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
SymmetryPreserving, depth=20
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
0.55499

Data

Summary

Molecule Mean score Mean # of func. eval.
H2line 0.469194 1577.125000
H4line 0.550370 70112.500000
H4ring 0.493115 58965.500000
H6line 0.653903 74578.125000
H6ring 0.807708 31468.500000
LiH 0.194728 8033.625000
BeH2 0.553429 20550.625000
H2O 0.717446 8384.000000
all 0.554986 34208.750000

H2

Score for molecule: 0.469194

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 -0.866721 0.267000 0.078562 0.28505 2480
0.6 -1.116286 -0.946484 0.036501 -0.133301 0.29459 1550
0.7 -1.136189 -0.980395 -0.120452 -0.276246 0.30676 1488
0.8 -1.134148 -0.988599 -0.227924 -0.373473 0.32122 1426
0.9 -1.120560 -0.981760 -0.301706 -0.440506 0.33901 1426
1.0 -1.101150 -0.966030 -0.352291 -0.487411 0.36087 1364
1.1 -1.079193 -0.944939 -0.386515 -0.520769 0.38764 1550
1.2 -1.056741 -0.920870 -0.408860 -0.544731 0.41943 1612
1.3 -1.035186 -0.895495 -0.422402 -0.562093 0.45592 1488
1.4 -1.015468 -0.870026 -0.429384 -0.574826 0.49632 1550
1.5 -0.998149 -0.845415 -0.431513 -0.584247 0.53909 1550
1.6 -0.983473 -0.822367 -0.430109 -0.591214 0.58228 1550
1.7 -0.971427 -0.801112 -0.426192 -0.596506 0.62474 1488
1.8 -0.961817 -0.782010 -0.420541 -0.600347 0.66438 1612
1.9 -0.954339 -0.765223 -0.413749 -0.602862 0.69966 1550
2.0 -0.948641 -0.750631 -0.406260 -0.604267 0.73014 1550

H4 (line)

Score for molecule: 0.550370

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 -1.639015 -0.622827 -0.624347 0.015163 59782
0.6 -1.960194 -1.943031 -1.096479 -1.096912 0.020373 8804
0.7 -2.106997 -2.089836 -1.365653 -1.363340 0.020028 38056
0.8 -2.167561 -2.144907 -1.514584 -1.511473 0.029929 7810
0.9 -2.180317 -2.149477 -1.590935 -1.588599 0.048363 21726
1.0 -2.166387 -2.127975 -1.649658 -1.618526 0.01409 8946
1.1 -2.137971 -2.089540 -1.712390 -1.621186 0.10051 3692
1.2 -2.102608 -2.041733 -1.755108 -1.606866 0.25141 7952
1.3 -2.065229 -1.991135 -1.784935 -1.581144 0.46272 20590
1.4 -2.029070 -1.936114 -1.806226 -1.550207 0.73173 5538
1.5 -1.996150 -1.883040 -1.821715 -1.642644 0.37813 117008
1.6 -1.967560 -1.844626 -1.833158 -1.636533 0.54828 128368
1.7 -1.943692 -1.806318 -1.841705 -1.624573 0.78204 47428
1.8 -1.924431 -1.768190 -1.848128 -1.620611 0.93413 131066
1.9 -1.909332 -1.643922 -1.852960 -1.602569 0.26644 221662
2.0 -1.897781 -1.785204 -1.856584 -1.570875 4.2026 293372

H4 (ring)

Score for molecule: 0.493115

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 -0.590791 -0.516291 -0.483479 0.14358 214420
0.6 -1.191866 -1.167329 -1.074424 -1.051849 0.016702 6390
0.7 -1.528728 -1.493586 -1.394620 -1.380329 0.15548 52398
0.8 -1.728281 -1.685609 -1.586733 -1.567921 0.16856 4828
0.9 -1.846741 -1.811118 -1.699536 -1.680038 0.10953 89034
1.0 -1.915107 -1.874285 -1.764318 -1.737383 0.092086 8662
1.1 -1.951594 -1.903570 -1.799889 -1.764233 0.08153 14484
1.2 -1.967550 -1.913398 -1.818375 -1.768615 0.029437 4828
1.3 -1.970378 -1.902801 -1.827838 -1.767642 0.051778 49700
1.4 -1.965081 -1.890968 -1.833411 -1.750371 0.067804 7526
1.5 -1.955125 -1.832271 -1.837877 -1.766659 0.4404 45724
1.6 -1.942939 -1.826785 -1.842283 -1.736671 0.10473 67024
1.7 -1.930208 -1.809275 -1.846685 -1.706449 0.23112 14200
1.8 -1.918054 -1.832912 -1.850812 -1.676523 1.3258 146260
1.9 -1.907157 -1.806082 -1.854423 -1.654204 1.8801 104228
2.0 -1.897849 -1.793998 -1.857411 -1.632597 2.9912 113742

H6 (line)

Score for molecule: 0.653903

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 -2.173208 -1.370202 -1.382581 0.075187 156732
0.6 -2.796419 -2.764626 -2.092813 -2.074306 0.018882 97014
0.7 -3.077995 -3.038195 -2.480042 -2.457323 0.028568 68598
0.8 -3.204412 -3.153763 -2.679755 -2.652868 0.045289 55500
0.9 -3.244542 -3.181876 -2.770171 -2.736925 0.062019 25530
1.0 -3.236066 -3.159027 -2.845129 -2.760019 0.020644 59052
1.1 -3.200684 -3.105410 -2.880194 -2.738427 0.14507 56832
1.2 -3.151729 -3.034476 -2.890590 -2.695473 0.29817 26640
1.3 -3.097826 -2.953978 -2.887273 -2.638353 0.49903 14874
1.4 -3.044600 -2.869647 -2.877099 -2.573671 0.767 6660
1.5 -2.995565 -2.787051 -2.864310 -2.542573 0.86261 101454
1.6 -2.952668 -2.700132 -2.851423 -2.529913 0.68124 192474
1.7 -2.916689 -2.626896 -2.839788 -2.465038 1.1048 132534
1.8 -2.887569 -2.551786 -2.829994 -2.412628 1.4169 116328
1.9 -2.864703 -2.483092 -2.822145 -2.360165 1.8884 43734
2.0 -2.847192 -2.419380 -2.816081 -2.308981 2.5486 39294

H6 (ring)

Score for molecule: 0.807708

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 -0.176609 -0.347911 1.220465 0.0087056 49284
0.6 -2.529473 -1.264450 -1.444157 -0.147208 0.029417 7770
0.7 -2.935542 -1.875213 -2.068995 -0.985881 0.026295 12210
0.8 -3.134937 -2.213717 -2.434334 -1.519854 0.0096203 22200
0.9 -3.219318 -3.150235 -2.648379 -2.516723 0.1096 112554
1.0 -3.237477 -3.157047 -2.771400 -2.616421 0.15995 29526
1.1 -3.217049 -3.122506 -2.838464 -2.657901 0.22721 37074
1.2 -3.174998 -3.062703 -2.870746 -2.661451 0.31881 24198
1.3 -3.122534 -2.987941 -2.881621 -2.640673 0.44147 25752
1.4 -3.067346 -2.905086 -2.879867 -2.603451 0.6089 27972
1.5 -3.014648 -2.818756 -2.871343 -2.556900 0.82726 21978
1.6 -2.967691 -2.732113 -2.859930 -2.504525 1.112 22866
1.7 -2.928060 -2.647344 -2.848091 -2.449615 1.4726 28638
1.8 -2.896015 -2.565972 -2.837244 -2.394145 1.9237 30414
1.9 -2.870937 -2.489033 -2.828055 -2.339833 2.4793 21534
2.0 -2.851786 -2.417176 -2.820683 -2.287520 3.1686 29526

LiH

Score for molecule: 0.194728

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 -7.029009 -6.990633 -6.984262 0.24909 53058
0.6 -7.319319 -7.299019 -7.238552 -7.234585 0.20222 13764
0.7 -7.505052 -7.484733 -7.402653 -7.400747 0.17981 3108
0.8 -7.634167 -7.614312 -7.514699 -7.513497 0.15613 888
0.9 -7.723424 -7.703684 -7.591579 -7.592431 0.15618 6438
1.0 -7.784460 -7.765197 -7.644499 -7.645786 0.14683 888
1.1 -7.825537 -7.806634 -7.681108 -7.682576 0.14105 2442
1.2 -7.852431 -7.833535 -7.706531 -7.708047 0.13991 1332
1.3 -7.869140 -7.849990 -7.724156 -7.725831 0.14364 4440
1.4 -7.878454 -7.858643 -7.736236 -7.737792 0.15024 888
1.5 -7.882362 -7.861581 -7.744300 -7.746286 0.16491 7326
1.6 -7.882324 -7.860265 -7.749415 -7.751218 0.17954 2220
1.7 -7.879434 -7.855746 -7.752348 -7.753826 0.19802 1998
1.8 -7.874524 -7.847537 -7.753661 -7.758010 0.25926 19092
1.9 -7.868241 -7.838809 -7.753774 -7.758385 0.2974 4662
2.0 -7.861088 -7.828416 -7.752995 -7.758308 0.3514 5994

BeH2

Score for molecule: 0.553429

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 -13.102307 -13.380043 -12.910206 0.38015 41134
0.6 -14.405649 -13.809719 -14.095460 -13.526316 0.086356 26724
0.7 -14.871330 -14.244754 -14.559923 -13.935357 0.0064541 13362
0.8 -15.172805 -14.526453 -14.861490 -14.200458 0.047152 21222
0.9 -15.364151 -14.525768 -15.055753 -14.184306 0.10721 28558
1.0 -15.481741 -15.052389 -15.179340 -14.629287 0.39914 34322
1.1 -15.549638 -15.123247 -15.255934 -14.692860 0.46538 11790
1.2 -15.583812 -15.163503 -15.300966 -14.729544 0.53426 12576
1.3 -15.595047 -15.181937 -15.324723 -14.748006 0.60522 15720
1.4 -15.590743 -15.185540 -15.334210 -14.754165 0.68156 12052
1.5 -15.576051 -15.179173 -15.334269 -14.751857 0.76736 22270
1.6 -15.554624 -15.165811 -15.328291 -14.743481 0.86597 18078
1.7 -15.529121 -15.146774 -15.318687 -14.731340 0.97417 11266
1.8 -15.501545 -15.124267 -15.307190 -14.716602 1.0975 8122
1.9 -15.473451 -15.394520 -15.295051 -15.062033 0.86371 36156
2.0 -15.446094 -15.354412 -15.283153 -15.032890 0.97324 15458

H2O

Score for molecule: 0.717446

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 -73.051465 -72.085718 -71.750951 0.23632 20436
0.6 -74.146204 -74.080418 -73.205037 -72.843730 0.31399 7598
0.7 -74.643693 -74.578216 -73.845590 -73.486379 0.36804 1310
0.8 -74.883002 -74.816511 -74.229468 -73.874504 0.44141 786
0.9 -74.987693 -74.908637 -74.463993 -74.128131 0.49037 6026
1.0 -75.019855 -74.935563 -74.606163 -74.273861 0.59951 1572
1.1 -75.012625 -74.919136 -74.689275 -74.359219 0.73162 1310
1.2 -74.985126 -74.878092 -74.734667 -74.404518 0.89082 786
1.3 -74.948779 -74.823735 -74.756594 -74.423255 1.0838 786
1.4 -74.910271 -74.771157 -74.764526 -74.585644 0.27286 51876
1.5 -74.873436 -74.704150 -74.764648 -74.554503 0.37558 786
1.6 -74.840495 -74.637434 -74.760965 -74.515611 0.53179 25414
1.7 -74.812706 -74.572688 -74.756009 -74.475024 0.72258 786
1.8 -74.790571 -74.511122 -74.751236 -74.433242 0.97992 786
1.9 -74.773909 -74.453656 -74.747304 -74.391155 1.3492 786
2.0 -74.761988 -74.401167 -74.744346 -74.346629 2.0913 13100