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
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
0.72086

Data

Summary

Molecule Mean score Mean # of func. eval.
H2line 0.118444
H4line 1.376086
H4ring 0.585376
H6line 1.571463
H6ring 1.109070
LiH 0.198651
BeH2 0.263645
H2O 0.544121
all 0.720857

H2

Score for molecule: 0.118444

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 -1.042994 0.267000 0.267000 0.0092015
0.6 -1.116286 -1.101129 0.036501 0.036501 0.013148
0.7 -1.136189 -1.117346 -0.120452 -0.120452 0.018551
0.8 -1.134148 -1.110845 -0.227924 -0.227924 0.025714
0.9 -1.120560 -1.091907 -0.301706 -0.301706 0.034991
1.0 -1.101150 -1.066107 -0.352291 -0.352291 0.046795
1.1 -1.079193 -1.036538 -0.386515 -0.386515 0.06158
1.2 -1.056741 -1.005103 -0.408860 -0.408860 0.079703
1.3 -1.035186 -0.973110 -0.422402 -0.422402 0.1013
1.4 -1.015468 -0.941484 -0.429384 -0.429384 0.12624
1.5 -0.998149 -0.910868 -0.431513 -0.431513 0.15403
1.6 -0.983473 -0.881732 -0.430109 -0.430109 0.18386
1.7 -0.971427 -0.854335 -0.426192 -0.426192 0.21476
1.8 -0.961817 -0.828841 -0.420541 -0.420541 0.24567
1.9 -0.954339 -0.805333 -0.413749 -0.413749 0.27564
2.0 -0.948641 -0.783793 -0.406260 -0.406260 0.30393

H4 (line)

Score for molecule: 1.376086

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 -1.628600 -0.622827 -0.604328 0.0058417
0.6 -1.960194 -1.929555 -1.096479 -1.076086 0.011863
0.7 -2.106997 -2.069189 -1.365653 -1.343407 0.020993
0.8 -2.167561 -2.121380 -1.514584 -1.490636 0.034048
0.9 -2.180317 -2.124248 -1.590935 -1.565309 0.051653
1.0 -2.166387 -2.098538 -1.649658 -1.595635 0.026757
1.1 -2.137971 -2.056019 -1.712390 -1.598482 0.075088
1.2 -2.102608 -2.003859 -1.755108 -1.584110 0.20791
1.3 -2.065229 -1.946733 -1.784935 -1.559054 0.38312
1.4 -2.029070 -1.887786 -1.806226 -1.527677 0.61596
1.5 -1.996150 -1.493064 -1.821715 -1.437590 0.68198
1.6 -1.967560 -1.772197 -1.833158 -1.457488 1.3415
1.7 -1.943692 -1.717915 -1.841705 -1.422688 1.8948
1.8 -1.924431 -1.666865 -1.848128 -1.389991 2.6286
1.9 -1.909332 -1.619377 -1.852960 -1.222095 6.0475
2.0 -1.897781 -1.575608 -1.856584 -1.205262 7.9897

H4 (ring)

Score for molecule: 0.585376

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 -0.521790 -0.516291 -0.515414 0.93205
0.6 -1.191866 -1.091098 -1.074424 -1.073310 0.84853
0.7 -1.528728 -1.415139 -1.394620 -1.386847 0.78903
0.8 -1.728281 -1.601670 -1.586733 -1.563664 0.7315
0.9 -1.846741 -1.706756 -1.699536 -1.659721 0.68048
1.0 -1.915107 -1.761069 -1.764318 -1.705661 0.63255
1.1 -1.951594 -1.782546 -1.799889 -1.719464 0.58419
1.2 -1.967550 -1.782358 -1.818375 -1.712382 0.53091
1.3 -1.970378 -1.767809 -1.827838 -1.691798 0.46673
1.4 -1.965081 -1.743872 -1.833411 -1.662750 0.38389
1.5 -1.955125 -1.713995 -1.837877 -1.628742 0.27288
1.6 -1.942939 -1.680630 -1.842283 -1.592272 0.12218
1.7 -1.930208 -1.645557 -1.846685 -1.555158 0.082336
1.8 -1.918054 -1.610057 -1.850812 -1.518722 0.35832
1.9 -1.907157 -1.575065 -1.854423 -1.483911 0.72858
2.0 -1.897849 -1.541252 -1.857411 -1.451403 1.2218

H6 (line)

Score for molecule: 1.571463

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 -2.186777 -1.370202 -1.335374 0.0040954
0.6 -2.796419 -2.748986 -2.092813 -2.054420 0.01285
0.7 -3.077995 -3.020138 -2.480042 -2.437782 0.026084
0.8 -3.204412 -3.134603 -2.679755 -2.633544 0.044977
0.9 -3.244542 -3.160734 -2.770171 -2.719671 0.070217
1.0 -3.236066 -3.135523 -2.845129 -2.740253 0.011082
1.1 -3.200684 -3.079958 -2.880194 -2.721078 0.11978
1.2 -3.151729 -3.006738 -2.890590 -2.677761 0.25978
1.3 -3.097826 -2.924050 -2.887273 -2.620200 0.44311
1.4 -3.044600 -2.554890 -2.877099 -2.477805 0.5398
1.5 -2.995565 -2.750139 -2.864310 -2.486279 1.0103
1.6 -2.952668 -2.664973 -2.851423 -2.417450 1.4448
1.7 -2.916689 -2.583402 -2.839788 -2.350593 2.0274
1.8 -2.887569 -2.506432 -2.829994 -2.168145 4.8755
1.9 -2.864703 -2.434676 -2.822145 -2.126288 6.2463
2.0 -2.847192 -2.368415 -2.816081 -2.088187 8.0074

H6 (ring)

Score for molecule: 1.109070

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 -1.695248 -0.347911 -0.289846 0.014718
0.6 -2.529473 -2.485100 -1.444157 -1.369976 0.027465
0.7 -2.935542 -2.883924 -2.068995 -1.977192 0.046375
0.8 -3.134937 -3.075227 -2.434334 -2.323429 0.073073
0.9 -3.219318 -3.150226 -2.648379 -2.516577 0.10983
1.0 -3.237477 -3.157035 -2.771400 -2.616436 0.15989
1.1 -3.217049 -3.122494 -2.838464 -2.657687 0.22775
1.2 -3.174998 -3.062687 -2.870746 -2.661198 0.31959
1.3 -3.122534 -2.987935 -2.881621 -2.640167 0.44354
1.4 -3.067346 -2.905080 -2.879867 -2.603317 0.60958
1.5 -3.014648 -2.818749 -2.871343 -2.556625 0.82912
1.6 -2.967691 -2.732107 -2.859930 -2.504303 1.114
1.7 -2.928060 -2.647335 -2.848091 -2.449353 1.4757
1.8 -2.896015 -2.565964 -2.837244 -2.393954 1.9268
1.9 -2.870937 -2.489027 -2.828055 -2.339665 2.4831
2.0 -2.851786 -2.417171 -2.820683 -2.140833 7.8846

LiH

Score for molecule: 0.198651

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 -7.028379 -6.990633 -6.967006 0.029883
0.6 -7.319319 -7.299506 -7.238552 -7.213421 0.065839
0.7 -7.505052 -7.485916 -7.402653 -7.371265 0.11966
0.8 -7.634167 -7.615742 -7.514699 -7.478061 0.15245
0.9 -7.723424 -7.705722 -7.591579 -7.551319 0.1711
1.0 -7.784460 -7.767338 -7.644499 -7.601865 0.18227
1.1 -7.825537 -7.808725 -7.681108 -7.636815 0.19028
1.2 -7.852431 -7.835599 -7.706531 -7.660855 0.19769
1.3 -7.869140 -7.851938 -7.724156 -7.677091 0.20597
1.4 -7.878454 -7.860511 -7.736236 -7.687574 0.216
1.5 -7.882362 -7.863339 -7.744300 -7.693760 0.22828
1.6 -7.882324 -7.861852 -7.749415 -7.696630 0.24311
1.7 -7.879434 -7.857122 -7.752348 -7.696897 0.26076
1.8 -7.874524 -7.849989 -7.753661 -7.695142 0.28119
1.9 -7.868241 -7.841101 -7.753774 -7.691804 0.30428
2.0 -7.861088 -7.830889 -7.752995 -7.687164 0.32965

BeH2

Score for molecule: 0.263645

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 -13.646056 -13.380043 -13.330624 0.017794
0.6 -14.405649 -14.369995 -14.095460 -14.042911 0.054468
0.7 -14.871330 -14.841354 -14.559923 -14.504693 0.081095
0.8 -15.172805 -15.145928 -14.861490 -14.804785 0.095811
0.9 -15.364151 -15.338416 -15.055753 -14.997788 0.10451
1.0 -15.481741 -15.455622 -15.179340 -15.119435 0.11173
1.1 -15.549638 -15.521958 -15.255934 -15.193025 0.11994
1.2 -15.583812 -15.553533 -15.300966 -15.233767 0.13053
1.3 -15.595047 -15.561225 -15.324723 -15.251815 0.14459
1.4 -15.590743 -15.552441 -15.334210 -15.254130 0.16285
1.5 -15.576051 -15.532163 -15.334269 -15.245372 0.18615
1.6 -15.554624 -15.503973 -15.328291 -15.228902 0.21534
1.7 -15.529121 -15.470569 -15.318687 -15.113930 0.69477
1.8 -15.501545 -15.433572 -15.307190 -15.088708 0.77441
1.9 -15.473451 -15.394434 -15.295051 -15.154248 0.34633
2.0 -15.446094 -15.354395 -15.283153 -15.032097 0.978

H2O

Score for molecule: 0.544121

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 -73.123904 -72.085718 -72.053406 0.017655
0.6 -74.146204 -74.127382 -73.205037 -73.167684 0.019689
0.7 -74.643693 -74.618466 -73.845590 -73.800768 0.024552
0.8 -74.883002 -74.850014 -74.229468 -74.174702 0.033325
0.9 -74.987693 -74.944877 -74.463993 -74.275667 0.27785
1.0 -75.019855 -74.964242 -74.606163 -74.383725 0.40326
1.1 -75.012625 -74.941513 -74.689275 -74.437473 0.55881
1.2 -74.985126 -74.895063 -74.734667 -74.608811 0.14291
1.3 -74.948779 -74.835638 -74.756594 -74.604638 0.20197
1.4 -74.910271 -74.771120 -74.764526 -74.584351 0.28148
1.5 -74.873436 -74.703662 -74.764648 -74.552554 0.38901
1.6 -74.840495 -74.515354 -74.760965 -74.483588 0.60057
1.7 -74.812706 -74.572578 -74.756009 -74.474365 0.73225
1.8 -74.790571 -74.373665 -74.751236 -74.250393 2.1339
1.9 -74.773909 -74.453565 -74.747304 -74.389710 1.4001
2.0 -74.761988 -74.401072 -74.744346 -74.357166 1.4887