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
sequential minimal optimization
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
9.34274

Data

Summary

Molecule Mean score Mean # of func. eval.
H2line 0.143823
H4line 1.423798
H4ring 1.604450
H6line 1.945449
H6ring 2.773144
LiH 0.152283
BeH2 0.139059
H2O 66.559926
all 9.342742

H2

Score for molecule: 0.143823

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 -1.032171 0.267000 0.267000 0.017387
0.6 -1.116286 -1.097115 0.036501 0.036502 0.01663
0.7 -1.136189 -1.101499 -0.120452 -0.120452 0.034152
0.8 -1.134148 -1.095850 -0.227924 -0.227924 0.04226
0.9 -1.120560 -1.070634 -0.301706 -0.301705 0.06097
1.0 -1.101150 -1.041253 -0.352291 -0.352286 0.079978
1.1 -1.079193 -1.014938 -0.386515 -0.386515 0.092763
1.2 -1.056741 -0.987414 -0.408860 -0.408853 0.107
1.3 -1.035186 -0.946789 -0.422402 -0.422386 0.14423
1.4 -1.015468 -0.933682 -0.429384 -0.429383 0.13955
1.5 -0.998149 -0.895553 -0.431513 -0.431480 0.181
1.6 -0.983473 -0.858806 -0.430109 -0.430109 0.22529
1.7 -0.971427 -0.833632 -0.426192 -0.426192 0.25273
1.8 -0.961817 -0.816965 -0.420541 -0.420529 0.26759
1.9 -0.954339 -0.786921 -0.413749 -0.413680 0.30957
2.0 -0.948641 -0.769467 -0.406260 -0.406121 0.33009

H4 (line)

Score for molecule: 1.423798

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 -1.596387 -0.622827 -0.587333 0.020612
0.6 -1.960194 -1.890516 -1.096479 -1.050436 0.027364
0.7 -2.106997 -2.073599 -1.365653 -1.325631 0.0089353
0.8 -2.167561 -2.123960 -1.514584 -1.461994 0.013767
0.9 -2.180317 -2.148118 -1.590935 -1.540431 0.031057
1.0 -2.166387 -2.056158 -1.649658 -1.560853 0.041462
1.1 -2.137971 -2.078509 -1.712390 -1.567465 0.20082
1.2 -2.102608 -2.064002 -1.755108 -1.560232 0.4497
1.3 -2.065229 -2.012634 -1.784935 -1.526158 0.73559
1.4 -2.029070 -1.756629 -1.806226 -1.503508 0.13586
1.5 -1.996150 -1.766060 -1.821715 -1.456654 0.77375
1.6 -1.967560 -1.691015 -1.833158 -1.473283 0.62
1.7 -1.943692 -1.713645 -1.841705 -1.423405 1.8459
1.8 -1.924431 -1.709111 -1.848128 -1.401183 3.0356
1.9 -1.909332 -1.728222 -1.852960 -1.363765 5.4652
2.0 -1.897781 -1.651580 -1.856584 -1.224160 9.3752

H4 (ring)

Score for molecule: 1.604450

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 -0.537084 -0.516291 -0.467152 0.25477
0.6 -1.191866 -1.157541 -1.074424 -1.073598 0.28523
0.7 -1.528728 -1.508055 -1.394620 -1.383176 0.068825
0.8 -1.728281 -1.704920 -1.586733 -1.560087 0.023216
0.9 -1.846741 -1.821331 -1.699536 -1.656622 0.11891
1.0 -1.915107 -1.887305 -1.764318 -1.702843 0.22332
1.1 -1.951594 -1.921528 -1.799889 -1.717234 0.34665
1.2 -1.967550 -1.935460 -1.818375 -1.711803 0.4993
1.3 -1.970378 -1.956076 -1.827838 -1.683424 0.91282
1.4 -1.965081 -1.775471 -1.833411 -1.658440 0.11118
1.5 -1.955125 -1.915522 -1.837877 -1.632594 1.4131
1.6 -1.942939 -1.899986 -1.842283 -1.599283 1.9874
1.7 -1.930208 -1.882947 -1.846685 -1.563721 2.822
1.8 -1.918054 -1.898733 -1.850812 -1.513623 4.7273
1.9 -1.907157 -1.687280 -1.854423 -1.516339 2.2416
2.0 -1.897849 -1.875804 -1.857411 -1.445713 9.6356

H6 (line)

Score for molecule: 1.945449

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 -2.156050 -1.370202 -1.297868 0.003834
0.6 -2.796419 -2.696395 -2.092813 -2.030301 0.053316
0.7 -3.077995 -3.034683 -2.480042 -2.425540 0.018712
0.8 -3.204412 -3.162316 -2.679755 -2.632029 0.01073
0.9 -3.244542 -3.215032 -2.770171 -2.723878 0.035378
1.0 -3.236066 -3.176797 -2.845129 -2.731947 0.13791
1.1 -3.200684 -3.145685 -2.880194 -2.578361 0.77017
1.2 -3.151729 -3.065529 -2.890590 -2.679202 0.47939
1.3 -3.097826 -2.949635 -2.887273 -2.554028 0.8789
1.4 -3.044600 -2.923550 -2.877099 -2.549610 1.2325
1.5 -2.995565 -2.920293 -2.864310 -2.501942 2.1873
1.6 -2.952668 -2.870937 -2.851423 -2.391073 3.7396
1.7 -2.916689 -2.795140 -2.839788 -2.255502 6.0173
1.8 -2.887569 -2.223120 -2.829994 -2.214964 0.85834
1.9 -2.864703 -2.261261 -2.822145 -2.213781 0.11564
2.0 -2.847192 -2.661814 -2.816081 -2.176853 14.588

H6 (ring)

Score for molecule: 2.773144

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 -1.664142 -0.347911 -0.273776 0.0038624
0.6 -2.529473 -2.442858 -1.444157 -1.332233 0.02332
0.7 -2.935542 -2.871959 -2.068995 -1.949344 0.064704
0.8 -3.134937 -3.076717 -2.434334 -2.303996 0.10294
0.9 -3.219318 -3.155460 -2.648379 -2.498192 0.1512
1.0 -3.237477 -3.156136 -2.771400 -2.587520 0.22001
1.1 -3.217049 -3.127123 -2.838464 -2.629840 0.31353
1.2 -3.174998 -3.110921 -2.870746 -2.619826 0.61411
1.3 -3.122534 -3.051202 -2.881621 -2.609295 0.83431
1.4 -3.067346 -2.981682 -2.879867 -2.546536 1.321
1.5 -3.014648 -2.895206 -2.871343 -2.456748 2.0596
1.6 -2.967691 -2.855138 -2.859930 -2.399815 3.2253
1.7 -2.928060 -2.810184 -2.848091 -2.371950 4.48
1.8 -2.896015 -2.780798 -2.837244 -2.295554 7.2566
1.9 -2.870937 -2.752027 -2.828055 -2.252781 10.642
2.0 -2.851786 -2.678873 -2.820683 -2.241642 13.058

LiH

Score for molecule: 0.152283

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 -7.005496 -6.990633 -6.934709 0.18787
0.6 -7.319319 -7.273963 -7.238552 -7.190530 0.033018
0.7 -7.505052 -7.431186 -7.402653 -7.314689 0.13769
0.8 -7.634167 -7.588622 -7.514699 -7.443835 0.21193
0.9 -7.723424 -7.685592 -7.591579 -7.544893 0.067159
1.0 -7.784460 -7.743652 -7.644499 -7.576731 0.19263
1.1 -7.825537 -7.783291 -7.681108 -7.626660 0.084487
1.2 -7.852431 -7.822028 -7.706531 -7.650913 0.17283
1.3 -7.869140 -7.831492 -7.724156 -7.667693 0.12977
1.4 -7.878454 -7.843999 -7.736236 -7.670253 0.22169
1.5 -7.882362 -7.818134 -7.744300 -7.665977 0.10209
1.6 -7.882324 -7.834885 -7.749415 -7.683897 0.13602
1.7 -7.879434 -7.804363 -7.752348 -7.663619 0.10747
1.8 -7.874524 -7.817989 -7.753661 -7.675212 0.18132
1.9 -7.868241 -7.795570 -7.753774 -7.662618 0.16149
2.0 -7.861088 -7.823547 -7.752995 -7.682046 0.30907

BeH2

Score for molecule: 0.139059

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 -13.568592 -13.380043 -13.272403 0.044298
0.6 -14.405649 -14.313566 -14.095460 -14.007759 0.014125
0.7 -14.871330 -14.785368 -14.559923 -14.460352 0.0437
0.8 -15.172805 -15.065361 -14.861490 -14.746300 0.024882
0.9 -15.364151 -15.285913 -15.055753 -14.986300 0.028485
1.0 -15.481741 -15.391370 -15.179340 -15.073184 0.052197
1.1 -15.549638 -15.443625 -15.255934 -15.133723 0.055149
1.2 -15.583812 -15.499397 -15.300966 -15.210546 0.021227
1.3 -15.595047 -15.511962 -15.324723 -15.227995 0.050466
1.4 -15.590743 -15.503010 -15.334210 -15.214596 0.12428
1.5 -15.576051 -15.483393 -15.334269 -15.205657 0.1487
1.6 -15.554624 -15.478193 -15.328291 -15.205204 0.20614
1.7 -15.529121 -15.437703 -15.318687 -15.179518 0.22691
1.8 -15.501545 -15.364778 -15.307190 -15.131493 0.2003
1.9 -15.473451 -15.372765 -15.295051 -15.118805 0.42354
2.0 -15.446094 -15.319964 -15.283153 -15.065688 0.56054

H2O

Score for molecule: 66.559926

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 -73.025315 -72.085718 -72.031754 0.055484
0.6 -74.146204 -73.961243 -73.205037 -73.073722 0.056999
0.7 -74.643693 -74.580188 -73.845590 -73.773675 0.010538
0.8 -74.883002 -74.768103 -74.229468 -74.090831 0.036323
0.9 -74.987693 -74.803665 -74.463993 -74.345284 0.12473
1.0 -75.019855 -74.935836 -74.606163 -74.520874 0.0030727
1.1 -75.012625 -74.779713 -74.689275 -74.523884 0.20881
1.2 -74.985126 -74.868818 -74.734667 -74.568675 0.19837
1.3 -74.948779 -74.652227 -74.756594 -74.530600 0.36713
1.4 -74.910271 -74.597835 -74.764526 -74.495553 0.29822
1.5 -74.873436 -74.560806 -74.764648 -74.491292 0.36102
1.6 -74.840495 -74.321667 -74.760965 -74.308574 0.83537
1.7 -74.812706 -74.504852 -74.756009 -74.364603 1.4737
1.8 -74.790571 -74.490760 -74.751236 -74.346346 2.6714
1.9 -74.773909 -74.409575 -74.747304 -74.324868 2.1839
2.0 -74.761988 -73.279642 -74.744346 -54.630259 1056.1