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

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Overview

Author
QunaSys
Date
20190801
Case
1 (Expectation value)
Method
Algorithm
QSE
Ansatz
HardwareEfficient, depth=5
Optimizer
BFGS
Mapping
jordan-wigner
Comment
Quantum subspace expansion algorithm with single electron excitations is applied to the ground state of the system obtained by VQE.
Score
0.72388

Data

Summary

Molecule Mean score Mean # of func. eval.
H2line 0.118449
H4line 1.605162
H4ring 0.585382
H6line 1.549971
H6ring 0.734562
LiH 0.281990
BeH2 0.263662
H2O 0.651829
all 0.723876

H2

Score for molecule: 0.118449

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 -1.042995 0.267000 0.267001 0.0092004
0.6 -1.116286 -1.101113 0.036501 0.036504 0.01316
0.7 -1.136189 -1.117345 -0.120452 -0.120451 0.018552
0.8 -1.134148 -1.110842 -0.227924 -0.227922 0.025714
0.9 -1.120560 -1.091909 -0.301706 -0.301705 0.034988
1.0 -1.101150 -1.066108 -0.352291 -0.352291 0.046794
1.1 -1.079193 -1.036536 -0.386515 -0.386515 0.061582
1.2 -1.056741 -1.005097 -0.408860 -0.408858 0.079709
1.3 -1.035186 -0.973108 -0.422402 -0.422401 0.1013
1.4 -1.015468 -0.941474 -0.429384 -0.429385 0.12625
1.5 -0.998149 -0.910871 -0.431513 -0.431513 0.15403
1.6 -0.983473 -0.881728 -0.430109 -0.430110 0.18387
1.7 -0.971427 -0.854334 -0.426192 -0.426192 0.21476
1.8 -0.961817 -0.828841 -0.420541 -0.420542 0.24567
1.9 -0.954339 -0.805326 -0.413749 -0.413750 0.27565
2.0 -0.948641 -0.783785 -0.406260 -0.406262 0.30395

H4 (line)

Score for molecule: 1.605162

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 -1.628607 -0.622827 -0.604335 0.0058412
0.6 -1.960194 -1.929552 -1.096479 -1.076086 0.011866
0.7 -2.106997 -2.069168 -1.365653 -1.343387 0.020992
0.8 -2.167561 -2.121371 -1.514584 -1.230948 0.36364
0.9 -2.180317 -2.124252 -1.590935 -1.565312 0.051651
1.0 -2.166387 -2.098526 -1.649658 -1.595630 0.02677
1.1 -2.137971 -2.056019 -1.712390 -1.598481 0.07509
1.2 -2.102608 -2.003861 -1.755108 -1.584114 0.2079
1.3 -2.065229 -1.946737 -1.784935 -1.559058 0.38311
1.4 -2.029070 -1.887781 -1.806226 -1.527673 0.61596
1.5 -1.996150 -1.493064 -1.821715 -1.276454 0.24178
1.6 -1.967560 -1.772194 -1.833158 -1.457489 1.3415
1.7 -1.943692 -1.717909 -1.841705 -1.244162 3.6452
1.8 -1.924431 -1.666861 -1.848128 -1.235435 4.6542
1.9 -1.909332 -1.619371 -1.852960 -1.222092 6.0474
2.0 -1.897781 -1.575608 -1.856584 -1.205264 7.9897

H4 (ring)

Score for molecule: 0.585382

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 -0.521781 -0.516291 -0.515408 0.93209
0.6 -1.191866 -1.091095 -1.074424 -1.073309 0.84856
0.7 -1.528728 -1.415136 -1.394620 -1.386847 0.78906
0.8 -1.728281 -1.601670 -1.586733 -1.563665 0.7315
0.9 -1.846741 -1.706759 -1.699536 -1.659725 0.68049
1.0 -1.915107 -1.761065 -1.764318 -1.705659 0.63256
1.1 -1.951594 -1.782537 -1.799889 -1.719460 0.58421
1.2 -1.967550 -1.782354 -1.818375 -1.712382 0.53094
1.3 -1.970378 -1.767811 -1.827838 -1.691800 0.46674
1.4 -1.965081 -1.743871 -1.833411 -1.662749 0.38389
1.5 -1.955125 -1.713993 -1.837877 -1.628740 0.27288
1.6 -1.942939 -1.680631 -1.842283 -1.592272 0.12217
1.7 -1.930208 -1.645557 -1.846685 -1.555159 0.082322
1.8 -1.918054 -1.610062 -1.850812 -1.518724 0.35836
1.9 -1.907157 -1.575068 -1.854423 -1.483915 0.72856
2.0 -1.897849 -1.541251 -1.857411 -1.451405 1.2218

H6 (line)

Score for molecule: 1.549971

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 -2.186751 -1.370202 -1.335354 0.0041016
0.6 -2.796419 -2.748971 -2.092813 -2.054405 0.012849
0.7 -3.077995 -3.020121 -2.480042 -2.437766 0.026087
0.8 -3.204412 -3.134602 -2.679755 -2.391477 0.4164
0.9 -3.244542 -3.160728 -2.770171 -2.719667 0.070219
1.0 -3.236066 -3.135526 -2.845129 -2.740258 0.011078
1.1 -3.200684 -3.079956 -2.880194 -2.721078 0.11978
1.2 -3.151729 -3.006740 -2.890590 -2.677764 0.25977
1.3 -3.097826 -2.620200 -2.887273 -2.523382 0.54017
1.4 -3.044600 -2.554899 -2.877099 -2.477814 0.5398
1.5 -2.995565 -2.486288 -2.864310 -2.427040 0.5486
1.6 -2.952668 -2.417455 -2.851423 -2.205429 1.0942
1.7 -2.916689 -2.583396 -2.839788 -2.350589 2.0274
1.8 -2.887569 -2.506436 -2.829994 -2.168147 4.8755
1.9 -2.864703 -2.434676 -2.822145 -2.126291 6.2462
2.0 -2.847192 -2.368417 -2.816081 -2.088190 8.0074

H6 (ring)

Score for molecule: 0.734562

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 -1.695267 -0.347911 -0.289846 0.014732
0.6 -2.529473 -2.485093 -1.444157 -1.369969 0.027465
0.7 -2.935542 -2.883906 -2.068995 -1.977175 0.046373
0.8 -3.134937 -3.075211 -2.434334 -2.323408 0.073081
0.9 -3.219318 -3.150222 -2.648379 -2.516570 0.10984
1.0 -3.237477 -3.157028 -2.771400 -2.616429 0.15989
1.1 -3.217049 -3.122492 -2.838464 -2.657682 0.22775
1.2 -3.174998 -3.062692 -2.870746 -2.661199 0.31961
1.3 -3.122534 -2.987928 -2.881621 -2.640160 0.44354
1.4 -3.067346 -2.905083 -2.879867 -2.522476 1.0408
1.5 -3.014648 -2.818746 -2.871343 -2.468278 1.4456
1.6 -2.967691 -2.504300 -2.859930 -2.408875 0.11447
1.7 -2.928060 -2.347422 -2.848091 -2.255221 0.15296
1.8 -2.896015 -2.565962 -2.837244 -2.393952 1.9268
1.9 -2.870937 -2.489029 -2.828055 -2.339665 2.4831
2.0 -2.851786 -2.417167 -2.820683 -2.287562 3.167

LiH

Score for molecule: 0.281990

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 -7.028406 -6.990633 -6.967032 0.029911
0.6 -7.319319 -7.299538 -7.238552 -7.213452 0.065852
0.7 -7.505052 -7.485936 -7.402653 -7.371285 0.11966
0.8 -7.634167 -7.615764 -7.514699 -7.478077 0.15249
0.9 -7.723424 -7.705745 -7.591579 -7.551338 0.17113
1.0 -7.784460 -7.767349 -7.644499 -7.601877 0.18227
1.1 -7.825537 -7.808728 -7.681108 -7.636820 0.19026
1.2 -7.852431 -7.835608 -7.706531 -7.600194 0.61353
1.3 -7.869140 -7.851946 -7.724156 -7.616741 0.62229
1.4 -7.878454 -7.860534 -7.736236 -7.687597 0.216
1.5 -7.882362 -7.863347 -7.744300 -7.693769 0.22827
1.6 -7.882324 -7.861852 -7.749415 -7.696627 0.24313
1.7 -7.879434 -7.857127 -7.752348 -7.696901 0.26077
1.8 -7.874524 -7.850007 -7.753661 -7.634593 0.7823
1.9 -7.868241 -7.841108 -7.753774 -7.691808 0.30431
2.0 -7.861088 -7.830888 -7.752995 -7.687160 0.32967

BeH2

Score for molecule: 0.263662

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 -13.646090 -13.380043 -13.330658 0.017795
0.6 -14.405649 -14.370066 -14.095460 -14.042972 0.054499
0.7 -14.871330 -14.841411 -14.559923 -14.504749 0.0811
0.8 -15.172805 -15.145971 -14.861490 -14.804831 0.095804
0.9 -15.364151 -15.338440 -15.055753 -14.997805 0.10453
1.0 -15.481741 -15.455631 -15.179340 -15.119437 0.11175
1.1 -15.549638 -15.521916 -15.255934 -15.192984 0.11994
1.2 -15.583812 -15.553557 -15.300966 -15.233783 0.13055
1.3 -15.595047 -15.561253 -15.324723 -15.251841 0.1446
1.4 -15.590743 -15.552439 -15.334210 -15.254124 0.16287
1.5 -15.576051 -15.532192 -15.334269 -15.245396 0.18618
1.6 -15.554624 -15.504060 -15.328291 -15.228986 0.21535
1.7 -15.529121 -15.470573 -15.318687 -15.113931 0.69479
1.8 -15.501545 -15.433611 -15.307190 -15.088740 0.77444
1.9 -15.473451 -15.394524 -15.295051 -15.154333 0.34636
2.0 -15.446094 -15.354386 -15.283153 -15.032082 0.97804

H2O

Score for molecule: 0.651829

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 -73.124101 -72.085718 -72.053600 0.017658
0.6 -74.146204 -74.127405 -73.205037 -73.117949 0.072557
0.7 -74.643693 -74.618687 -73.845590 -73.800986 0.024556
0.8 -74.883002 -74.850204 -74.229468 -74.174858 0.033376
0.9 -74.987693 -74.944967 -74.463993 -74.275758 0.27785
1.0 -75.019855 -74.964631 -74.606163 -74.522428 0.06892
1.1 -75.012625 -74.941770 -74.689275 -74.437726 0.55882
1.2 -74.985126 -74.895175 -74.734667 -74.608895 0.14302
1.3 -74.948779 -74.836079 -74.756594 -74.605079 0.20197
1.4 -74.910271 -74.771148 -74.764526 -74.584363 0.28159
1.5 -74.873436 -74.553029 -74.764648 -74.515982 0.65945
1.6 -74.840495 -74.515406 -74.760965 -74.483637 0.60054
1.7 -74.812706 -74.572701 -74.756009 -74.474494 0.73215
1.8 -74.790571 -74.511129 -74.751236 -74.432335 1.0032
1.9 -74.773909 -74.453661 -74.747304 -74.350002 2.8962
2.0 -74.761988 -74.401148 -74.744346 -74.333093 2.8574