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
MCVQE
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
1.42782

Data

Summary

Molecule Mean score Mean # of func. eval.
H2line 0.000000 16.750000
H4line 2.215663 205.000000
H4ring 2.034061 180.000000
H6line 2.871602 1109.500000
H6ring 2.374321 1004.500000
LiH 0.113110 445.625000
BeH2 0.232451 1150.000000
H2O 1.581369 1289.750000
all 1.427822 675.140625

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 3.3588e-16 24
0.6 -1.116286 -1.116286 0.036501 0.036501 1.9262e-16 16
0.7 -1.136189 -1.136189 -0.120452 -0.120452 2.5139e-14 16
0.8 -1.134148 -1.134148 -0.227924 -0.227924 5.8805e-15 16
0.9 -1.120560 -1.120560 -0.301706 -0.301706 1.3558e-14 16
1.0 -1.101150 -1.101150 -0.352291 -0.352291 7.3535e-14 16
1.1 -1.079193 -1.079193 -0.386515 -0.386515 1.1861e-14 16
1.2 -1.056741 -1.056741 -0.408860 -0.408860 1.0008e-13 20
1.3 -1.035186 -1.035186 -0.422402 -0.422402 1.2537e-13 16
1.4 -1.015468 -1.015468 -0.429384 -0.429384 1.0873e-13 16
1.5 -0.998149 -0.998149 -0.431513 -0.431513 8.2292e-15 16
1.6 -0.983473 -0.983473 -0.430109 -0.430109 3.1499e-14 16
1.7 -0.971427 -0.971427 -0.426192 -0.426192 4.0725e-15 16
1.8 -0.961817 -0.961817 -0.420541 -0.420541 3.692e-15 16
1.9 -0.954339 -0.954339 -0.413749 -0.413749 5.1754e-14 16
2.0 -0.948641 -0.948641 -0.406260 -0.406260 1.0071e-13 16

H4 (line)

Score for molecule: 2.215663

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 -1.649204 -0.622827 -0.614247 0.00453 336
0.6 -1.960194 -1.955734 -1.096479 -1.087263 0.0055057 208
0.7 -2.106997 -2.102058 -1.365653 -1.355943 0.0064358 240
0.8 -2.167561 -2.162194 -1.514584 -1.504691 0.0069322 256
0.9 -2.180317 -2.174512 -1.590935 -1.581187 0.006691 224
1.0 -2.166387 -2.160315 -1.649658 -1.613574 0.05808 240
1.1 -2.137971 -2.131558 -1.712390 -1.619056 0.20424 176
1.2 -2.102608 -2.095706 -1.755108 -1.608051 0.40332 224
1.3 -2.065229 -2.057752 -1.784935 -1.587014 0.67944 208
1.4 -2.029070 -2.020930 -1.806226 -1.560214 1.0674 144
1.5 -1.996150 -1.987210 -1.821715 -1.530523 1.6181 192
1.6 -1.967560 -1.957909 -1.833158 -1.499521 2.4106 192
1.7 -1.943692 -1.933533 -1.841705 -1.468121 3.5635 192
1.8 -1.924431 -1.914147 -1.848128 -1.436574 5.259 128
1.9 -1.909332 -1.898459 -1.852960 -1.374827 8.2888 144
2.0 -1.897781 -1.885622 -1.856584 -1.355501 11.868 176

H4 (ring)

Score for molecule: 2.034061

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 -0.609985 -0.516291 -0.516265 0.0012628 416
0.6 -1.191866 -1.191602 -1.074424 -1.074387 0.001924 112
0.7 -1.528728 -1.528294 -1.394620 -1.388185 0.044747 224
0.8 -1.728281 -1.727591 -1.586733 -1.565310 0.14648 144
0.9 -1.846741 -1.845704 -1.699536 -1.661720 0.24985 208
1.0 -1.915107 -1.913625 -1.764318 -1.708074 0.36318 144
1.1 -1.951594 -1.949540 -1.799889 -1.722397 0.49726 160
1.2 -1.967550 -1.964829 -1.818375 -1.715918 0.66859 144
1.3 -1.970378 -1.966891 -1.827838 -1.696081 0.8999 160
1.4 -1.965081 -1.960807 -1.833411 -1.667898 1.2246 160
1.5 -1.955125 -1.950113 -1.837877 -1.634883 1.6886 176
1.6 -1.942939 -1.937331 -1.842283 -1.599491 2.3564 144
1.7 -1.930208 -1.924218 -1.846685 -1.563452 3.3194 144
1.8 -1.918054 -1.911931 -1.850812 -1.527954 4.7104 192
1.9 -1.907157 -1.901133 -1.854423 -1.493792 6.7245 192
2.0 -1.897849 -1.892096 -1.857411 -1.461505 9.648 160

H6 (line)

Score for molecule: 2.871602

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 -2.220516 -1.370202 -1.350932 0.017172 1512
0.6 -2.796419 -2.791423 -2.092813 -2.071923 0.022589 1288
0.7 -3.077995 -3.072550 -2.480042 -2.457806 0.02808 1288
0.8 -3.204412 -3.198673 -2.679755 -2.656518 0.033352 1120
0.9 -3.244542 -3.238382 -2.770171 -2.746511 0.036891 1232
1.0 -3.236066 -3.229548 -2.845129 -2.771865 0.17073 1064
1.1 -3.200684 -3.193655 -2.880194 -2.758813 0.3568 1400
1.2 -3.151729 -3.143966 -2.890590 -2.723258 0.61105 1232
1.3 -3.097826 -3.089182 -2.887273 -2.675129 0.96651 1064
1.4 -3.044600 -3.034554 -2.877099 -2.621366 1.4668 840
1.5 -2.995565 -2.983923 -2.864310 -2.565995 2.1841 840
1.6 -2.952668 -2.939174 -2.851423 -2.511973 3.2194 1176
1.7 -2.916689 -2.901522 -2.839788 -2.460776 4.7314 1064
1.8 -2.887569 -2.870874 -2.829994 -2.413804 6.9386 1064
1.9 -2.864703 -2.847287 -2.822145 -2.370971 10.192 784
2.0 -2.847192 -2.829546 -2.816081 -2.332704 14.97 784

H6 (ring)

Score for molecule: 2.374321

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 -1.732791 -0.347911 -0.297046 0.036627 1624
0.6 -2.529473 -2.529264 -1.444157 -1.379086 0.059764 728
0.7 -2.935542 -2.935232 -2.068995 -1.988503 0.092532 840
0.8 -3.134937 -3.134499 -2.434334 -2.337279 0.1379 1008
0.9 -3.219318 -3.218678 -2.648379 -2.533400 0.20026 1120
1.0 -3.237477 -3.236544 -2.771400 -2.636800 0.28679 952
1.1 -3.217049 -3.215658 -2.838464 -2.682320 0.40876 952
1.2 -3.174998 -3.172877 -2.870746 -2.691028 0.58372 952
1.3 -3.122534 -3.119186 -2.881621 -2.676297 0.83838 1176
1.4 -3.067346 -3.062312 -2.879867 -2.646983 1.2153 1120
1.5 -3.014648 -3.006886 -2.871343 -2.609409 1.7736 1008
1.6 -2.967691 -2.956385 -2.859930 -2.567981 2.6043 896
1.7 -2.928060 -2.912421 -2.848091 -2.525837 3.8342 1008
1.8 -2.896015 -2.875106 -2.837244 -2.485169 5.6349 952
1.9 -2.870937 -2.843077 -2.828055 -2.447514 8.2244 840
2.0 -2.851786 -2.819812 -2.820683 -2.413679 12.058 896

LiH

Score for molecule: 0.113110

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 -7.048043 -6.990633 -6.980421 0.13476 1242
0.6 -7.319319 -7.315703 -7.238552 -7.224652 0.12733 874
0.7 -7.505052 -7.499323 -7.402653 -7.385928 0.10739 414
0.8 -7.634167 -7.627772 -7.514699 -7.495201 0.10967 414
0.9 -7.723424 -7.715664 -7.591579 -7.571479 0.093605 368
1.0 -7.784460 -7.776616 -7.644499 -7.623445 0.094379 230
1.1 -7.825537 -7.817605 -7.681108 -7.659569 0.094218 184
1.2 -7.852431 -7.843997 -7.706531 -7.685190 0.08846 460
1.3 -7.869140 -7.860692 -7.724156 -7.702364 0.092038 276
1.4 -7.878454 -7.869794 -7.736236 -7.714020 0.095314 322
1.5 -7.882362 -7.873356 -7.744300 -7.721547 0.099563 368
1.6 -7.882324 -7.873039 -7.749415 -7.725750 0.10819 322
1.7 -7.879434 -7.869627 -7.752348 -7.727697 0.11681 368
1.8 -7.874524 -7.864396 -7.753661 -7.727414 0.13337 276
1.9 -7.868241 -7.857424 -7.753774 -7.725986 0.14826 506
2.0 -7.861088 -7.849470 -7.752995 -7.723390 0.1664 506

BeH2

Score for molecule: 0.232451

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 -13.687855 -13.380043 -13.353224 0.079741 2300
0.6 -14.405649 -14.404124 -14.095460 -14.060730 0.10705 1380
0.7 -14.871330 -14.870002 -14.559923 -14.520005 0.12392 1196
0.8 -15.172805 -15.171428 -14.861490 -14.819100 0.13174 1564
0.9 -15.364151 -15.362907 -15.055753 -15.011737 0.13869 1656
1.0 -15.481741 -15.480270 -15.179340 -15.134153 0.14456 828
1.1 -15.549638 -15.547946 -15.255934 -15.209021 0.15396 644
1.2 -15.583812 -15.581725 -15.300966 -15.251596 0.16717 460
1.3 -15.595047 -15.592628 -15.324723 -15.272156 0.18551 644
1.4 -15.590743 -15.587731 -15.334210 -15.277481 0.2094 828
1.5 -15.576051 -15.572231 -15.334269 -15.272572 0.23938 920
1.6 -15.554624 -15.549756 -15.328291 -15.260549 0.27779 828
1.7 -15.529121 -15.523313 -15.318687 -15.243534 0.32953 1012
1.8 -15.501545 -15.494323 -15.307190 -15.223698 0.39242 1012
1.9 -15.473451 -15.464463 -15.295051 -15.202074 0.47079 1012
2.0 -15.446094 -15.434921 -15.283153 -15.179500 0.56757 2116

H2O

Score for molecule: 1.581369

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 -73.132154 -72.085718 -72.073995 0.0059252 1809
0.6 -74.146204 -74.141377 -73.205037 -73.190021 0.010825 1340
0.7 -74.643693 -74.638459 -73.845590 -73.826524 0.017331 335
0.8 -74.883002 -74.877194 -74.229468 -74.206104 0.026863 737
0.9 -74.987693 -74.980848 -74.463993 -74.434803 0.042667 1809
1.0 -75.019855 -75.011660 -74.606163 -74.568249 0.07184 469
1.1 -75.012625 -75.003433 -74.689275 -74.643102 0.11437 1876
1.2 -74.985126 -74.974466 -74.734667 -74.677689 0.18493 737
1.3 -74.948779 -74.936929 -74.756594 -74.686961 0.30067 737
1.4 -74.910271 -74.897379 -74.764526 -74.680837 0.48576 1675
1.5 -74.873436 -74.859793 -74.764648 -74.665629 0.7848 938
1.6 -74.840495 -74.827521 -74.760965 -74.643914 1.3087 2345
1.7 -74.812706 -74.798265 -74.756009 -74.621784 2.1127 804
1.8 -74.790571 -74.776373 -74.751236 -74.598090 3.5324 1206
1.9 -74.773909 -74.758947 -74.747304 -74.575492 5.8954 1005
2.0 -74.761988 -74.747005 -74.744346 -74.545763 10.407 2814