BQM QPU solvers do not yield optimal solutions

Mohammad D (Report)

November 08, 2022 23:16

Hi Mark,

One of our experts noticed the chain strength is way too high. They were able to get better results with a smaller chain strength value i.e. using coefficient of 0.17 instead of 1.2.

With a lower coefficient the top few samples still have 0 broken chains but the energy value is much lower. The values are still higher than SA but not as outrageous, and they can definitely be tuned further. The solutions can also be refined by tuning other parameters such as the anneal schedules, anneal time, etc...

1

Tanjid I (Report)

October 25, 2022 00:26

Hi Mark,

Thank you for reaching out and using D-Wave Systems.

Can you please provide a bit more details about the problem that you are working on, or provide any code snippet so that we have a better understanding of the scope of the issue you are experiencing?

Best Regards,
Tanjid

0

Mark O (Report)

October 26, 2022 06:38

Hi Tanjid,

Thanks for the reply. The actual problem comes from portfolio optimization and is quite complicated, so I'll spare you the details. Instead, I'm attaching the final bqm here with the script:

from dimod import BinaryQuadraticModel
bqm = BinaryQuadraticModel(
    {
        0: -0.20357375733333333,
        1: -0.40342836266666665,
        2: -0.7919801173333333,
        3: -0.21229905799999998,
        4: -0.42159623199999996,
        5: -0.831184928,
        6: -0.198094002,
        7: -0.392176008,
        8: -0.768304032,
        9: 0.15833333333333333,
        10: 0.06041666666666666,
        11: 0.025520833333333333,
        12: 0.011588541666666665,
        13: 0.4666666666666667,
        14: 1.5333333333333332,
        15: 0.15833333333333333,
        16: 0.06041666666666666,
        17: 0.025520833333333333,
        18: 0.011588541666666665,
        19: 0.4666666666666667,
        20: 1.5333333333333332,
        21: 0.15833333333333333,
        22: 0.06041666666666666,
        23: 0.025520833333333333,
        24: 0.011588541666666665,
        25: 0.4666666666666667,
        26: 1.5333333333333332,
        27: 0.075,
        28: 0.01875,
        29: 0.0046875,
        30: 0.001171875,
        31: 0.3,
        32: 1.2,
        33: 0.075,
        34: 0.01875,
        35: 0.0046875,
        36: 0.001171875,
        37: 0.3,
        38: 1.2,
        39: 0.075,
        40: 0.01875,
        41: 0.0046875,
        42: 0.001171875,
        43: 0.3,
        44: 1.2,
        45: -1.7249999999999999,
        46: -0.8812499999999999,
        47: -0.44531249999999994,
        48: -0.223828125,
        49: -3.3,
        50: -5.999999999999999,
        51: -9.599999999999998,
        52: 0.375,
        53: 0.16874999999999998,
        54: 0.0796875,
        55: 0.038671875,
        56: 0.8999999999999999,
        57: 2.4,
    },
    {
        (1, 0): 0.0074383040000000015,
        (2, 0): 0.014876608000000003,
        (2, 1): 0.029753216000000006,
        (3, 0): 0.0029667960000000003,
        (3, 1): 0.0059335920000000006,
        (3, 2): 0.011867184000000001,
        (4, 0): 0.0059335920000000006,
        (4, 1): 0.011867184000000001,
        (4, 2): 0.023734368000000002,
        (4, 3): 0.006003768000000001,
        (5, 0): 0.011867184000000001,
        (5, 1): 0.023734368000000002,
        (5, 2): 0.047468736000000004,
        (5, 3): 0.012007536000000003,
        (5, 4): 0.024015072000000005,
        (6, 0): 0.0038409480000000003,
        (6, 1): 0.0076818960000000006,
        (6, 2): 0.015363792000000001,
        (6, 3): 0.0029643420000000005,
        (6, 4): 0.005928684000000001,
        (6, 5): 0.011857368000000002,
        (7, 0): 0.0076818960000000006,
        (7, 1): 0.015363792000000001,
        (7, 2): 0.030727584000000002,
        (7, 3): 0.005928684000000001,
        (7, 4): 0.011857368000000002,
        (7, 5): 0.023714736000000004,
        (7, 6): 0.008023992,
        (8, 0): 0.015363792000000001,
        (8, 1): 0.030727584000000002,
        (8, 2): 0.061455168000000004,
        (8, 3): 0.011857368000000002,
        (8, 4): 0.023714736000000004,
        (8, 5): 0.04742947200000001,
        (8, 6): 0.016047984,
        (8, 7): 0.032095968,
        (9, 0): 0.00848,
        (9, 1): 0.01696,
        (9, 2): 0.03392,
        (9, 3): -0.00039,
        (9, 4): -0.00078,
        (9, 5): -0.00156,
        (9, 6): 0.00993,
        (9, 7): 0.01986,
        (9, 8): 0.03972,
        (10, 0): 0.00424,
        (10, 1): 0.00848,
        (10, 2): 0.01696,
        (10, 3): -0.000195,
        (10, 4): -0.00039,
        (10, 5): -0.00078,
        (10, 6): 0.004965,
        (10, 7): 0.00993,
        (10, 8): 0.01986,
        (10, 9): 0.075,
        (11, 0): 0.00212,
        (11, 1): 0.00424,
        (11, 2): 0.00848,
        (11, 3): -9.75e-05,
        (11, 4): -0.000195,
        (11, 5): -0.00039,
        (11, 6): 0.0024825,
        (11, 7): 0.004965,
        (11, 8): 0.00993,
        (11, 9): 0.0375,
        (11, 10): 0.01875,
        (12, 0): 0.00106,
        (12, 1): 0.00212,
        (12, 2): 0.00424,
        (12, 3): -4.875e-05,
        (12, 4): -9.75e-05,
        (12, 5): -0.000195,
        (12, 6): 0.00124125,
        (12, 7): 0.0024825,
        (12, 8): 0.004965,
        (12, 9): 0.01875,
        (12, 10): 0.009375,
        (12, 11): 0.0046875,
        (13, 0): 0.01696,
        (13, 1): 0.03392,
        (13, 2): 0.06784,
        (13, 3): -0.00078,
        (13, 4): -0.00156,
        (13, 5): -0.00312,
        (13, 6): 0.01986,
        (13, 7): 0.03972,
        (13, 8): 0.07944,
        (13, 9): 0.3,
        (13, 10): 0.15,
        (13, 11): 0.075,
        (13, 12): 0.0375,
        (14, 0): 0.03392,
        (14, 1): 0.06784,
        (14, 2): 0.13568,
        (14, 3): -0.00156,
        (14, 4): -0.00312,
        (14, 5): -0.00624,
        (14, 6): 0.03972,
        (14, 7): 0.07944,
        (14, 8): 0.15888,
        (14, 9): 0.6,
        (14, 10): 0.3,
        (14, 11): 0.15,
        (14, 12): 0.075,
        (14, 13): 1.2,
        (15, 0): -0.0043,
        (15, 1): -0.0086,
        (15, 2): -0.0172,
        (15, 3): 0.00036,
        (15, 4): 0.00072,
        (15, 5): 0.00144,
        (15, 6): -0.0035700000000000003,
        (15, 7): -0.0071400000000000005,
        (15, 8): -0.014280000000000001,
        (16, 0): -0.00215,
        (16, 1): -0.0043,
        (16, 2): -0.0086,
        (16, 3): 0.00018,
        (16, 4): 0.00036,
        (16, 5): 0.00072,
        (16, 6): -0.0017850000000000001,
        (16, 7): -0.0035700000000000003,
        (16, 8): -0.0071400000000000005,
        (16, 15): 0.075,
        (17, 0): -0.001075,
        (17, 1): -0.00215,
        (17, 2): -0.0043,
        (17, 3): 9e-05,
        (17, 4): 0.00018,
        (17, 5): 0.00036,
        (17, 6): -0.0008925000000000001,
        (17, 7): -0.0017850000000000001,
        (17, 8): -0.0035700000000000003,
        (17, 15): 0.0375,
        (17, 16): 0.01875,
        (18, 0): -0.0005375,
        (18, 1): -0.001075,
        (18, 2): -0.00215,
        (18, 3): 4.5e-05,
        (18, 4): 9e-05,
        (18, 5): 0.00018,
        (18, 6): -0.00044625000000000003,
        (18, 7): -0.0008925000000000001,
        (18, 8): -0.0017850000000000001,
        (18, 15): 0.01875,
        (18, 16): 0.009375,
        (18, 17): 0.0046875,
        (19, 0): -0.0086,
        (19, 1): -0.0172,
        (19, 2): -0.0344,
        (19, 3): 0.00072,
        (19, 4): 0.00144,
        (19, 5): 0.00288,
        (19, 6): -0.0071400000000000005,
        (19, 7): -0.014280000000000001,
        (19, 8): -0.028560000000000002,
        (19, 15): 0.3,
        (19, 16): 0.15,
        (19, 17): 0.075,
        (19, 18): 0.0375,
        (20, 0): -0.0172,
        (20, 1): -0.0344,
        (20, 2): -0.0688,
        (20, 3): 0.00144,
        (20, 4): 0.00288,
        (20, 5): 0.00576,
        (20, 6): -0.014280000000000001,
        (20, 7): -0.028560000000000002,
        (20, 8): -0.057120000000000004,
        (20, 15): 0.6,
        (20, 16): 0.3,
        (20, 17): 0.15,
        (20, 18): 0.075,
        (20, 19): 1.2,
        (21, 0): -0.00418,
        (21, 1): -0.00836,
        (21, 2): -0.01672,
        (21, 3): 2.9999999999999947e-05,
        (21, 4): 5.999999999999989e-05,
        (21, 5): 0.00011999999999999979,
        (21, 6): -0.00636,
        (21, 7): -0.01272,
        (21, 8): -0.02544,
        (22, 0): -0.00209,
        (22, 1): -0.00418,
        (22, 2): -0.00836,
        (22, 3): 1.4999999999999973e-05,
        (22, 4): 2.9999999999999947e-05,
        (22, 5): 5.999999999999989e-05,
        (22, 6): -0.00318,
        (22, 7): -0.00636,
        (22, 8): -0.01272,
        (22, 21): 0.075,
        (23, 0): -0.001045,
        (23, 1): -0.00209,
        (23, 2): -0.00418,
        (23, 3): 7.499999999999987e-06,
        (23, 4): 1.4999999999999973e-05,
        (23, 5): 2.9999999999999947e-05,
        (23, 6): -0.00159,
        (23, 7): -0.00318,
        (23, 8): -0.00636,
        (23, 21): 0.0375,
        (23, 22): 0.01875,
        (24, 0): -0.0005225,
        (24, 1): -0.001045,
        (24, 2): -0.00209,
        (24, 3): 3.7499999999999933e-06,
        (24, 4): 7.499999999999987e-06,
        (24, 5): 1.4999999999999973e-05,
        (24, 6): -0.000795,
        (24, 7): -0.00159,
        (24, 8): -0.00318,
        (24, 21): 0.01875,
        (24, 22): 0.009375,
        (24, 23): 0.0046875,
        (25, 0): -0.00836,
        (25, 1): -0.01672,
        (25, 2): -0.03344,
        (25, 3): 5.999999999999989e-05,
        (25, 4): 0.00011999999999999979,
        (25, 5): 0.00023999999999999957,
        (25, 6): -0.01272,
        (25, 7): -0.02544,
        (25, 8): -0.05088,
        (25, 21): 0.3,
        (25, 22): 0.15,
        (25, 23): 0.075,
        (25, 24): 0.0375,
        (26, 0): -0.01672,
        (26, 1): -0.03344,
        (26, 2): -0.06688,
        (26, 3): 0.00011999999999999979,
        (26, 4): 0.00023999999999999957,
        (26, 5): 0.00047999999999999914,
        (26, 6): -0.02544,
        (26, 7): -0.05088,
        (26, 8): -0.10176,
        (26, 21): 0.6,
        (26, 22): 0.3,
        (26, 23): 0.15,
        (26, 24): 0.075,
        (26, 25): 1.2,
        (27, 0): -0.00848,
        (27, 1): -0.01696,
        (27, 2): -0.03392,
        (27, 3): 0.00039,
        (27, 4): 0.00078,
        (27, 5): 0.00156,
        (27, 6): -0.00993,
        (27, 7): -0.01986,
        (27, 8): -0.03972,
        (27, 9): -0.15,
        (27, 10): -0.075,
        (27, 11): -0.0375,
        (27, 12): -0.01875,
        (27, 13): -0.3,
        (27, 14): -0.6,
        (28, 0): -0.00424,
        (28, 1): -0.00848,
        (28, 2): -0.01696,
        (28, 3): 0.000195,
        (28, 4): 0.00039,
        (28, 5): 0.00078,
        (28, 6): -0.004965,
        (28, 7): -0.00993,
        (28, 8): -0.01986,
        (28, 9): -0.075,
        (28, 10): -0.0375,
        (28, 11): -0.01875,
        (28, 12): -0.009375,
        (28, 13): -0.15,
        (28, 14): -0.3,
        (28, 27): 0.075,
        (29, 0): -0.00212,
        (29, 1): -0.00424,
        (29, 2): -0.00848,
        (29, 3): 9.75e-05,
        (29, 4): 0.000195,
        (29, 5): 0.00039,
        (29, 6): -0.0024825,
        (29, 7): -0.004965,
        (29, 8): -0.00993,
        (29, 9): -0.0375,
        (29, 10): -0.01875,
        (29, 11): -0.009375,
        (29, 12): -0.0046875,
        (29, 13): -0.075,
        (29, 14): -0.15,
        (29, 27): 0.0375,
        (29, 28): 0.01875,
        (30, 0): -0.00106,
        (30, 1): -0.00212,
        (30, 2): -0.00424,
        (30, 3): 4.875e-05,
        (30, 4): 9.75e-05,
        (30, 5): 0.000195,
        (30, 6): -0.00124125,
        (30, 7): -0.0024825,
        (30, 8): -0.004965,
        (30, 9): -0.01875,
        (30, 10): -0.009375,
        (30, 11): -0.0046875,
        (30, 12): -0.00234375,
        (30, 13): -0.0375,
        (30, 14): -0.075,
        (30, 27): 0.01875,
        (30, 28): 0.009375,
        (30, 29): 0.0046875,
        (31, 0): -0.01696,
        (31, 1): -0.03392,
        (31, 2): -0.06784,
        (31, 3): 0.00078,
        (31, 4): 0.00156,
        (31, 5): 0.00312,
        (31, 6): -0.01986,
        (31, 7): -0.03972,
        (31, 8): -0.07944,
        (31, 9): -0.3,
        (31, 10): -0.15,
        (31, 11): -0.075,
        (31, 12): -0.0375,
        (31, 13): -0.6,
        (31, 14): -1.2,
        (31, 27): 0.3,
        (31, 28): 0.15,
        (31, 29): 0.075,
        (31, 30): 0.0375,
        (32, 0): -0.03392,
        (32, 1): -0.06784,
        (32, 2): -0.13568,
        (32, 3): 0.00156,
        (32, 4): 0.00312,
        (32, 5): 0.00624,
        (32, 6): -0.03972,
        (32, 7): -0.07944,
        (32, 8): -0.15888,
        (32, 9): -0.6,
        (32, 10): -0.3,
        (32, 11): -0.15,
        (32, 12): -0.075,
        (32, 13): -1.2,
        (32, 14): -2.4,
        (32, 27): 0.6,
        (32, 28): 0.3,
        (32, 29): 0.15,
        (32, 30): 0.075,
        (32, 31): 1.2,
        (33, 0): 0.0043,
        (33, 1): 0.0086,
        (33, 2): 0.0172,
        (33, 3): -0.00036,
        (33, 4): -0.00072,
        (33, 5): -0.00144,
        (33, 6): 0.0035700000000000003,
        (33, 7): 0.0071400000000000005,
        (33, 8): 0.014280000000000001,
        (33, 15): -0.15,
        (33, 16): -0.075,
        (33, 17): -0.0375,
        (33, 18): -0.01875,
        (33, 19): -0.3,
        (33, 20): -0.6,
        (34, 0): 0.00215,
        (34, 1): 0.0043,
        (34, 2): 0.0086,
        (34, 3): -0.00018,
        (34, 4): -0.00036,
        (34, 5): -0.00072,
        (34, 6): 0.0017850000000000001,
        (34, 7): 0.0035700000000000003,
        (34, 8): 0.0071400000000000005,
        (34, 15): -0.075,
        (34, 16): -0.0375,
        (34, 17): -0.01875,
        (34, 18): -0.009375,
        (34, 19): -0.15,
        (34, 20): -0.3,
        (34, 33): 0.075,
        (35, 0): 0.001075,
        (35, 1): 0.00215,
        (35, 2): 0.0043,
        (35, 3): -9e-05,
        (35, 4): -0.00018,
        (35, 5): -0.00036,
        (35, 6): 0.0008925000000000001,
        (35, 7): 0.0017850000000000001,
        (35, 8): 0.0035700000000000003,
        (35, 15): -0.0375,
        (35, 16): -0.01875,
        (35, 17): -0.009375,
        (35, 18): -0.0046875,
        (35, 19): -0.075,
        (35, 20): -0.15,
        (35, 33): 0.0375,
        (35, 34): 0.01875,
        (36, 0): 0.0005375,
        (36, 1): 0.001075,
        (36, 2): 0.00215,
        (36, 3): -4.5e-05,
        (36, 4): -9e-05,
        (36, 5): -0.00018,
        (36, 6): 0.00044625000000000003,
        (36, 7): 0.0008925000000000001,
        (36, 8): 0.0017850000000000001,
        (36, 15): -0.01875,
        (36, 16): -0.009375,
        (36, 17): -0.0046875,
        (36, 18): -0.00234375,
        (36, 19): -0.0375,
        (36, 20): -0.075,
        (36, 33): 0.01875,
        (36, 34): 0.009375,
        (36, 35): 0.0046875,
        (37, 0): 0.0086,
        (37, 1): 0.0172,
        (37, 2): 0.0344,
        (37, 3): -0.00072,
        (37, 4): -0.00144,
        (37, 5): -0.00288,
        (37, 6): 0.0071400000000000005,
        (37, 7): 0.014280000000000001,
        (37, 8): 0.028560000000000002,
        (37, 15): -0.3,
        (37, 16): -0.15,
        (37, 17): -0.075,
        (37, 18): -0.0375,
        (37, 19): -0.6,
        (37, 20): -1.2,
        (37, 33): 0.3,
        (37, 34): 0.15,
        (37, 35): 0.075,
        (37, 36): 0.0375,
        (38, 0): 0.0172,
        (38, 1): 0.0344,
        (38, 2): 0.0688,
        (38, 3): -0.00144,
        (38, 4): -0.00288,
        (38, 5): -0.00576,
        (38, 6): 0.014280000000000001,
        (38, 7): 0.028560000000000002,
        (38, 8): 0.057120000000000004,
        (38, 15): -0.6,
        (38, 16): -0.3,
        (38, 17): -0.15,
        (38, 18): -0.075,
        (38, 19): -1.2,
        (38, 20): -2.4,
        (38, 33): 0.6,
        (38, 34): 0.3,
        (38, 35): 0.15,
        (38, 36): 0.075,
        (38, 37): 1.2,
        (39, 0): 0.00418,
        (39, 1): 0.00836,
        (39, 2): 0.01672,
        (39, 3): -2.9999999999999947e-05,
        (39, 4): -5.999999999999989e-05,
        (39, 5): -0.00011999999999999979,
        (39, 6): 0.00636,
        (39, 7): 0.01272,
        (39, 8): 0.02544,
        (39, 21): -0.15,
        (39, 22): -0.075,
        (39, 23): -0.0375,
        (39, 24): -0.01875,
        (39, 25): -0.3,
        (39, 26): -0.6,
        (40, 0): 0.00209,
        (40, 1): 0.00418,
        (40, 2): 0.00836,
        (40, 3): -1.4999999999999973e-05,
        (40, 4): -2.9999999999999947e-05,
        (40, 5): -5.999999999999989e-05,
        (40, 6): 0.00318,
        (40, 7): 0.00636,
        (40, 8): 0.01272,
        (40, 21): -0.075,
        (40, 22): -0.0375,
        (40, 23): -0.01875,
        (40, 24): -0.009375,
        (40, 25): -0.15,
        (40, 26): -0.3,
        (40, 39): 0.075,
        (41, 0): 0.001045,
        (41, 1): 0.00209,
        (41, 2): 0.00418,
        (41, 3): -7.499999999999987e-06,
        (41, 4): -1.4999999999999973e-05,
        (41, 5): -2.9999999999999947e-05,
        (41, 6): 0.00159,
        (41, 7): 0.00318,
        (41, 8): 0.00636,
        (41, 21): -0.0375,
        (41, 22): -0.01875,
        (41, 23): -0.009375,
        (41, 24): -0.0046875,
        (41, 25): -0.075,
        (41, 26): -0.15,
        (41, 39): 0.0375,
        (41, 40): 0.01875,
        (42, 0): 0.0005225,
        (42, 1): 0.001045,
        (42, 2): 0.00209,
        (42, 3): -3.7499999999999933e-06,
        (42, 4): -7.499999999999987e-06,
        (42, 5): -1.4999999999999973e-05,
        (42, 6): 0.000795,
        (42, 7): 0.00159,
        (42, 8): 0.00318,
        (42, 21): -0.01875,
        (42, 22): -0.009375,
        (42, 23): -0.0046875,
        (42, 24): -0.00234375,
        (42, 25): -0.0375,
        (42, 26): -0.075,
        (42, 39): 0.01875,
        (42, 40): 0.009375,
        (42, 41): 0.0046875,
        (43, 0): 0.00836,
        (43, 1): 0.01672,
        (43, 2): 0.03344,
        (43, 3): -5.999999999999989e-05,
        (43, 4): -0.00011999999999999979,
        (43, 5): -0.00023999999999999957,
        (43, 6): 0.01272,
        (43, 7): 0.02544,
        (43, 8): 0.05088,
        (43, 21): -0.3,
        (43, 22): -0.15,
        (43, 23): -0.075,
        (43, 24): -0.0375,
        (43, 25): -0.6,
        (43, 26): -1.2,
        (43, 39): 0.3,
        (43, 40): 0.15,
        (43, 41): 0.075,
        (43, 42): 0.0375,
        (44, 0): 0.01672,
        (44, 1): 0.03344,
        (44, 2): 0.06688,
        (44, 3): -0.00011999999999999979,
        (44, 4): -0.00023999999999999957,
        (44, 5): -0.00047999999999999914,
        (44, 6): 0.02544,
        (44, 7): 0.05088,
        (44, 8): 0.10176,
        (44, 21): -0.6,
        (44, 22): -0.3,
        (44, 23): -0.15,
        (44, 24): -0.075,
        (44, 25): -1.2,
        (44, 26): -2.4,
        (44, 39): 0.6,
        (44, 40): 0.3,
        (44, 41): 0.15,
        (44, 42): 0.075,
        (44, 43): 1.2,
        (45, 0): 0.015,
        (45, 1): 0.03,
        (45, 2): 0.06,
        (45, 3): 0.015,
        (45, 4): 0.03,
        (45, 5): 0.06,
        (45, 6): 0.015,
        (45, 7): 0.03,
        (45, 8): 0.06,
        (46, 0): 0.0075,
        (46, 1): 0.015,
        (46, 2): 0.03,
        (46, 3): 0.0075,
        (46, 4): 0.015,
        (46, 5): 0.03,
        (46, 6): 0.0075,
        (46, 7): 0.015,
        (46, 8): 0.03,
        (46, 45): 0.075,
        (47, 0): 0.00375,
        (47, 1): 0.0075,
        (47, 2): 0.015,
        (47, 3): 0.00375,
        (47, 4): 0.0075,
        (47, 5): 0.015,
        (47, 6): 0.00375,
        (47, 7): 0.0075,
        (47, 8): 0.015,
        (47, 45): 0.0375,
        (47, 46): 0.01875,
        (48, 0): 0.001875,
        (48, 1): 0.00375,
        (48, 2): 0.0075,
        (48, 3): 0.001875,
        (48, 4): 0.00375,
        (48, 5): 0.0075,
        (48, 6): 0.001875,
        (48, 7): 0.00375,
        (48, 8): 0.0075,
        (48, 45): 0.01875,
        (48, 46): 0.009375,
        (48, 47): 0.0046875,
        (49, 0): 0.03,
        (49, 1): 0.06,
        (49, 2): 0.12,
        (49, 3): 0.03,
        (49, 4): 0.06,
        (49, 5): 0.12,
        (49, 6): 0.03,
        (49, 7): 0.06,
        (49, 8): 0.12,
        (49, 45): 0.3,
        (49, 46): 0.15,
        (49, 47): 0.075,
        (49, 48): 0.0375,
        (50, 0): 0.06,
        (50, 1): 0.12,
        (50, 2): 0.24,
        (50, 3): 0.06,
        (50, 4): 0.12,
        (50, 5): 0.24,
        (50, 6): 0.06,
        (50, 7): 0.12,
        (50, 8): 0.24,
        (50, 45): 0.6,
        (50, 46): 0.3,
        (50, 47): 0.15,
        (50, 48): 0.075,
        (50, 49): 1.2,
        (51, 0): 0.12,
        (51, 1): 0.24,
        (51, 2): 0.48,
        (51, 3): 0.12,
        (51, 4): 0.24,
        (51, 5): 0.48,
        (51, 6): 0.12,
        (51, 7): 0.24,
        (51, 8): 0.48,
        (51, 45): 1.2,
        (51, 46): 0.6,
        (51, 47): 0.3,
        (51, 48): 0.15,
        (51, 49): 2.4,
        (51, 50): 4.8,
        (52, 0): -0.015,
        (52, 1): -0.03,
        (52, 2): -0.06,
        (52, 3): -0.015,
        (52, 4): -0.03,
        (52, 5): -0.06,
        (52, 6): -0.015,
        (52, 7): -0.03,
        (52, 8): -0.06,
        (53, 0): -0.0075,
        (53, 1): -0.015,
        (53, 2): -0.03,
        (53, 3): -0.0075,
        (53, 4): -0.015,
        (53, 5): -0.03,
        (53, 6): -0.0075,
        (53, 7): -0.015,
        (53, 8): -0.03,
        (53, 52): 0.075,
        (54, 0): -0.00375,
        (54, 1): -0.0075,
        (54, 2): -0.015,
        (54, 3): -0.00375,
        (54, 4): -0.0075,
        (54, 5): -0.015,
        (54, 6): -0.00375,
        (54, 7): -0.0075,
        (54, 8): -0.015,
        (54, 52): 0.0375,
        (54, 53): 0.01875,
        (55, 0): -0.001875,
        (55, 1): -0.00375,
        (55, 2): -0.0075,
        (55, 3): -0.001875,
        (55, 4): -0.00375,
        (55, 5): -0.0075,
        (55, 6): -0.001875,
        (55, 7): -0.00375,
        (55, 8): -0.0075,
        (55, 52): 0.01875,
        (55, 53): 0.009375,
        (55, 54): 0.0046875,
        (56, 0): -0.03,
        (56, 1): -0.06,
        (56, 2): -0.12,
        (56, 3): -0.03,
        (56, 4): -0.06,
        (56, 5): -0.12,
        (56, 6): -0.03,
        (56, 7): -0.06,
        (56, 8): -0.12,
        (56, 52): 0.3,
        (56, 53): 0.15,
        (56, 54): 0.075,
        (56, 55): 0.0375,
        (57, 0): -0.06,
        (57, 1): -0.12,
        (57, 2): -0.24,
        (57, 3): -0.06,
        (57, 4): -0.12,
        (57, 5): -0.24,
        (57, 6): -0.06,
        (57, 7): -0.12,
        (57, 8): -0.24,
        (57, 52): 0.6,
        (57, 53): 0.3,
        (57, 54): 0.15,
        (57, 55): 0.075,
        (57, 56): 1.2,
    },
    11.1,
    "BINARY",
)

from neal import SimulatedAnnealingSampler
from dwave.system import DWaveSampler
from dwave.system import EmbeddingComposite

sampleset_sa = SimulatedAnnealingSampler().sample(bqm, num_reads=1000)
optimal_energy = sampleset_sa.first.energy
print(f"Optimal energy from simulated annealing: {optimal_energy}")
max_chain_strength = max(
    (
        max(bqm.linear.values()),
        max(bqm.quadratic.values())
    )
)
sampler = DWaveSampler(solver={"topology__type": "pegasus"})
composite = EmbeddingComposite(sampler)
sampleset = composite.sample(
    bqm, num_reads=1000, chain_strength=max_chain_strength * 1.2
)
print(f"DWave min energy: {sampleset.first.energy}")

0

Mohammad D (Report)

November 03, 2022 23:42

Hi Mark,

Thank you for sharing your script. In order to give advice on how to optimize for a better solution, we need more information than the final BQM (with the biases).

It would be helpful to also have the problem formulation, the data being used for the input model, as well as the constraints being used.

0

Mark O (Report)

November 08, 2022 14:49

Hi Mohammad,

Unfortunately, our model is very complicated and we can't disclose the details it before publication.

When using pegasus or zephyr the chain length is consistently below 4, and we can't identify any other source of error. From the dwave documentation is appears that writing your problem as a QUBO and keeping chains short are the main requirements for successful use of the quantum annealing. Moreover, we're not using more than 20% of the whole chip, so the problem size shouldn't be a problem either.

It appears that quantum annealing is not as generically applicable for optimization as it is advertised. If we're missing something, could you please suggest steps on how we could please debug the annealing process.

Thank you

0

Mark O (Report)

November 09, 2022 15:39

Hi Mohammad,

Thanks again for looking into the issue. You're right, choosing a smaller chain strength significantly improves the results! However, the dwave docs suggest using at least a chain strength equal to the maximum bias from the original problem, which in our case produces a way to strong chain strength. I presume the embedding makes our problem somewhat hard to solve using annealing ...

Thanks again, I think now we know how to proceed.

0

Richard W (Report)

January 02, 2023 19:34

Hello Mark,

What is the current status of your effort to obtain optimal solutions on the Pegasus array of qubits?

Thanks

0

Mark O (Report)

January 04, 2023 13:36

Hi Richard,

no, we still can't get optimal solutions reliably. We think that the issue has to do with the embedding, which requires a strong coupling strength. To be able to reliably get optimal solutions we have to find a better embedding heuristic, which is probably what we'll work on next.

Thanks for your help.

Mark

0

BQM QPU solvers do not yield optimal solutions

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