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

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Overview

Author
QunaSys
Date
20191004
Case
1 (Expectation value)
Method
Algorithm
VQD
Ansatz
SymmetryPreserving, depth=20
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
0.36909

Data

Summary

Molecule Mean score Mean # of func. eval.
H2line 0.000000 1484.125000
H4line 0.024502 151869.000000
H4ring 0.070829 135743.125000
H6line 0.240317 131590.500000
H6ring 1.020201 296286.750000
LiH 0.163199 9435.000000
BeH2 0.512640 18995.000000
H2O 0.921066 9612.125000
all 0.369094 94376.953125

H2

Score for molecule: 0.000000

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 -1.055160 0.267000 0.267000 2.9281e-09 4216
0.6 -1.116286 -1.116286 0.036501 0.036501 2.3283e-07 1488
0.7 -1.136189 -1.136189 -0.120452 -0.120453 1.7445e-06 1674
0.8 -1.134148 -1.134147 -0.227924 -0.227924 5.0414e-07 1550
0.9 -1.120560 -1.120560 -0.301706 -0.301706 2.0075e-07 1240
1.0 -1.101150 -1.101150 -0.352291 -0.352291 1.1349e-07 1240
1.1 -1.079193 -1.079193 -0.386515 -0.386515 2.0111e-07 1240
1.2 -1.056741 -1.056741 -0.408860 -0.408860 7.1478e-08 1240
1.3 -1.035186 -1.035186 -0.422402 -0.422402 5.2976e-08 1178
1.4 -1.015468 -1.015468 -0.429384 -0.429384 2.1652e-08 1240
1.5 -0.998149 -0.998149 -0.431513 -0.431513 2.8203e-08 1240
1.6 -0.983473 -0.983473 -0.430109 -0.430109 8.3216e-08 1240
1.7 -0.971427 -0.971427 -0.426192 -0.426192 6.9938e-08 1240
1.8 -0.961817 -0.961817 -0.420541 -0.420541 6.3395e-08 1240
1.9 -0.954339 -0.954339 -0.413749 -0.413749 5.6313e-08 1240
2.0 -0.948641 -0.948641 -0.406260 -0.406260 5.2868e-08 1240

H4 (line)

Score for molecule: 0.024502

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 -1.651372 -0.622827 -0.622015 0.00090511 153928
0.6 -1.960194 -1.957390 -1.096479 -1.095847 0.0025144 37488
0.7 -2.106997 -2.105505 -1.365653 -1.363883 0.00037447 90312
0.8 -2.167561 -2.165749 -1.514584 -1.512507 0.00040629 87614
0.9 -2.180317 -2.179376 -1.590935 -1.588579 0.0024001 82502
1.0 -2.166387 -2.164526 -1.649658 -1.620720 0.052398 117434
1.1 -2.137971 -2.136660 -1.712390 -1.711187 0.00025411 138308
1.2 -2.102608 -2.100316 -1.755108 -1.754192 0.0039601 257872
1.3 -2.065229 -2.059136 -1.784935 -1.783645 0.017136 254748
1.4 -2.029070 -2.022599 -1.806226 -1.805078 0.023891 76254
1.5 -1.996150 -1.991164 -1.821715 -1.819469 0.015713 235152
1.6 -1.967560 -1.961199 -1.833158 -1.830823 0.029961 275764
1.7 -1.943692 -1.933091 -1.841705 -1.838284 0.070395 211438
1.8 -1.924431 -1.920514 -1.848128 -1.847743 0.04629 146828
1.9 -1.909332 -1.904882 -1.852960 -1.850880 0.042045 88324
2.0 -1.897781 -1.894179 -1.856584 -1.856418 0.083396 175938

H4 (ring)

Score for molecule: 0.070829

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 -0.608611 -0.516291 -0.515541 0.008195 243956
0.6 -1.191866 -1.190363 -1.074424 -1.073440 0.0044139 34648
0.7 -1.528728 -1.527075 -1.394620 -1.386975 0.044672 73272
0.8 -1.728281 -1.726085 -1.586733 -1.563771 0.14671 26412
0.9 -1.846741 -1.840692 -1.699536 -1.698821 0.036229 196812
1.0 -1.915107 -1.906944 -1.764318 -1.763497 0.048686 26838
1.1 -1.951594 -1.944199 -1.799889 -1.799253 0.044556 78668
1.2 -1.967550 -1.957261 -1.818375 -1.817940 0.066058 30530
1.3 -1.970378 -1.956296 -1.827838 -1.826868 0.091981 36778
1.4 -1.965081 -1.961088 -1.833411 -1.832448 0.023008 118144
1.5 -1.955125 -1.946841 -1.837877 -1.834360 0.040654 232312
1.6 -1.942939 -1.937336 -1.842283 -1.842194 0.054773 176932
1.7 -1.930208 -1.922851 -1.846685 -1.845856 0.078158 37062
1.8 -1.918054 -1.911797 -1.850812 -1.849516 0.073777 288828
1.9 -1.907157 -1.895337 -1.854423 -1.852369 0.18519 257446
2.0 -1.897849 -1.890230 -1.857411 -1.857320 0.1862 313252

H6 (line)

Score for molecule: 0.240317

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 -2.186979 -1.370202 -1.352482 0.023871 209790
0.6 -2.796419 -2.749076 -2.092813 -2.072089 0.037834 79698
0.7 -3.077995 -3.020308 -2.480042 -2.457140 0.058174 85248
0.8 -3.204412 -3.134704 -2.679755 -2.652718 0.081332 55056
0.9 -3.244542 -3.160899 -2.770171 -2.740334 0.11342 75258
1.0 -3.236066 -3.135733 -2.845129 -2.766266 0.054921 101010
1.1 -3.200684 -3.080060 -2.880194 -2.745947 0.042506 100788
1.2 -3.151729 -3.006836 -2.890590 -2.703142 0.16296 47952
1.3 -3.097826 -2.924161 -2.887273 -2.650872 0.29796 117882
1.4 -3.044600 -2.837423 -2.877099 -2.588226 0.48773 47508
1.5 -2.995565 -2.750255 -2.864310 -2.625206 0.047282 457542
1.6 -2.952668 -2.665237 -2.851423 -2.598057 0.33647 257298
1.7 -2.916689 -2.583496 -2.839788 -2.551116 0.57894 184260
1.8 -2.887569 -2.506619 -2.829994 -2.494351 0.78692 120990
1.9 -2.864703 -2.447377 -2.822145 -2.434860 0.7059 116106
2.0 -2.847192 -2.400610 -2.816081 -2.368602 0.028849 49062

H6 (ring)

Score for molecule: 1.020201

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 -1.722942 -0.347911 -0.310952 0.019475 688866
0.6 -2.529473 -2.516462 -1.444157 -1.394053 0.034177 21534
0.7 -2.935542 -2.917989 -2.068995 -2.004488 0.054187 185148
0.8 -3.134937 -3.115132 -2.434334 -2.365762 0.069606 235764
0.9 -3.219318 -3.193759 -2.648379 -2.541178 0.143 261294
1.0 -3.237477 -3.203576 -2.771400 -2.653313 0.18063 128094
1.1 -3.217049 -3.174810 -2.838464 -2.662568 0.35304 168054
1.2 -3.174998 -3.121485 -2.870746 -2.694396 0.40373 364746
1.3 -3.122534 -3.054029 -2.881621 -2.642015 0.71022 178266
1.4 -3.067346 -2.966129 -2.879867 -2.651088 0.68041 372738
1.5 -3.014648 -2.883812 -2.871343 -2.623849 0.81405 270174
1.6 -2.967691 -2.826226 -2.859930 -2.576266 1.3196 291486
1.7 -2.928060 -2.753691 -2.848091 -2.516052 1.9716 402708
1.8 -2.896015 -2.686925 -2.837244 -2.478728 2.5425 246864
1.9 -2.870937 -2.623277 -2.828055 -2.455965 2.9016 352758
2.0 -2.851786 -2.564641 -2.820683 -2.405228 4.1253 572094

LiH

Score for molecule: 0.163199

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 -7.028311 -6.990633 -6.984926 0.27196 69708
0.6 -7.319319 -7.299400 -7.238552 -7.234115 0.19168 12876
0.7 -7.505052 -7.485752 -7.402653 -7.399734 0.15996 7770
0.8 -7.634167 -7.615535 -7.514699 -7.512429 0.13696 1776
0.9 -7.723424 -7.705484 -7.591579 -7.590050 0.12447 7770
1.0 -7.784460 -7.767072 -7.644499 -7.643209 0.11502 2220
1.1 -7.825537 -7.808439 -7.681108 -7.679900 0.11002 2664
1.2 -7.852431 -7.835306 -7.706531 -7.705281 0.1088 2220
1.3 -7.869140 -7.851644 -7.724156 -7.723169 0.11387 9324
1.4 -7.878454 -7.860234 -7.736236 -7.735241 0.12112 2664
1.5 -7.882362 -7.863059 -7.744300 -7.743173 0.13165 2664
1.6 -7.882324 -7.861577 -7.749415 -7.748541 0.14952 8436
1.7 -7.879434 -7.856868 -7.752348 -7.751390 0.17003 3108
1.8 -7.874524 -7.849755 -7.753661 -7.752689 0.19689 5106
1.9 -7.868241 -7.840860 -7.753774 -7.753210 0.23428 8658
2.0 -7.861088 -7.830667 -7.752995 -7.752294 0.27495 3996

BeH2

Score for molecule: 0.512640

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 -13.657178 -13.380043 -13.310446 0.11879 55282
0.6 -14.405649 -14.377521 -14.095460 -14.001774 0.21135 20174
0.7 -14.871330 -14.847298 -14.559923 -14.447557 0.28366 17816
0.8 -15.172805 -15.150553 -14.861490 -14.736283 0.33071 17292
0.9 -15.364151 -15.338868 -15.055753 -14.920413 0.35687 30654
1.0 -15.481741 -15.456038 -15.179340 -15.036546 0.3872 21484
1.1 -15.549638 -15.522327 -15.255934 -15.105798 0.41819 10480
1.2 -15.583812 -15.553872 -15.300966 -15.143956 0.44925 11528
1.3 -15.595047 -15.561522 -15.324723 -15.159911 0.48567 18864
1.4 -15.590743 -15.552665 -15.334210 -15.161331 0.52547 8122
1.5 -15.576051 -15.532384 -15.334269 -15.152053 0.57303 14410
1.6 -15.554624 -15.504224 -15.328291 -15.135827 0.62768 13886
1.7 -15.529121 -15.470717 -15.318687 -15.114233 0.69403 10742
1.8 -15.501545 -15.433712 -15.307190 -15.089059 0.77332 5240
1.9 -15.473451 -15.394603 -15.295051 -15.061396 0.86775 11004
2.0 -15.446094 -15.375707 -15.283153 -15.033650 1.0993 36942

H2O

Score for molecule: 0.921066

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 -73.124081 -72.085718 -72.055815 0.015534 33012
0.6 -74.146204 -74.127439 -73.205037 -73.169608 0.017706 3144
0.7 -74.643693 -74.618640 -73.845590 -73.802677 0.022377 1572
0.8 -74.883002 -74.850131 -74.229468 -74.176381 0.030934 1572
0.9 -74.987693 -74.944918 -74.463993 -74.397940 0.044451 2096
1.0 -75.019855 -74.964564 -74.606163 -74.523906 0.065185 1572
1.1 -75.012625 -74.941730 -74.689275 -74.587849 0.094425 2882
1.2 -74.985126 -74.895150 -74.734667 -74.610068 0.13824 2358
1.3 -74.948779 -74.836073 -74.756594 -74.606245 0.19587 2096
1.4 -74.910271 -74.771066 -74.764526 -74.367936 1.766 27772
1.5 -74.873436 -74.704058 -74.764648 -74.332181 2.4184 1572
1.6 -74.840495 -74.637443 -74.760965 -74.407579 1.8903 37204
1.7 -74.812706 -74.572702 -74.756009 -74.387657 2.2638 2358
1.8 -74.790571 -74.511146 -74.751236 -74.366248 2.6837 1572
1.9 -74.773909 -74.453683 -74.747304 -74.345555 3.0642 1572
2.0 -74.761988 -74.401184 -74.744346 -74.383082 0.026056 31440