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
VQD
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
1.10719

Data

Summary

Molecule Mean score Mean # of func. eval.
H2line 0.000000 30.625000
H4line 1.735547 449.000000
H4ring 2.004990 300.000000
H6line 1.250130 3244.500000
H6ring 2.309841 1491.000000
LiH 0.071946 1055.125000
BeH2 0.221119 2357.500000
H2O 1.263943 2487.375000
all 1.107189 1426.890625

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 7.6986e-11 40
0.6 -1.116286 -1.116286 0.036501 0.036501 7.512e-15 28
0.7 -1.136189 -1.136189 -0.120452 -0.120452 8.5256e-15 24
0.8 -1.134148 -1.134148 -0.227924 -0.227924 6.8606e-15 28
0.9 -1.120560 -1.120560 -0.301706 -0.301706 8.2705e-14 28
1.0 -1.101150 -1.101150 -0.352291 -0.352291 9.7552e-14 28
1.1 -1.079193 -1.079193 -0.386515 -0.386515 5.0328e-14 28
1.2 -1.056741 -1.056741 -0.408860 -0.408860 2.4745e-13 32
1.3 -1.035186 -1.035186 -0.422402 -0.422402 6.2687e-14 28
1.4 -1.015468 -1.015468 -0.429384 -0.429384 5.3798e-14 58
1.5 -0.998149 -0.998149 -0.431513 -0.431513 3.5464e-14 28
1.6 -0.983473 -0.983473 -0.430109 -0.430109 3.2502e-14 28
1.7 -0.971427 -0.971427 -0.426192 -0.426192 8.5522e-14 28
1.8 -0.961817 -0.961817 -0.420541 -0.420541 2.5844e-14 28
1.9 -0.954339 -0.954339 -0.413749 -0.413749 1.4458e-13 28
2.0 -0.948641 -0.948641 -0.406260 -0.406260 1.31e-13 28

H4 (line)

Score for molecule: 1.735547

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 -0.622041 0.00075628 480
0.6 -1.960194 -1.960188 -1.096479 -1.095718 0.00087425 336
0.7 -2.106997 -2.106988 -1.365653 -1.364940 0.0009496 352
0.8 -2.167561 -2.167544 -1.514584 -1.513921 0.00098964 384
0.9 -2.180317 -2.180280 -1.590935 -1.590320 0.00098154 432
1.0 -2.166387 -2.166304 -1.649658 -1.622912 0.051599 640
1.1 -2.137971 -2.137798 -1.712390 -1.628204 0.19741 256
1.2 -2.102608 -2.102281 -1.755108 -1.616686 0.39739 368
1.3 -2.065229 -2.064655 -1.784935 -1.594834 0.67617 352
1.4 -2.029070 -2.028136 -1.806226 -1.567516 1.067 432
1.5 -1.996150 -1.994730 -1.821715 -1.537173 1.6231 512
1.6 -1.967560 -1.965540 -1.833158 -1.505977 2.4193 480
1.7 -1.943692 -1.940995 -1.841705 -1.475281 3.5664 496
1.8 -1.924431 -1.921046 -1.848128 -1.445972 5.2262 400
1.9 -1.909332 -1.905336 -1.852960 -1.554149 5.2298 640
2.0 -1.897781 -1.893337 -1.856584 -1.551001 7.3098 624

H4 (ring)

Score for molecule: 2.004990

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 -0.516291 0.0012879 576
0.6 -1.191866 -1.191648 -1.074424 -1.074425 0.0018515 240
0.7 -1.528728 -1.528369 -1.394620 -1.388269 0.044672 320
0.8 -1.728281 -1.727730 -1.586733 -1.565491 0.14618 256
0.9 -1.846741 -1.845949 -1.699536 -1.662064 0.24918 304
1.0 -1.915107 -1.914017 -1.764318 -1.708682 0.36174 272
1.1 -1.951594 -1.950146 -1.799889 -1.723365 0.49488 224
1.2 -1.967550 -1.965692 -1.818375 -1.717392 0.66449 256
1.3 -1.970378 -1.968072 -1.827838 -1.698172 0.89352 240
1.4 -1.965081 -1.962324 -1.833411 -1.670724 1.2146 256
1.5 -1.955125 -1.951956 -1.837877 -1.638517 1.6733 208
1.6 -1.942939 -1.939451 -1.842283 -1.604425 2.3284 416
1.7 -1.930208 -1.926539 -1.846685 -1.569513 3.2746 208
1.8 -1.918054 -1.914373 -1.850812 -1.535121 4.6402 288
1.9 -1.907157 -1.903633 -1.854423 -1.502242 6.6117 448
2.0 -1.897849 -1.894623 -1.857411 -1.470854 9.4792 288

H6 (line)

Score for molecule: 1.250130

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 -2.225022 -1.370202 -1.359398 0.012539 2856
0.6 -2.796419 -2.796293 -2.092813 -2.080604 0.017173 2520
0.7 -3.077995 -3.077810 -2.480042 -2.466619 0.022138 2408
0.8 -3.204412 -3.204137 -2.679755 -2.665466 0.026711 2520
0.9 -3.244542 -3.244132 -2.770171 -2.755263 0.030562 2632
1.0 -3.236066 -3.235439 -2.845129 -2.780418 0.16392 2240
1.1 -3.200684 -3.199705 -2.880194 -2.767056 0.34996 2072
1.2 -3.151729 -3.150212 -2.890590 -2.731216 0.6045 2184
1.3 -3.097826 -3.095513 -2.887273 -2.682893 0.95971 2184
1.4 -3.044600 -3.041198 -2.877099 -2.628631 1.4631 1064
1.5 -2.995565 -2.990777 -2.864310 -2.582452 2.1109 7000
1.6 -2.952668 -2.946276 -2.851423 -2.685814 1.5726 7672
1.7 -2.916689 -2.908621 -2.839788 -2.677785 2.0017 4424
1.8 -2.887569 -2.877960 -2.829994 -2.686682 2.3222 5264
1.9 -2.864703 -2.853893 -2.822145 -2.668645 3.3528 2352
2.0 -2.847192 -2.835697 -2.816081 -2.649295 4.9916 2520

H6 (ring)

Score for molecule: 2.309841

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 -1.732814 -0.347911 -0.297081 0.036617 2520
0.6 -2.529473 -2.529299 -1.444157 -1.379150 0.059737 1344
0.7 -2.935542 -2.935289 -2.068995 -1.988608 0.092477 1344
0.8 -3.134937 -3.134582 -2.434334 -2.337462 0.13776 1568
0.9 -3.219318 -3.218824 -2.648379 -2.533687 0.20002 1624
1.0 -3.237477 -3.236788 -2.771400 -2.637275 0.2863 1680
1.1 -3.217049 -3.216072 -2.838464 -2.683101 0.40779 1512
1.2 -3.174998 -3.173577 -2.870746 -2.692289 0.58187 1400
1.3 -3.122534 -3.120398 -2.881621 -2.678322 0.83501 1400
1.4 -3.067346 -3.064122 -2.879867 -2.650274 1.2074 1344
1.5 -3.014648 -3.009738 -2.871343 -2.614518 1.7579 1120
1.6 -2.967691 -2.960384 -2.859930 -2.575637 2.5704 1120
1.7 -2.928060 -2.917657 -2.848091 -2.536944 3.7608 1736
1.8 -2.896015 -2.881973 -2.837244 -2.500670 5.488 1232
1.9 -2.870937 -2.852943 -2.828055 -2.468125 7.9738 1120
2.0 -2.851786 -2.830149 -2.820683 -2.439445 11.562 1792

LiH

Score for molecule: 0.071946

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 -7.050141 -6.990633 -6.980382 0.17063 3542
0.6 -7.319319 -7.319274 -7.238552 -7.231791 0.083149 1518
0.7 -7.505052 -7.505014 -7.402653 -7.396628 0.058475 1150
0.8 -7.634167 -7.634127 -7.514699 -7.508373 0.052612 920
0.9 -7.723424 -7.723382 -7.591579 -7.586607 0.037403 1748
1.0 -7.784460 -7.784412 -7.644499 -7.639023 0.038783 460
1.1 -7.825537 -7.825512 -7.681108 -7.675022 0.04196 460
1.2 -7.852431 -7.852406 -7.706531 -7.699796 0.04599 414
1.3 -7.869140 -7.869123 -7.724156 -7.716842 0.050326 690
1.4 -7.878454 -7.878438 -7.736236 -7.728096 0.05713 552
1.5 -7.882362 -7.882351 -7.744300 -7.736647 0.055349 1150
1.6 -7.882324 -7.882300 -7.749415 -7.740888 0.063971 644
1.7 -7.879434 -7.879407 -7.752348 -7.742831 0.074678 966
1.8 -7.874524 -7.874484 -7.753661 -7.742831 0.089284 736
1.9 -7.868241 -7.868182 -7.753774 -7.741716 0.10482 782
2.0 -7.861088 -7.861044 -7.752995 -7.739270 0.12657 1150

BeH2

Score for molecule: 0.221119

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 -13.689361 -13.380043 -13.356075 0.075401 4508
0.6 -14.405649 -14.405173 -14.095460 -14.062787 0.1038 3036
0.7 -14.871330 -14.870960 -14.559923 -14.521812 0.12119 2300
0.8 -15.172805 -15.172488 -14.861490 -14.820860 0.12949 2852
0.9 -15.364151 -15.363872 -15.055753 -15.013915 0.13476 3404
1.0 -15.481741 -15.481431 -15.179340 -15.136565 0.14043 1564
1.1 -15.549638 -15.549354 -15.255934 -15.211962 0.14875 1840
1.2 -15.583812 -15.583487 -15.300966 -15.255217 0.16059 1380
1.3 -15.595047 -15.594651 -15.324723 -15.276530 0.17681 1472
1.4 -15.590743 -15.590295 -15.334210 -15.282777 0.19874 1656
1.5 -15.576051 -15.575474 -15.334269 -15.278777 0.22712 2024
1.6 -15.554624 -15.553856 -15.328291 -15.267630 0.26463 1380
1.7 -15.529121 -15.528074 -15.318687 -15.252316 0.31042 2208
1.8 -15.501545 -15.500087 -15.307190 -15.233922 0.36948 1932
1.9 -15.473451 -15.471396 -15.295051 -15.213979 0.44291 2024
2.0 -15.446094 -15.443193 -15.283153 -15.193345 0.53337 4140

H2O

Score for molecule: 1.263943

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 -73.137576 -72.085718 -72.080760 0.0046486 2948
0.6 -74.146204 -74.145894 -73.205037 -73.197636 0.0075337 1809
0.7 -74.643693 -74.643527 -73.845590 -73.834713 0.01342 1005
0.8 -74.883002 -74.882812 -74.229468 -74.215272 0.021432 1675
0.9 -74.987693 -74.987505 -74.463993 -74.445200 0.035526 3015
1.0 -75.019855 -75.019299 -74.606163 -74.581848 0.057433 1407
1.1 -75.012625 -75.012463 -74.689275 -74.658440 0.094864 3618
1.2 -74.985126 -74.984689 -74.734667 -74.695960 0.1528 1675
1.3 -74.948779 -74.948450 -74.756594 -74.708843 0.24675 2211
1.4 -74.910271 -74.909881 -74.764526 -74.705660 0.40122 3886
1.5 -74.873436 -74.872792 -74.764648 -74.693428 0.64875 1541
1.6 -74.840495 -74.839968 -74.760965 -74.677339 1.0449 4288
1.7 -74.812706 -74.812079 -74.756009 -74.658274 1.7128 1675
1.8 -74.790571 -74.790077 -74.751236 -74.639616 2.8251 2077
1.9 -74.773909 -74.773152 -74.747304 -74.622251 4.6718 1876
2.0 -74.761988 -74.760476 -74.744346 -74.596681 8.2841 5092