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
UCCSD
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
1.59806

Data

Summary

Molecule Mean score Mean # of func. eval.
H2line 0.000000
H4line 2.276645
H4ring 2.047970
H6line 3.105733
H6ring 2.554515
LiH 0.448352
BeH2 0.283154
H2O 2.068094
all 1.598058

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 0
0.6 -1.116286 -1.116286 0.036501 0.036501 0
0.7 -1.136189 -1.136189 -0.120452 -0.120452 9.8451e-10
0.8 -1.134148 -1.134148 -0.227924 -0.227924 0
0.9 -1.120560 -1.120560 -0.301706 -0.301706 0
1.0 -1.101150 -1.101150 -0.352291 -0.352291 0
1.1 -1.079193 -1.079193 -0.386515 -0.386515 0
1.2 -1.056741 -1.056741 -0.408860 -0.408860 7.7175e-09
1.3 -1.035186 -1.035186 -0.422402 -0.422402 3.2638e-09
1.4 -1.015468 -1.015468 -0.429384 -0.429384 1.0237e-08
1.5 -0.998149 -0.998149 -0.431513 -0.431513 1.7648e-09
1.6 -0.983473 -0.983473 -0.430109 -0.430109 3.6143e-09
1.7 -0.971427 -0.971427 -0.426192 -0.426192 0
1.8 -0.961817 -0.961817 -0.420541 -0.420541 3.695e-09
1.9 -0.954339 -0.954339 -0.413749 -0.413749 1.8498e-09
2.0 -0.948641 -0.948641 -0.406260 -0.406260 0

H4 (line)

Score for molecule: 2.276645

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 -1.653110 -0.622827 -0.604400 0.017879
0.6 -1.960194 -1.960187 -1.096479 -1.076025 0.023673
0.7 -2.106997 -2.106981 -1.365653 -1.343469 0.029903
0.8 -2.167561 -2.167546 -1.514584 -1.490908 0.036236
0.9 -2.180317 -2.180280 -1.590935 -1.566320 0.041701
1.0 -2.166387 -2.166302 -1.649658 -1.597960 0.099883
1.1 -2.137971 -2.137787 -1.712390 -1.602774 0.25714
1.2 -2.102608 -2.102274 -1.755108 -1.590545 0.4726
1.3 -2.065229 -2.064643 -1.784935 -1.568678 0.76945
1.4 -2.029070 -2.028124 -1.806226 -1.540425 1.1885
1.5 -1.996150 -1.994723 -1.821715 -1.509679 1.7806
1.6 -1.967560 -1.965552 -1.833158 -1.478286 2.6254
1.7 -1.943692 -1.941063 -1.841705 -1.447971 3.8349
1.8 -1.924431 -1.921243 -1.848128 -1.420010 5.569
1.9 -1.909332 -1.905790 -1.852960 -1.395288 8.0559
2.0 -1.897781 -1.894257 -1.856584 -1.374214 11.623

H4 (ring)

Score for molecule: 2.047970

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 -0.610009 -0.516291 -0.516277 0.001143
0.6 -1.191866 -1.191649 -1.074424 -1.074418 0.0017943
0.7 -1.528728 -1.528369 -1.394620 -1.388227 0.044983
0.8 -1.728281 -1.727731 -1.586733 -1.565347 0.14721
0.9 -1.846741 -1.845949 -1.699536 -1.661723 0.25149
1.0 -1.915107 -1.914017 -1.764318 -1.708025 0.3661
1.1 -1.951594 -1.950148 -1.799889 -1.722228 0.50238
1.2 -1.967550 -1.965693 -1.818375 -1.715595 0.67654
1.3 -1.970378 -1.968073 -1.827838 -1.695549 0.91192
1.4 -1.965081 -1.962325 -1.833411 -1.667160 1.2417
1.5 -1.955125 -1.951957 -1.837877 -1.633919 1.7125
1.6 -1.942939 -1.939452 -1.842283 -1.598429 2.388
1.7 -1.930208 -1.926541 -1.846685 -1.562516 3.3584
1.8 -1.918054 -1.914376 -1.850812 -1.527573 4.7524
1.9 -1.907157 -1.903637 -1.854423 -1.494491 6.7587
2.0 -1.897849 -1.894629 -1.857411 -1.463869 9.6521

H6 (line)

Score for molecule: 3.105733

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 -2.225024 -1.370202 -1.339291 0.036061
0.6 -2.796419 -2.796296 -2.092813 -2.059354 0.047378
0.7 -3.077995 -3.077811 -2.480042 -2.444292 0.059479
0.8 -3.204412 -3.204136 -2.679755 -2.642405 0.070663
0.9 -3.244542 -3.244128 -2.770171 -2.731763 0.080094
1.0 -3.236066 -3.235432 -2.845129 -2.756664 0.22467
1.1 -3.200684 -3.199698 -2.880194 -2.743215 0.42433
1.2 -3.151729 -3.150198 -2.890590 -2.707160 0.69656
1.3 -3.097826 -3.095517 -2.887273 -2.658832 1.074
1.4 -3.044600 -3.041233 -2.877099 -2.604479 1.6075
1.5 -2.995565 -2.990902 -2.864310 -2.549077 2.3662
1.6 -2.952668 -2.946592 -2.851423 -2.338822 5.0029
1.7 -2.916689 -2.909320 -2.839788 -2.446497 5.0184
1.8 -2.887569 -2.879321 -2.829994 -2.403154 7.2702
1.9 -2.864703 -2.856127 -2.822145 -2.365784 10.522
2.0 -2.847192 -2.839429 -2.816081 -2.335698 15.192

H6 (ring)

Score for molecule: 2.554515

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 -1.732811 -0.347911 -0.296988 0.036682
0.6 -2.529473 -2.529299 -1.444157 -1.378993 0.059881
0.7 -2.935542 -2.935289 -2.068995 -1.988366 0.092756
0.8 -3.134937 -3.134582 -2.434334 -2.337068 0.13833
0.9 -3.219318 -3.218821 -2.648379 -2.532994 0.20123
1.0 -3.237477 -3.236788 -2.771400 -2.636144 0.28872
1.1 -3.217049 -3.216072 -2.838464 -2.681172 0.41289
1.2 -3.174998 -3.173579 -2.870746 -2.689048 0.59253
1.3 -3.122534 -3.120410 -2.881621 -2.672959 0.85732
1.4 -3.067346 -3.064126 -2.879867 -2.641715 1.2531
1.5 -3.014648 -3.009739 -2.871343 -2.601394 1.8495
1.6 -2.967691 -2.960384 -2.859930 -2.556741 2.7457
1.7 -2.928060 -2.917660 -2.848091 -2.511004 4.0852
1.8 -2.896015 -2.881976 -2.837244 -2.466711 6.0658
1.9 -2.870937 -2.852946 -2.828055 -2.425651 8.9643
2.0 -2.851786 -2.830151 -2.820683 -2.387609 13.228

LiH

Score for molecule: 0.448352

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 -7.050134 -6.990633 -6.954544 0.6041
0.6 -7.319319 -7.319196 -7.238552 -7.211427 0.33432
0.7 -7.505052 -7.504960 -7.402653 -7.369091 0.32686
0.8 -7.634167 -7.634137 -7.514699 -7.474099 0.33958
0.9 -7.723424 -7.723356 -7.591579 -7.546619 0.3405
1.0 -7.784460 -7.784402 -7.644499 -7.597430 0.33588
1.1 -7.825537 -7.825502 -7.681108 -7.631529 0.34304
1.2 -7.852431 -7.852395 -7.706531 -7.655290 0.35096
1.3 -7.869140 -7.869097 -7.724156 -7.671217 0.36484
1.4 -7.878454 -7.878431 -7.736236 -7.680556 0.39135
1.5 -7.882362 -7.882344 -7.744300 -7.685815 0.42348
1.6 -7.882324 -7.882293 -7.749415 -7.687897 0.46261
1.7 -7.879434 -7.879406 -7.752348 -7.686242 0.51995
1.8 -7.874524 -7.874486 -7.753661 -7.683018 0.58418
1.9 -7.868241 -7.868216 -7.753774 -7.676735 0.67281
2.0 -7.861088 -7.861071 -7.752995 -7.668756 0.77916

BeH2

Score for molecule: 0.283154

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 -13.689382 -13.380043 -13.349537 0.096567
0.6 -14.405649 -14.405165 -14.095460 -14.058108 0.11886
0.7 -14.871330 -14.870929 -14.559923 -14.517636 0.13451
0.8 -15.172805 -15.172503 -14.861490 -14.816629 0.14313
0.9 -15.364151 -15.363881 -15.055753 -15.009202 0.15007
1.0 -15.481741 -15.481479 -15.179340 -15.130942 0.15918
1.1 -15.549638 -15.549342 -15.255934 -15.205232 0.17162
1.2 -15.583812 -15.583480 -15.300966 -15.246956 0.18977
1.3 -15.595047 -15.594664 -15.324723 -15.266545 0.2138
1.4 -15.590743 -15.590284 -15.334210 -15.270552 0.24636
1.5 -15.576051 -15.575453 -15.334269 -15.264089 0.28779
1.6 -15.554624 -15.553870 -15.328291 -15.249856 0.34322
1.7 -15.529121 -15.528057 -15.318687 -15.230713 0.413
1.8 -15.501545 -15.500069 -15.307190 -15.208420 0.5006
1.9 -15.473451 -15.471363 -15.295051 -15.183918 0.61123
2.0 -15.446094 -15.443118 -15.283153 -15.157845 0.75077

H2O

Score for molecule: 2.068094

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 -73.137436 -72.085718 -72.060695 0.02359
0.6 -74.146204 -74.146084 -73.205037 -73.176928 0.029738
0.7 -74.643693 -74.643625 -73.845590 -73.812904 0.040868
0.8 -74.883002 -74.882909 -74.229468 -74.190344 0.059724
0.9 -74.987693 -74.987408 -74.463993 -74.416134 0.090842
1.0 -75.019855 -75.019671 -74.606163 -74.547885 0.14043
1.1 -75.012625 -75.012440 -74.689275 -74.618511 0.21828
1.2 -74.985126 -74.984915 -74.734667 -74.649519 0.33912
1.3 -74.948779 -74.948483 -74.756594 -74.655335 0.52535
1.4 -74.910271 -74.909930 -74.764526 -74.645734 0.81273
1.5 -74.873436 -74.872943 -74.764648 -74.627605 1.2552
1.6 -74.840495 -74.840016 -74.760965 -74.604165 1.9656
1.7 -74.812706 -74.812394 -74.756009 -74.579067 3.1154
1.8 -74.790571 -74.790164 -74.751236 -74.553143 5.0256
1.9 -74.773909 -74.773091 -74.747304 -74.529109 8.1705
2.0 -74.761988 -74.760868 -74.744346 -74.544279 11.277