11·11·111·11··1·1···1··1··11··1··1··11·1··11·11·1·1··1··11·1··11·11·11··11·11·111·11··1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1····1·1···1··1··11··1··1··11·1··11·11·1·1··1··11·1··11·11·11··11·11·111·11··1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1····1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1···1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11···1·1···1··1··11··1··1··11·1··11·11·1·1··1··11·1··11·11·11··11·11·111·11··1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1····1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1···1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11···1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1···1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1··1·1···1··1··11··1··1··11·1··11·11·1·1··1··11·1··11·11·11··11·11·111·11··1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1····1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1···1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11···1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1···1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1··1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1···1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·1·1···1··1··11··1··1··11·1··11·11·1·1··1··11·1··11·11·11··11·11·111·11··1·1···1··1··11··1··1··11·1··11·11·1·1··1··11·1··11·11·11··11·11·111·11··1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1····1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1···1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11···1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1···1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1··1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1···1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·1·1···1··1··11··1··1··11·1··11·11·1·1··1··11·1··11·11·11··11·11·111·11··1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1···1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·1·1···1··1··11··1··1··11·1··11·11·1·1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1···11·11·1·1···1·1···1··1··11··11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·1·1···1··1··11··1··1··11·1··11·11·1·1··1··11·1··11·11·11··11·11·111·11·11·11·1·1···1·1···1··1··11··1·1···1··1··11··1··1··11·1··11·11·1·1·1···1··1··11··1··1··11·1··11·11·1·1··1··11·1··11·11·11··11·11·111·11··1·1···1··1··11··1··1··11·1··11·11·1·1··1··11·1··11·11·11··11·11·111·11··1··1··11·1··11·11·11··11·11·111·11·1··11·11·111·11·11·11·1·1·· |
| check 12 (2016) | ·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11·1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1·1·1·1·1·11·11·1·1·11·111·111··1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1·1·1·1·1·11·11·1·1·11·111·111···1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1···1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1·1·1·1·1·11·11·1·1·11·111·111···1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1····1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1···1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1··1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1·1·1·1·1·11·11·1·1·11·111·111···1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1····1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1···1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1···1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1···1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1··1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1·1·1·1·1·11·11·1·1·11·111·111···1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1····1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1···1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1···1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1···1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1··1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11···1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1···1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1··1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11··1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11·1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1·1·1·1·1·11·11·1·1·11·111·111··1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1·1·1·1·1·11·11·1·1·11·111·111···1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1····1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1···1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1···1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1···1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1··1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11···1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1···1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1··1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11··1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11·1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1·1·1·1·1·11·11·1·1·11·111·111···1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1···1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1··1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11··1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11·1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1··1·111·1··1··1··1···1··1·1·1·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11·1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1·1·1·1·1·11·11·1·1·11·111·111·1·111·1··1··1··1···1··1·1·1·1··1···1··1·1·1··1··1·1·1·1·1·11·11·1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1·1·1·1·1·11·11·1·1·11·111·111··1··1···1··1·1·1··1··1·1·1·1·1·11·11··1··1·1·1·1·1·11·11·1·1·11·111·111···1··1·1·1·1·1·11·11·1·1·11·111·111··1·1·11·111·111·1·111·1··1· |
| check 13 (2016) | ··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111·1···1···1··1·11···1··1·11··1·11·111···1··1·11··1·11·111··1·11·111·1111··1···1···1··1·11···1··1·11··1·11·111···1··1·11··1·11·111··1·11·111·1111····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1··1···1···1··1·11···1··1·11··1·11·111···1··1·11··1·11·111··1·11·111·1111····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11··1···1···1··1·11···1··1·11··1·11·111···1··1·11··1·11·111··1·11·111·1111····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111··1···1···1··1·11···1··1·11··1·11·111···1··1·11··1·11·111··1·11·111·1111····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111·1···1···1··1·11···1··1·11··1·11·111···1··1·11··1·11·111··1·11·111·1111··1···1···1··1·11···1··1·11··1·11·111···1··1·11··1·11·111··1·11·111·1111····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111·1···1···1··1·11···1··1·11··1·11·111···1··1·11··1·11·111··1·11·111·1111····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111·1···1···1··1·11···1··1·11··1·11·111···1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···1··1111·1···1·1···1···1··1·11··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111·1···1···1··1·11···1··1·11··1·11·111···1··1·11··1·11·111··1·11·111·1111··1111·1···1·1···1···1··1·11·1···1···1··1·11···1··1·11··1·11·111·1···1···1··1·11···1··1·11··1·11·111···1··1·11··1·11·111··1·11·111·1111··1···1···1··1·11···1··1·11··1·11·111···1··1·11··1·11·111··1·11·111·1111····1··1·11··1·11·111··1·11·111·1111···1·11·111·1111··1111·1···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 n4026Noisy T states per run.
outputs k5
distance d2Exact, proved and witnessed here.
error coefficient A_{2}14,865Faults of weight 2 in the circuit shown that pass every check and damage the output. The output error is A_{2}\,p^{2} to leading order.
wires N14
checks r9
V_{\mathrm{ex}}not definedUndefined, because the gate's terms overlap.
\gamma_\rho = \log(n/V_{\mathrm{ex}})/\log dnot definedOverhead per extractable T state. Lower is better.
\gamma = \log(n/k)/\log d9.6532Overhead per output qubit.
\gamma_T = \log(n/T)/\log d9.3902Overhead per unit of T-count.
T-count6Minimal T-count of the output gate.
phase-polynomial degree2Minimised over changes of output basis.
effective width5Rank of the output rows modulo the check rows.
Output gate
0 T10 CS10 CCZon 5 output wires
As gates: \mathrm{CS}_{01}\cdot \mathrm{CS}_{02}\cdot \mathrm{CS}_{03}\cdot \mathrm{CS}_{04}\cdot \mathrm{CS}_{12}\cdot \mathrm{CS}_{13}\cdot \mathrm{CS}_{14}\cdot \mathrm{CS}_{23}\cdot \mathrm{CS}_{24}\cdot \mathrm{CS}_{34}\cdot \mathrm{CCZ}_{012}\cdot \mathrm{CCZ}_{013}\cdot \mathrm{CCZ}_{014}\cdot \mathrm{CCZ}_{023}\cdot \mathrm{CCZ}_{024}\cdot \mathrm{CCZ}_{034}\cdot \mathrm{CCZ}_{123}\cdot \mathrm{CCZ}_{124}\cdot \mathrm{CCZ}_{134}\cdot \mathrm{CCZ}_{234}
As monomials: 01+02+03+04+12+13+14+23+24+34+012+013+014+023+024+034+123+124+134+234 (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 5 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. 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 \mathrm{T}^3 on rotations 0, 6, 12, 28, 64, 135, 271, 527, 1023, 2014, 3926, 3946, 3956, 3957, 3958, 3959, 3961, 3982, 3992, 3996, 4008, 4012, 4018, 4020 and 5 more (listed below); \mathrm{T}^5 on rotations 1, 2, 3, 4, and \mathrm{T} on the rest. A power of \mathrm{T} costs one magic state, like \mathrm{T} itself. For a code this is a transversal \mathrm{T} gate, \mathrm{T}^j on each qubit.
All 29 rotations at T³
0, 6, 12, 28, 64, 135, 271, 527, 1023, 2014, 3926, 3946, 3956, 3957, 3958, 3959, 3961, 3982, 3992, 3996, 4008, 4012, 4018, 4020, 4021, 4022, 4023, 4024, 4025
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/4026.5.2.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-4026.5.2.a.txt", "w") as out:
out.write("\n".join(lines) + "\n")
Distance
d=2, exact. No fault of weight below 2 is both undetectable and damaging. One of weight 2 is.
Exactly 14,865 faults of weight 2 are undetectable and damaging, so A_{2}=14{,}865. If each rotation fails independently with probability p, an accepted run has a damaged output with probability A_{2}\,p^{2}+O(p^{3}).
A damaging fault of weight 2 sits on columns [0,1879].
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. Singh, C. Gidney, and C. Jones, "Borrowed Identities: Malleable Distillation Factories and a Unified Numerical Search," arXiv:2606.28518 (2026). arxiv.org/abs/2606.28518
Provenance
found by the two-group borrowed-identity search of Singh, Gidney and Jones (arXiv:2606.28518; borrowed_identities/): an identity circuit symmetric within its output and check blocks, with its output-only gates removed; a verified witness, not a maximum
Found by: borrowed-identity search: two-group
Discovery: pre-existing
1 recorded source
[
{
"regime": "borrowed-identity search: two-group",
"file": "borrowed_identities/circuits/unified_l3.json",
"label": "ls-0814",
"N": 14,
"d": 2,
"d_is_exact": true,
"origin": "https://github.com/shraggy/Magic_state_factory_search at 4627014, outputs/large_sweep.csv line 814",
"provenance": "unified search l=3, two-group s_total=4,s_O=1"
}
]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/4026.5.2.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[1493].