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open-standards/wai/quantum-conformance/landscape/table.md
Transaction Science 699a016d80 wai: the extension wai.quantum.landscape/1, its results and its workflow 
extensions/quantum-landscape.md states the job, the answer, how joules are
stated (priced, never called measured, sampling at its own rate, what the rate
leaves out), and the seam a GPU member or an FPGA board runs behind, with each
answer naming what ran it and how far it is held to the reference.

quantum-conformance/landscape holds the equal-budget table, published as it came
out (simulated annealing leads on the larger instances), the starting-temperature
data behind the default, a trial outside the job form, the browser build's parity
record, a stated result and the script that checks it. The docs page, the READMEs,
the version policy, the changelog entry and wai-quantum-landscape.yml come with it.

Co-Authored-By: Claude Opus 5.5 <[email protected]>
2026-11-06 02:19:10 -05:00

12 KiB
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Each cell is the runs that reached the target, out of the runs made, then the operations a run takes for a 99 in 100 chance of reaching it ("-" if no run did). Every solver in a row has the same budget of operations a run as the emulator's sampling mode. One operation is one coupling read, one cell updated or one move considered.

family variables pairs sweeps a start target emulator, sampling, default start emulator, sampling, hot start emulator, deterministic simulated annealing tabu search greedy descent
clusters 8 16 40 exact 100/100, 12,800 100/100, 12,800 60/100, 64,331 100/100, 12,801 100/100, 12,809 100/100, 12,812
clusters 8 16 320 exact 100/100, 102,400 100/100, 102,400 60/100, 514,650 100/100, 102,401 100/100, 102,411 100/100, 102,413
clusters 12 24 40 exact 100/100, 19,200 97/100, 25,215 55/100, 110,730 100/100, 19,200 100/100, 19,212 100/100, 19,219
clusters 12 24 320 exact 100/100, 153,600 100/100, 153,600 55/100, 885,845 100/100, 153,601 100/100, 153,613 100/100, 153,620
clusters 16 32 40 exact 100/100, 25,600 97/100, 33,620 4/100, 2,887,961 100/100, 25,602 100/100, 25,618 100/100, 25,625
clusters 16 32 320 exact 100/100, 204,800 100/100, 204,800 4/100, 23,103,693 100/100, 204,801 100/100, 204,818 100/100, 204,829
clusters 24 48 40 best known 100/100, 38,400 94/100, 62,855 20/100, 792,487 100/100, 38,401 100/100, 38,423 99/100, 38,434
clusters 24 48 320 best known 100/100, 307,200 100/100, 307,200 20/100, 6,339,902 100/100, 307,202 100/100, 307,224 100/100, 307,237
clusters 32 64 40 best known 97/100, 67,241 73/100, 180,079 19/100, 1,118,942 99/100, 51,201 100/100, 51,232 82/100, 137,622
clusters 32 64 320 best known 100/100, 409,600 96/100, 586,005 19/100, 8,951,539 100/100, 409,601 100/100, 409,633 100/100, 409,650
clusters 48 96 40 best known 96/100, 109,875 46/100, 573,977 0/100, - 98/100, 90,409 90/100, 153,679 62/100, 365,865
clusters 48 96 320 best known 99/100, 614,400 100/100, 614,400 0/100, - 99/100, 614,401 100/100, 614,448 98/100, 723,347
clusters 64 128 40 best known 94/100, 167,614 35/100, 1,094,679 0/100, - 97/100, 134,484 60/100, 514,966 22/100, 1,899,749
clusters 64 128 320 best known 100/100, 819,200 93/100, 1,418,648 0/100, - 99/100, 819,201 94/100, 1,341,027 40/100, 7,386,135
clusters 96 192 40 best known 56/100, 861,596 4/100, 17,327,770 0/100, - 86/100, 359,777 18/100, 3,566,727 3/100, 23,245,467
clusters 96 192 320 best known 98/100, 1,446,523 80/100, 3,516,030 0/100, - 99/100, 1,228,802 68/100, 4,966,754 8/100, 67,874,513
clusters 128 256 40 best known 46/100, 1,530,607 0/100, - 0/100, - 79/100, 604,330 7/100, 13,005,283 0/100, -
clusters 128 256 320 best known 91/100, 3,133,422 67/100, 6,805,596 0/100, - 94/100, 2,681,840 26/100, 25,060,253 0/100, -
sparse-glass 8 24 40 exact 100/100, 17,920 100/100, 17,920 21/100, 350,092 100/100, 17,922 100/100, 17,929 100/100, 17,937
sparse-glass 8 24 320 exact 100/100, 143,360 100/100, 143,360 21/100, 2,800,740 100/100, 143,362 100/100, 143,371 100/100, 143,379
sparse-glass 12 36 40 exact 100/100, 26,880 100/100, 26,880 27/100, 393,335 100/100, 26,882 100/100, 26,894 100/100, 26,905
sparse-glass 12 36 320 exact 100/100, 215,040 100/100, 215,040 27/100, 3,146,685 100/100, 215,042 100/100, 215,053 100/100, 215,066
sparse-glass 16 48 40 exact 100/100, 35,840 90/100, 71,680 27/100, 524,447 100/100, 35,842 100/100, 35,859 100/100, 35,872
sparse-glass 16 48 320 exact 100/100, 286,720 100/100, 286,720 27/100, 4,195,580 100/100, 286,722 100/100, 286,737 100/100, 286,756
sparse-glass 24 72 40 best known 100/100, 53,760 68/100, 217,277 0/100, - 100/100, 53,762 97/100, 70,640 90/100, 107,634
sparse-glass 24 72 320 best known 100/100, 430,080 100/100, 430,080 0/100, - 100/100, 430,082 100/100, 430,107 100/100, 430,128
sparse-glass 32 96 40 best known 100/100, 71,680 74/100, 245,048 3/100, 10,837,399 99/100, 71,682 98/100, 84,423 96/100, 102,657
sparse-glass 32 96 320 best known 100/100, 573,440 100/100, 573,440 3/100, 86,699,195 100/100, 573,442 100/100, 573,473 100/100, 573,513
sparse-glass 48 144 40 best known 77/100, 336,909 28/100, 1,507,280 2/100, 24,508,987 82/100, 288,757 58/100, 571,075 38/100, 1,036,727
sparse-glass 48 144 320 best known 85/100, 2,087,998 83/100, 2,235,485 2/100, 196,071,898 87/100, 1,941,551 79/100, 2,538,320 91/100, 1,645,239
sparse-glass 64 192 40 best known 68/100, 579,407 2/100, 32,678,649 0/100, - 90/100, 286,725 28/100, 2,010,616 12/100, 5,169,468
sparse-glass 64 192 320 best known 94/100, 1,877,286 87/100, 2,588,728 0/100, - 100/100, 1,146,882 65/100, 5,031,245 42/100, 9,696,787
sparse-glass 96 288 40 best known 37/100, 2,143,332 0/100, - 0/100, - 76/100, 693,922 4/100, 24,270,642 1/100, 98,616,355
sparse-glass 96 288 320 best known 87/100, 3,883,092 69/100, 6,764,413 0/100, - 93/100, 2,979,166 9/100, 84,007,918 7/100, 109,179,042
sparse-glass 128 384 40 best known 36/100, 2,958,621 0/100, - 0/100, - 71/100, 1,066,673 5/100, 25,753,943 0/100, -
sparse-glass 128 384 320 best known 70/100, 8,773,582 45/100, 17,668,955 0/100, - 84/100, 5,764,091 14/100, 70,040,338 0/100, -
dense-glass 8 28 40 exact 100/100, 20,480 100/100, 20,480 88/100, 44,482 100/100, 20,482 100/100, 20,484 100/100, 20,506
dense-glass 8 28 320 exact 100/100, 163,840 100/100, 163,840 88/100, 355,857 100/100, 163,842 100/100, 163,848 100/100, 163,862
dense-glass 12 66 40 exact 100/100, 46,080 100/100, 46,080 78/100, 140,150 100/100, 46,083 100/100, 46,086 100/100, 46,126
dense-glass 12 66 320 exact 100/100, 368,640 100/100, 368,640 78/100, 1,121,206 100/100, 368,643 100/100, 368,660 100/100, 368,687
dense-glass 16 120 40 exact 100/100, 81,920 100/100, 81,920 39/100, 763,217 100/100, 81,927 100/100, 81,947 100/100, 82,007
dense-glass 16 120 320 exact 100/100, 655,360 100/100, 655,360 39/100, 6,105,739 100/100, 655,367 100/100, 655,385 100/100, 655,447
dense-glass 24 276 40 best known 100/100, 184,320 95/100, 283,344 25/100, 2,950,566 100/100, 184,332 100/100, 184,359 100/100, 184,502
dense-glass 24 276 320 best known 100/100, 1,474,560 100/100, 1,474,560 25/100, 23,604,528 100/100, 1,474,569 100/100, 1,474,593 100/100, 1,474,770
dense-glass 32 496 40 best known 94/100, 536,367 53/100, 1,998,645 4/100, 36,965,909 99/100, 327,697 95/100, 503,811 100/100, 328,039
dense-glass 32 496 320 best known 98/100, 3,085,916 94/100, 4,290,940 4/100, 295,727,278 100/100, 2,621,451 100/100, 2,621,481 100/100, 2,621,820
dense-glass 48 1,128 40 best known 94/100, 1,206,826 22/100, 13,665,303 3/100, 111,470,394 100/100, 737,340 92/100, 1,344,361 100/100, 738,037
dense-glass 48 1,128 320 best known 100/100, 5,898,240 96/100, 8,438,473 3/100, 891,763,156 100/100, 5,898,264 100/100, 5,898,330 100/100, 5,899,028
dense-glass 64 2,016 40 best known 81/100, 3,634,597 4/100, 147,863,639 0/100, - 97/100, 1,721,561 54/100, 7,773,386 91/100, 2,509,220
dense-glass 64 2,016 320 best known 96/100, 15,001,731 90/100, 20,971,520 0/100, - 100/100, 10,485,791 87/100, 23,668,679 100/100, 10,487,106
selection 8 10 40 exact 100/100, 8,960 100/100, 8,960 100/100, 8,960 100/100, 8,960 100/100, 8,967 100/100, 8,969
selection 8 10 320 exact 100/100, 71,680 100/100, 71,680 100/100, 71,680 100/100, 71,680 100/100, 71,686 100/100, 71,687
selection 12 10 40 exact 100/100, 10,240 100/100, 10,240 99/100, 10,240 100/100, 10,240 100/100, 10,250 100/100, 10,251
selection 12 10 320 exact 100/100, 81,920 100/100, 81,920 99/100, 81,920 100/100, 81,920 100/100, 81,930 100/100, 81,932
selection 16 10 40 exact 100/100, 11,520 100/100, 11,520 100/100, 11,520 100/100, 11,520 100/100, 11,536 100/100, 11,535
selection 16 10 320 exact 100/100, 92,160 100/100, 92,160 100/100, 92,160 100/100, 92,160 100/100, 92,175 100/100, 92,175
selection 24 15 40 planted 100/100, 17,280 100/100, 17,280 100/100, 17,280 100/100, 17,280 100/100, 17,309 100/100, 17,305
selection 24 15 320 planted 100/100, 138,240 100/100, 138,240 100/100, 138,240 100/100, 138,240 100/100, 138,265 100/100, 138,264
selection 32 28 40 planted 100/100, 28,160 100/100, 28,160 100/100, 28,160 100/100, 28,161 100/100, 28,185 100/100, 28,195
selection 32 28 320 planted 100/100, 225,280 100/100, 225,280 100/100, 225,280 100/100, 225,280 100/100, 225,311 100/100, 225,314
selection 48 66 40 planted 100/100, 57,600 100/100, 57,600 100/100, 57,600 100/100, 57,601 100/100, 57,625 100/100, 57,671
selection 48 66 320 planted 100/100, 460,800 100/100, 460,800 100/100, 460,800 100/100, 460,800 100/100, 460,845 100/100, 460,871
selection 64 120 40 planted 100/100, 97,280 100/100, 97,280 100/100, 97,280 100/100, 97,283 100/100, 97,344 100/100, 97,388
selection 64 120 320 planted 100/100, 778,240 100/100, 778,240 100/100, 778,240 100/100, 778,240 100/100, 778,294 100/100, 778,362
selection 96 276 40 planted 100/100, 207,360 100/100, 207,360 100/100, 207,360 100/100, 207,404 100/100, 207,475 100/100, 207,611
selection 96 276 320 planted 100/100, 1,658,880 100/100, 1,658,880 100/100, 1,658,880 100/100, 1,658,880 100/100, 1,658,968 100/100, 1,659,129
selection 128 496 40 planted 100/100, 358,400 100/100, 358,400 100/100, 358,400 100/100, 358,400 100/100, 358,502 100/100, 358,865
selection 128 496 320 planted 100/100, 2,867,200 100/100, 2,867,200 100/100, 2,867,200 100/100, 2,867,200 100/100, 2,867,325 100/100, 2,867,566

Of 68 rows, the emulator's sampling mode at the default start reached the target more often than every classical solver in 2, tied the best of them in 45, and was behind the best of them in 21.

Of 68 rows, the emulator's sampling mode at the hot start, the largest row of couplings reached the target more often than every classical solver in 0, tied the best of them in 38, and was behind the best of them in 30.

The default start is the square root of the mean couplings a variable has, and at least 1. On instances the rows do not use, 40 runs at each start, mean energy (and the runs that reached the lowest energy found):

  • clusters, 32 variables, target -16: 0.5: -16.00 (40); 1: -16.00 (40); 1.5: -16.00 (40); 2 default: -16.00 (40); 3: -16.00 (40); 4: -16.00 (40); 6: -15.93 (37); 8: -15.72 (29); 9 hot: -15.65 (28)
  • clusters, 64 variables, target -26: 0.5: -25.80 (33); 1: -26.00 (40); 1.5: -25.88 (35); 2 default: -25.68 (28); 3: -25.40 (22); 4: -25.15 (12); 6: -24.48 (6); 8 hot: -23.35 (1)
  • sparse-glass, 32 variables, target -19: 0.5: -19.00 (40); 1: -18.95 (38); 1.5: -18.90 (36); 2: -18.93 (37); 2.449 default: -18.82 (33); 3: -18.93 (37); 4: -18.90 (36); 6: -18.62 (26); 8: -18.55 (25); 13 hot: -18.18 (15)
  • sparse-glass, 64 variables, target -51: 0.5: -50.98 (39); 1: -51.00 (40); 1.5: -51.00 (40); 2: -50.98 (39); 2.449 default: -51.00 (40); 3: -51.00 (40); 4: -50.85 (34); 6: -50.50 (26); 8: -50.10 (15); 12 hot: -49.10 (4)
  • dense-glass, 32 variables, target -128: 0.5: -127.90 (38); 1: -127.95 (39); 1.5: -127.90 (38); 2: -127.95 (39); 3: -128.00 (40); 4: -128.00 (40); 5.568 default: -127.95 (39); 6: -127.95 (39); 8: -128.00 (40); 31 hot: -127.08 (23)
  • dense-glass, 64 variables, target -362: 0.5: -360.55 (29); 1: -362.00 (40); 1.5: -362.00 (40); 2: -362.00 (40); 3: -362.00 (40); 4: -361.95 (39); 6: -362.00 (40); 7.937 default: -361.90 (38); 8: -362.00 (40); 63 hot: -352.85 (0)