Competition
Calculating excitation gaps of small molecules (ES-Gap)
Record Detail

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Overview

Author
QunaSys
Date
20191005
Case
1 (Expectation value)
Method
Algorithm
VQD
Ansatz
HardwareEfficient, depth=8
Optimizer
BFGS
Mapping
jordan-wigner
Comment
SSVQE with weights $w_0=4, w_1=1$ is used. Initial states are taken as the CIS (configuration interaction singles) states.
Score
1.55351

Data

Summary

Molecule Mean score Mean # of func. eval.
H2line 0.000021 2997.000000
H4line 1.343693 6898.500000
H4ring 4.952590 14882.875000
H6line 3.007636 53709.750000
H6ring 0.715583 31896.125000
LiH 0.717952 8978.875000
BeH2 0.701943 30035.500000
H2O 0.988701 12350.750000
all 1.553515 20218.671875

H2

Score for molecule: 0.000021

Bond length [A] Exact GS energy [Ha] Predicted GS energy [Ha] Exact ES energy [Ha] Predicted ES energy [Ha] Score for each bond length # of function evaluation
0.5 -1.055160 -1.055155 0.267000 0.266987 1.3626e-05 11100
0.6 -1.116286 -1.116278 0.036501 0.036485 2.071e-05 2812
0.7 -1.136189 -1.136180 -0.120452 -0.120466 2.3172e-05 2516
0.8 -1.134148 -1.134134 -0.227924 -0.227945 3.8029e-05 2738
0.9 -1.120560 -1.120554 -0.301706 -0.301719 2.4118e-05 3404
1.0 -1.101150 -1.101142 -0.352291 -0.352302 2.6384e-05 2220
1.1 -1.079193 -1.079182 -0.386515 -0.386526 3.2055e-05 1850
1.2 -1.056741 -1.056732 -0.408860 -0.408870 2.852e-05 2146
1.3 -1.035186 -1.035178 -0.422402 -0.422411 2.8679e-05 1998
1.4 -1.015468 -1.015462 -0.429384 -0.429392 2.4595e-05 2146
1.5 -0.998149 -0.998146 -0.431513 -0.431518 1.5746e-05 2738
1.6 -0.983473 -0.983470 -0.430109 -0.430114 1.2677e-05 2368
1.7 -0.971427 -0.971425 -0.426192 -0.426196 1.0458e-05 2146
1.8 -0.961817 -0.961815 -0.420541 -0.420543 7.8774e-06 3108
1.9 -0.954339 -0.954335 -0.413749 -0.413752 1.1532e-05 2072
2.0 -0.948641 -0.948635 -0.406260 -0.406268 2.4749e-05 2590

H4 (line)

Score for molecule: 1.343693

Bond length [A] Exact GS energy [Ha] Predicted GS energy [Ha] Exact ES energy [Ha] Predicted ES energy [Ha] Score for each bond length # of function evaluation
0.5 -1.653117 -1.640023 -0.622827 -0.604342 0.0052319 52852
0.6 -1.960194 -1.943180 -1.096479 -1.076097 0.0038995 2774
0.7 -2.106997 -2.085129 -1.365653 -1.343413 0.00050181 3358
0.8 -2.167561 -2.139759 -1.514584 -1.490641 0.0059106 3066
0.9 -2.180317 -2.145320 -1.590935 -1.565316 0.015912 3066
1.0 -2.166387 -2.122544 -1.649658 -1.595642 0.019687 3066
1.1 -2.137971 -2.083324 -1.712390 -1.598487 0.13924 2774
1.2 -2.102608 -2.034870 -1.755108 -1.584122 0.29712 2920
1.3 -2.065229 -1.981814 -1.784935 -1.559062 0.50824 2920
1.4 -2.029070 -1.927341 -1.806226 -1.527685 0.79343 3066
1.5 -1.996150 -1.873578 -1.821715 -1.493072 1.1814 3504
1.6 -1.967560 -1.821811 -1.833158 -1.457497 1.7106 3066
1.7 -1.943692 -1.773003 -1.841705 -1.422690 2.4349 3212
1.8 -1.924431 -1.727570 -1.848128 -1.389993 3.4242 4964
1.9 -1.909332 -1.685788 -1.852960 -1.366006 4.6727 12994
2.0 -1.897781 -1.647655 -1.856584 -1.347490 6.2862 2774

H4 (ring)

Score for molecule: 4.952590

Bond length [A] Exact GS energy [Ha] Predicted GS energy [Ha] Exact ES energy [Ha] Predicted ES energy [Ha] Score for each bond length # of function evaluation
0.5 -0.610130 -0.578318 -0.516291 0.724508 12.884 56794
0.6 -1.191866 -1.152343 -1.074424 -0.017021 8.6671 15038
0.7 -1.528728 -1.480847 -1.394620 -0.480527 6.459 3650
0.8 -1.728281 -1.671608 -1.586733 -0.782770 5.2794 38982
0.9 -1.846741 -1.780763 -1.699536 -0.983716 4.4146 3212
1.0 -1.915107 -1.839069 -1.764318 -1.118377 3.7795 12410
1.1 -1.951594 -1.864502 -1.799889 -1.208415 3.3247 3212
1.2 -1.967550 -1.868236 -1.818375 -1.270613 3.0062 51684
1.3 -1.970378 -1.857559 -1.827838 -1.309865 2.8424 3942
1.4 -1.965081 -1.837402 -1.833411 -1.334548 2.8191 15914
1.5 -1.955125 -1.811192 -1.837877 -1.349301 2.9395 3650
1.6 -1.942939 -1.781365 -1.842283 -1.357232 3.2137 8906
1.7 -1.930208 -1.749685 -1.846685 -1.360439 3.6604 5110
1.8 -1.918054 -1.717436 -1.850812 -1.360419 4.3095 6862
1.9 -1.907157 -1.685556 -1.854423 -1.358091 5.2098 3504
2.0 -1.897849 -1.654720 -1.857411 -1.354138 6.433 5256

H6 (line)

Score for molecule: 3.007636

Bond length [A] Exact GS energy [Ha] Predicted GS energy [Ha] Exact ES energy [Ha] Predicted ES energy [Ha] Score for each bond length # of function evaluation
0.5 -2.225106 -2.197670 -1.370202 0.252675 1.8662 351852
0.6 -2.796419 -2.761537 -2.092813 -0.827738 1.7484 34880
0.7 -3.077995 -3.034212 -2.480042 -1.467161 1.6207 47524
0.8 -3.204412 -3.150161 -2.679755 -1.848888 1.4802 53192
0.9 -3.244542 -3.177817 -2.770171 -2.073514 1.3279 29866
1.0 -3.236066 -3.154254 -2.845129 -2.202052 1.4357 11118
1.1 -3.200684 -3.100499 -2.880194 -2.276476 1.5711 56462
1.2 -3.151729 -3.029281 -2.890590 -2.306678 1.7671 13516
1.3 -3.097826 -2.948772 -2.887273 -2.312584 2.0215 17440
1.4 -3.044600 -2.864398 -2.877099 -2.302420 2.3551 11554
1.5 -2.995565 -2.779776 -2.864310 -2.282613 2.7878 18966
1.6 -2.952668 -2.697312 -2.851423 -2.253394 3.3846 81968
1.7 -2.916689 -2.618564 -2.839788 -2.215798 4.2375 52538
1.8 -2.887569 -2.544522 -2.829994 -2.184564 5.2519 17222
1.9 -2.864703 -2.475732 -2.822145 -2.149312 6.67 15478
2.0 -2.847192 -2.412451 -2.816081 -2.113897 8.5965 45780

H6 (ring)

Score for molecule: 0.715583

Bond length [A] Exact GS energy [Ha] Predicted GS energy [Ha] Exact ES energy [Ha] Predicted ES energy [Ha] Score for each bond length # of function evaluation
0.5 -1.732928 1.197436 -0.347911 1.414900 0.84299 101806
0.6 -2.529473 -0.175681 -1.444157 -0.147545 0.97408 39458
0.7 -2.935542 -1.071990 -2.068995 -1.020563 0.94065 51230
0.8 -3.134937 -1.560876 -2.434334 -1.396551 0.76545 34444
0.9 -3.219318 -1.848692 -2.648379 -1.774380 0.86984 22454
1.0 -3.237477 -2.091554 -2.771400 -2.000783 0.80525 27250
1.1 -3.217049 -2.142272 -2.838464 -2.078942 0.83272 32046
1.2 -3.174998 -2.250447 -2.870746 -2.213500 0.87857 31392
1.3 -3.122534 -2.336132 -2.881621 -2.290854 0.81206 15042
1.4 -3.067346 -2.325024 -2.879867 -2.310652 0.92334 26596
1.5 -3.014648 -2.317242 -2.871343 -2.232586 0.40926 22672
1.6 -2.967691 -2.311902 -2.859930 -2.239136 0.32474 21582
1.7 -2.928060 -2.301832 -2.848091 -2.277437 0.69494 22236
1.8 -2.896015 -2.277668 -2.837244 -2.277549 0.99798 20492
1.9 -2.870937 -2.291349 -2.828055 -2.239192 0.21626 14388
2.0 -2.851786 -2.214858 -2.820683 -2.178741 0.16121 27250

LiH

Score for molecule: 0.717952

Bond length [A] Exact GS energy [Ha] Predicted GS energy [Ha] Exact ES energy [Ha] Predicted ES energy [Ha] Score for each bond length # of function evaluation
0.5 -7.050225 -6.721909 -6.990633 -6.687477 0.42219 66054
0.6 -7.319319 -6.906632 -7.238552 -6.872704 0.57994 1744
0.7 -7.505052 -7.012064 -7.402653 -6.981477 0.70129 1744
0.8 -7.634167 -7.079057 -7.514699 -7.050337 0.7596 7630
0.9 -7.723424 -7.123028 -7.591579 -7.096959 0.80228 3052
1.0 -7.784460 -7.154210 -7.644499 -7.129641 0.82446 1526
1.1 -7.825537 -7.177148 -7.681108 -7.153048 0.83313 1526
1.2 -7.852431 -7.194299 -7.706531 -7.169786 0.83198 1308
1.3 -7.869140 -7.207193 -7.724156 -7.181551 0.82314 1308
1.4 -7.878454 -7.216875 -7.736236 -7.189647 0.80855 3270
1.5 -7.882362 -7.224105 -7.744300 -7.194798 0.78772 2180
1.6 -7.882324 -7.229459 -7.749415 -7.198005 0.76334 29430
1.7 -7.879434 -7.233386 -7.752348 -7.199215 0.73112 1308
1.8 -7.874524 -7.238820 -7.753661 -7.199086 0.67125 7630
1.9 -7.868241 -7.242583 -7.753774 -7.198284 0.613 4578
2.0 -7.861088 -7.247171 -7.752995 -7.196825 0.53423 9374

BeH2

Score for molecule: 0.701943

Bond length [A] Exact GS energy [Ha] Predicted GS energy [Ha] Exact ES energy [Ha] Predicted ES energy [Ha] Score for each bond length # of function evaluation
0.5 -13.689960 -12.137734 -13.380043 -11.498946 1.0612 78486
0.6 -14.405649 -12.806863 -14.095460 -12.487845 0.028464 39116
0.7 -14.871330 -13.284636 -14.559923 -13.085285 0.35984 20066
0.8 -15.172805 -13.587948 -14.861490 -13.462027 0.59552 12700
0.9 -15.364151 -14.524839 -15.055753 -13.729484 1.579 86106
1.0 -15.481741 -14.630680 -15.179340 -13.919694 1.3511 29210
1.1 -15.549638 -14.694231 -15.255934 -14.079035 1.0946 11938
1.2 -15.583812 -14.730947 -15.300966 -14.215323 0.82298 10922
1.3 -15.595047 -14.749102 -15.324723 -14.333281 0.53823 18796
1.4 -15.590743 -14.755363 -15.334210 -14.433328 0.25534 10414
1.5 -15.576051 -14.753297 -15.334269 -14.518138 0.027393 26162
1.6 -15.554624 -14.744469 -15.328291 -14.588310 0.31005 19304
1.7 -15.529121 -14.732607 -15.318687 -14.645968 0.58829 16256
1.8 -15.501545 -14.717702 -15.307190 -14.692023 0.86787 6858
1.9 -15.473451 -14.728707 -15.295051 -14.701779 0.84906 59436
2.0 -15.446094 -14.705776 -15.283153 -14.689834 0.90216 34798

H2O

Score for molecule: 0.988701

Bond length [A] Exact GS energy [Ha] Predicted GS energy [Ha] Exact ES energy [Ha] Predicted ES energy [Ha] Score for each bond length # of function evaluation
0.5 -73.137644 -70.547080 -72.085718 -69.876433 0.36246 43688
0.6 -74.146204 -71.765858 -73.205037 -71.378165 0.58807 17780
0.7 -74.643693 -72.548970 -73.845590 -72.267909 0.64784 12700
0.8 -74.883002 -73.084915 -74.229468 -72.832719 0.6141 11176
0.9 -74.987693 -73.459526 -74.463993 -73.217462 0.53778 2540
1.0 -75.019855 -73.725497 -74.606163 -73.490382 0.43167 1524
1.1 -75.012625 -73.915400 -74.689275 -73.687082 0.2939 1524
1.2 -74.985126 -74.049718 -74.734667 -73.829043 0.11892 1524
1.3 -74.948779 -74.165518 -74.756594 -73.941015 0.16816 20066
1.4 -74.910271 -74.223863 -74.764526 -74.089863 0.080581 18542
1.5 -74.873436 -74.239240 -74.764648 -74.143694 0.12172 2032
1.6 -74.840495 -74.258338 -74.760965 -74.120715 0.73045 22098
1.7 -74.812706 -74.281668 -74.756009 -74.130172 1.6721 13716
1.8 -74.790571 -74.296618 -74.751236 -74.126481 3.3253 2032
1.9 -74.773909 -74.304522 -74.747304 -74.123980 5.786 1524
2.0 -74.761988 -74.304943 -74.744346 -74.293303 0.34026 25146