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
SSVQE
Ansatz
UCCSD
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
1.61740

Data

Summary

Molecule Mean score Mean # of func. eval.
H2line 0.000000 17.000000
H4line 2.377233 247.000000
H4ring 2.093655 218.000000
H6line 3.087100 1190.000000
H6ring 2.543289 1127.000000
LiH 0.441376 439.875000
BeH2 0.283828 1184.500000
H2O 2.112695 1348.375000
all 1.617397 721.468750

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 1.1252e-14 32
0.6 -1.116286 -1.116286 0.036501 0.036501 9.2455e-15 16
0.7 -1.136189 -1.136189 -0.120452 -0.120452 8.4381e-14 16
0.8 -1.134148 -1.134148 -0.227924 -0.227924 1.1808e-12 16
0.9 -1.120560 -1.120560 -0.301706 -0.301706 5.5602e-12 16
1.0 -1.101150 -1.101150 -0.352291 -0.352291 1.6604e-11 16
1.1 -1.079193 -1.079193 -0.386515 -0.386515 2.0287e-11 16
1.2 -1.056741 -1.056741 -0.408860 -0.408860 5.1941e-11 16
1.3 -1.035186 -1.035186 -0.422402 -0.422402 6.5898e-11 16
1.4 -1.015468 -1.015468 -0.429384 -0.429384 7.7166e-11 16
1.5 -0.998149 -0.998149 -0.431513 -0.431513 7.749e-11 16
1.6 -0.983473 -0.983473 -0.430109 -0.430109 6.1671e-11 16
1.7 -0.971427 -0.971427 -0.426192 -0.426192 2.7343e-11 16
1.8 -0.961817 -0.961817 -0.420541 -0.420541 7.2708e-12 16
1.9 -0.954339 -0.954339 -0.413749 -0.413749 6.2844e-12 16
2.0 -0.948641 -0.948641 -0.406260 -0.406260 8.4457e-12 16

H4 (line)

Score for molecule: 2.377233

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 -1.653111 -0.622827 -0.604421 0.017859 400
0.6 -1.960194 -1.960187 -1.096479 -1.076056 0.023638 176
0.7 -2.106997 -2.106989 -1.365653 -1.343375 0.030039 272
0.8 -2.167561 -2.167545 -1.514584 -1.490691 0.036566 272
0.9 -2.180317 -2.180280 -1.590935 -1.566061 0.042142 256
1.0 -2.166387 -2.166304 -1.649658 -1.597469 0.10084 272
1.1 -2.137971 -2.137798 -1.712390 -1.601830 0.25938 176
1.2 -2.102608 -2.102280 -1.755108 -1.589350 0.47606 288
1.3 -2.065229 -2.064654 -1.784935 -1.566714 0.77649 272
1.4 -2.029070 -2.028136 -1.806226 -1.537904 1.1999 176
1.5 -1.996150 -1.994730 -1.821715 -1.505514 1.8046 256
1.6 -1.967560 -1.965540 -1.833158 -1.471748 2.674 272
1.7 -1.943692 -1.940994 -1.841705 -1.438898 3.9232 256
1.8 -1.924431 -1.921045 -1.848128 -1.406125 5.7484 144
1.9 -1.909332 -1.905332 -1.852960 -1.363569 8.6105 176
2.0 -1.897781 -1.893338 -1.856584 -1.344919 12.312 288

H4 (ring)

Score for molecule: 2.093655

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 -0.516194 0.00025068 448
0.6 -1.191866 -1.191648 -1.074424 -1.074271 0.00055097 160
0.7 -1.528728 -1.528369 -1.394620 -1.387962 0.046964 224
0.8 -1.728281 -1.727731 -1.586733 -1.564883 0.15048 160
0.9 -1.846741 -1.845949 -1.699536 -1.660971 0.25661 224
1.0 -1.915107 -1.914017 -1.764318 -1.706861 0.37382 192
1.1 -1.951594 -1.950147 -1.799889 -1.720514 0.51368 208
1.2 -1.967550 -1.965692 -1.818375 -1.713176 0.69275 192
1.3 -1.970378 -1.968073 -1.827838 -1.692293 0.93476 192
1.4 -1.965081 -1.962322 -1.833411 -1.662984 1.2734 176
1.5 -1.955125 -1.951956 -1.837877 -1.628778 1.7564 192
1.6 -1.942939 -1.939450 -1.842283 -1.592422 2.4477 192
1.7 -1.930208 -1.926539 -1.846685 -1.555764 3.4392 192
1.8 -1.918054 -1.914374 -1.850812 -1.520256 4.8612 256
1.9 -1.907157 -1.903633 -1.854423 -1.486832 6.9039 240
2.0 -1.897849 -1.894623 -1.857411 -1.455989 9.8468 240

H6 (line)

Score for molecule: 3.087100

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 -2.225020 -1.370202 -1.339420 0.035905 1792
0.6 -2.796419 -2.796288 -2.092813 -2.059634 0.046969 1344
0.7 -3.077995 -3.077805 -2.480042 -2.444318 0.059423 1400
0.8 -3.204412 -3.204135 -2.679755 -2.642205 0.071044 1344
0.9 -3.244542 -3.244129 -2.770171 -2.731224 0.08123 1232
1.0 -3.236066 -3.235413 -2.845129 -2.755797 0.22684 952
1.1 -3.200684 -3.199708 -2.880194 -2.741819 0.42871 1232
1.2 -3.151729 -3.150211 -2.890590 -2.705629 0.70247 1008
1.3 -3.097826 -3.095514 -2.887273 -2.656357 1.0857 1064
1.4 -3.044600 -3.041200 -2.877099 -2.600946 1.6284 728
1.5 -2.995565 -2.990777 -2.864310 -2.543914 2.4045 728
1.6 -2.952668 -2.946276 -2.851423 -2.489108 3.5154 1400
1.7 -2.916689 -2.908623 -2.839788 -2.437747 5.1232 1288
1.8 -2.887569 -2.877959 -2.829994 -2.391249 7.4534 1680
1.9 -2.864703 -2.853894 -2.822145 -2.350688 10.824 1008
2.0 -2.847192 -2.835696 -2.816081 -2.315946 15.706 840

H6 (ring)

Score for molecule: 2.543289

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 -1.732813 -0.347911 -0.296981 0.036689 1736
0.6 -2.529473 -2.529297 -1.444157 -1.378985 0.059888 728
0.7 -2.935542 -2.935288 -2.068995 -1.988352 0.09277 616
0.8 -3.134937 -3.134575 -2.434334 -2.337094 0.13828 1064
0.9 -3.219318 -3.218824 -2.648379 -2.533036 0.20116 1176
1.0 -3.237477 -3.236785 -2.771400 -2.636177 0.28865 1232
1.1 -3.217049 -3.216069 -2.838464 -2.681233 0.41272 1064
1.2 -3.174998 -3.173570 -2.870746 -2.689155 0.59215 784
1.3 -3.122534 -3.120408 -2.881621 -2.673156 0.85649 1008
1.4 -3.067346 -3.064123 -2.879867 -2.642317 1.2499 1120
1.5 -3.014648 -3.009739 -2.871343 -2.602206 1.8438 1064
1.6 -2.967691 -2.960384 -2.859930 -2.557899 2.735 1176
1.7 -2.928060 -2.917660 -2.848091 -2.512739 4.0635 1232
1.8 -2.896015 -2.881975 -2.837244 -2.468586 6.0339 1456
1.9 -2.870937 -2.852943 -2.828055 -2.427310 8.9256 1176
2.0 -2.851786 -2.830148 -2.820683 -2.389662 13.162 1400

LiH

Score for molecule: 0.441376

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 -7.050137 -6.990633 -6.957328 0.55743 1380
0.6 -7.319319 -7.319239 -7.238552 -7.208345 0.37301 736
0.7 -7.505052 -7.505018 -7.402653 -7.367613 0.34187 690
0.8 -7.634167 -7.634143 -7.514699 -7.473275 0.34653 368
0.9 -7.723424 -7.723388 -7.591579 -7.545877 0.34637 276
1.0 -7.784460 -7.784440 -7.644499 -7.595842 0.3475 230
1.1 -7.825537 -7.825508 -7.681108 -7.630503 0.35017 184
1.2 -7.852431 -7.852418 -7.706531 -7.654504 0.35651 276
1.3 -7.869140 -7.869120 -7.724156 -7.670591 0.36931 184
1.4 -7.878454 -7.878438 -7.736236 -7.680993 0.38833 276
1.5 -7.882362 -7.882325 -7.744300 -7.687163 0.41358 230
1.6 -7.882324 -7.882273 -7.749415 -7.689710 0.44882 184
1.7 -7.879434 -7.879404 -7.752348 -7.689370 0.49532 460
1.8 -7.874524 -7.874493 -7.753661 -7.686190 0.558 506
1.9 -7.868241 -7.868192 -7.753774 -7.681837 0.62802 460
2.0 -7.861088 -7.861059 -7.752995 -7.672842 0.74125 598

BeH2

Score for molecule: 0.283828

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 -13.689354 -13.380043 -13.349456 0.096737 3128
0.6 -14.405649 -14.405145 -14.095460 -14.058059 0.11895 1012
0.7 -14.871330 -14.870937 -14.559923 -14.517643 0.13451 1288
0.8 -15.172805 -15.172479 -14.861490 -14.816501 0.14346 1748
0.9 -15.364151 -15.363786 -15.055753 -15.008892 0.15077 1748
1.0 -15.481741 -15.481457 -15.179340 -15.130883 0.1593 736
1.1 -15.549638 -15.549342 -15.255934 -15.205158 0.17187 644
1.2 -15.583812 -15.583504 -15.300966 -15.246977 0.18979 736
1.3 -15.595047 -15.594668 -15.324723 -15.266437 0.21421 736
1.4 -15.590743 -15.590285 -15.334210 -15.270471 0.24668 920
1.5 -15.576051 -15.575474 -15.334269 -15.263809 0.28903 920
1.6 -15.554624 -15.553854 -15.328291 -15.249804 0.34337 736
1.7 -15.529121 -15.528069 -15.318687 -15.230770 0.41278 736
1.8 -15.501545 -15.500093 -15.307190 -15.208295 0.50137 920
1.9 -15.473451 -15.471370 -15.295051 -15.183856 0.61162 736
2.0 -15.446094 -15.443155 -15.283153 -15.156901 0.75679 2208

H2O

Score for molecule: 2.112695

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 -73.137144 -72.085718 -72.059740 0.02422 1675
0.6 -74.146204 -74.145224 -73.205037 -73.177065 0.028679 737
0.7 -74.643693 -74.643329 -73.845590 -73.813143 0.040199 603
0.8 -74.883002 -74.882691 -74.229468 -74.190448 0.059231 670
0.9 -74.987693 -74.987478 -74.463993 -74.416113 0.091017 2211
1.0 -75.019855 -75.019433 -74.606163 -74.548301 0.13885 536
1.1 -75.012625 -75.012196 -74.689275 -74.619565 0.21426 2077
1.2 -74.985126 -74.984576 -74.734667 -74.651382 0.33033 737
1.3 -74.948779 -74.947116 -74.756594 -74.657262 0.50821 737
1.4 -74.910271 -74.909508 -74.764526 -74.649148 0.7864 2412
1.5 -74.873436 -74.872992 -74.764648 -74.631939 1.2158 1407
1.6 -74.840495 -74.840164 -74.760965 -74.610309 1.8902 2144
1.7 -74.812706 -74.812022 -74.756009 -74.586466 2.9783 871
1.8 -74.790571 -74.789805 -74.751236 -74.562802 4.771 1273
1.9 -74.773909 -74.772718 -74.747304 -74.540452 7.7301 1005
2.0 -74.761988 -74.760377 -74.744346 -74.513447 12.996 2479