Competition
Calculating excitation gaps of small molecules (ES-Gap)
Record Detail

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Overview

Author
QunaSys
Date
20191005
Case
1 (Expectation value)
Method
Algorithm
MCVQE
Ansatz
HardwareEfficient, depth=8
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
3.61566

Data

Summary

Molecule Mean score Mean # of func. eval.
H2line 0.000002 2053.500000
H4line 0.853120 15877.500000
H4ring 7.821001 11753.000000
H6line 3.291478 23244.250000
H6ring 0.601509 23857.375000
LiH 14.396092 5177.500000
BeH2 0.526172 35560.000000
H2O 1.435869 7223.125000
all 3.615655 15593.281250

H2

Score for molecule: 0.000002

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 -1.055159 0.267000 0.267000 6.2931e-07 10434
0.6 -1.116286 -1.116285 0.036501 0.036501 7.717e-07 962
0.7 -1.136189 -1.136189 -0.120452 -0.120452 7.3008e-07 1554
0.8 -1.134148 -1.134146 -0.227924 -0.227924 1.9214e-06 1258
0.9 -1.120560 -1.120558 -0.301706 -0.301706 2.688e-06 1332
1.0 -1.101150 -1.101147 -0.352291 -0.352291 3.9419e-06 1036
1.1 -1.079193 -1.079192 -0.386515 -0.386515 1.2112e-06 1702
1.2 -1.056741 -1.056739 -0.408860 -0.408860 2.1073e-06 1332
1.3 -1.035186 -1.035185 -0.422402 -0.422402 1.8681e-06 1702
1.4 -1.015468 -1.015466 -0.429384 -0.429384 4.2056e-06 1628
1.5 -0.998149 -0.998146 -0.431513 -0.431513 5.6276e-06 1480
1.6 -0.983473 -0.983470 -0.430109 -0.430109 4.8536e-06 1554
1.7 -0.971427 -0.971426 -0.426192 -0.426192 7.7822e-07 2442
1.8 -0.961817 -0.961817 -0.420541 -0.420541 7.6659e-07 1480
1.9 -0.954339 -0.954338 -0.413749 -0.413749 1.4774e-06 1332
2.0 -0.948641 -0.948640 -0.406260 -0.406260 1.4554e-06 1628

H4 (line)

Score for molecule: 0.853120

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 -0.594868 -0.622827 0.163866 0.26357 78840
0.6 -1.960194 -1.064537 -1.096479 -0.484840 0.32883 3796
0.7 -2.106997 -1.330592 -1.365653 -0.884338 0.39805 4088
0.8 -2.167561 -1.477434 -1.514584 -1.132095 0.47113 4234
0.9 -2.180317 -1.552524 -1.590935 -1.285323 0.54664 4234
1.0 -2.166387 -1.584017 -1.649658 -1.380100 0.60537 4380
1.1 -2.137971 -1.588725 -1.712390 -1.437956 0.64573 2920
1.2 -2.102608 -1.576764 -1.755108 -1.472226 0.69917 4380
1.3 -2.065229 -1.554431 -1.784935 -1.491184 0.77436 4234
1.4 -2.029070 -1.525748 -1.806226 -1.499056 0.88022 3796
1.5 -1.996150 -1.498229 -1.821715 -1.493128 0.97076 3942
1.6 -1.967560 -1.490795 -1.833158 -1.458036 0.75626 3796
1.7 -1.943692 -1.464832 -1.841705 -1.421951 0.57953 16206
1.8 -1.924431 -1.424829 -1.848128 -1.385868 0.48938 4526
1.9 -1.909332 -1.601296 -1.852960 -1.252481 5.1877 98988
2.0 -1.897781 -1.074973 -1.856584 -1.035967 0.053172 11680

H4 (ring)

Score for molecule: 7.821001

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 -0.344936 -0.516291 2.252618 26.681 30222
0.6 -1.191866 -1.002721 -1.074424 1.191213 17.681 13578
0.7 -1.528728 -1.383367 -1.394620 0.487084 12.947 6424
0.8 -1.728281 -1.585976 -1.586733 -0.013329 10.11 17666
0.9 -1.846741 -1.716146 -1.699536 -0.342490 8.3316 4380
1.0 -1.915107 -1.732767 -1.764318 -0.645731 6.209 21608
1.1 -1.951594 -1.781292 -1.799889 -0.811207 5.3945 4088
1.2 -1.967550 -1.812424 -1.818375 -0.925059 4.9485 8468
1.3 -1.970378 -1.797955 -1.827838 -1.038184 4.3303 19272
1.4 -1.965081 -1.776066 -1.833411 -1.123859 3.9534 3066
1.5 -1.955125 -1.753314 -1.837877 -1.186394 3.8352 13432
1.6 -1.942939 -1.725534 -1.842283 -1.236224 3.8612 3942
1.7 -1.930208 -1.693755 -1.846685 -1.277504 3.9837 5256
1.8 -1.918054 -1.658427 -1.850812 -1.313133 4.1351 13286
1.9 -1.907157 -1.621010 -1.854423 -1.344354 4.2463 10804
2.0 -1.897849 -1.588192 -1.857411 -1.366284 4.4875 12556

H6 (line)

Score for molecule: 3.291478

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 0.274657 -1.370202 3.508183 2.7823 149766
0.6 -2.796419 -0.803068 -2.092813 1.578452 2.3847 43164
0.7 -3.077995 -1.439524 -2.480042 0.407939 2.0896 7194
0.8 -3.204412 -1.819717 -2.679755 -0.329684 1.84 4360
0.9 -3.244542 -2.044650 -2.770171 -0.810798 1.601 9592
1.0 -3.236066 -2.173226 -2.845129 -1.134506 1.657 4142
1.1 -3.200684 -2.242263 -2.880194 -1.357550 1.7605 5014
1.2 -3.151729 -2.273963 -2.890590 -1.513004 1.914 10028
1.3 -3.097826 -2.280824 -2.887273 -1.621133 2.1331 4360
1.4 -3.044600 -2.274937 -2.877099 -1.695424 2.4597 7630
1.5 -2.995565 -2.258573 -2.864310 -1.745224 2.9111 9156
1.6 -2.952668 -2.236210 -2.851423 -1.777083 3.5348 19402
1.7 -2.916689 -2.209695 -2.839788 -1.796289 4.3758 5668
1.8 -2.887569 -2.176690 -2.829994 -1.802712 5.4954 75428
1.9 -2.864703 -2.145569 -2.822145 -1.806348 6.9708 11554
2.0 -2.847192 -2.109124 -2.816081 -1.805681 8.7536 5450

H6 (ring)

Score for molecule: 0.601509

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 0.533154 -0.347911 1.211523 0.51021 88290
0.6 -2.529473 -0.697831 -1.444157 -0.158493 0.50306 5232
0.7 -2.935542 -1.399456 -2.068995 -0.999602 0.53857 6976
0.8 -3.134937 -1.806747 -2.434334 -1.535672 0.61308 20710
0.9 -3.219318 -2.077738 -2.648379 -1.820406 0.54928 22672
1.0 -3.237477 -2.202195 -2.771400 -2.056716 0.68786 32482
1.1 -3.217049 -2.290757 -2.838464 -2.188969 0.73114 33354
1.2 -3.174998 -2.343842 -2.870746 -2.216986 0.58306 19620
1.3 -3.122534 -2.314567 -2.881621 -2.299488 0.93741 12862
1.4 -3.067346 -2.335283 -2.879867 -2.259267 0.59453 26378
1.5 -3.014648 -2.363936 -2.871343 -2.173639 0.32791 10464
1.6 -2.967691 -2.319965 -2.859930 -2.177125 0.32554 19184
1.7 -2.928060 -2.245593 -2.848091 -2.231815 0.82771 30956
1.8 -2.896015 -2.227535 -2.837244 -2.186313 0.29859 23108
1.9 -2.870937 -2.226598 -2.828055 -2.121380 1.4537 10246
2.0 -2.851786 -2.165069 -2.820683 -2.129533 0.14253 19184

LiH

Score for molecule: 14.396092

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 -6.631405 -6.990633 -4.276557 38.516 23762
0.6 -7.319319 -6.802681 -7.238552 -4.685274 25.216 2180
0.7 -7.505052 -6.905200 -7.402653 -4.966507 17.933 1090
0.8 -7.634167 -6.969822 -7.514699 -5.163210 14.122 654
0.9 -7.723424 -7.014125 -7.591579 -5.300154 12 654
1.0 -7.784460 -7.049227 -7.644499 -5.392818 10.835 1962
1.1 -7.825537 -7.074208 -7.681108 -5.459049 10.183 1744
1.2 -7.852431 -7.095225 -7.706531 -5.503835 9.9074 2616
1.3 -7.869140 -7.109906 -7.724156 -5.536667 9.8511 872
1.4 -7.878454 -7.124352 -7.736236 -5.556566 10.024 3706
1.5 -7.882362 -7.133288 -7.744300 -5.572052 10.308 1090
1.6 -7.882324 -7.140401 -7.749415 -5.581847 10.726 654
1.7 -7.879434 -7.148429 -7.752348 -5.584991 11.302 12644
1.8 -7.874524 -7.153104 -7.753661 -5.587070 11.957 1090
1.9 -7.868241 -7.157036 -7.753774 -5.586320 12.722 654
2.0 -7.861088 -7.225852 -7.752995 -5.525152 14.734 27468

BeH2

Score for molecule: 0.526172

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 -11.345604 -13.380043 -10.956123 0.25672 96520
0.6 -14.405649 -12.291260 -14.095460 -11.902067 0.2547 39624
0.7 -14.871330 -12.848634 -14.559923 -12.478731 0.18784 11684
0.8 -15.172805 -13.197977 -14.861490 -12.813576 0.23477 14986
0.9 -15.364151 -13.458305 -15.055753 -13.101744 0.15617 145288
1.0 -15.481741 -13.650853 -15.179340 -13.297786 0.16754 20828
1.1 -15.549638 -13.825789 -15.255934 -13.475112 0.19398 10414
1.2 -15.583812 -13.962357 -15.300966 -13.614757 0.22893 9906
1.3 -15.595047 -14.081787 -15.324723 -13.710951 0.37182 14986
1.4 -15.590743 -14.213229 -15.334210 -13.844375 0.43784 60452
1.5 -15.576051 -14.282061 -15.334269 -13.939776 0.41567 47752
1.6 -15.554624 -14.361464 -15.328291 -13.997368 0.60868 29464
1.7 -15.529121 -14.428479 -15.318687 -14.067293 0.71638 10160
1.8 -15.501545 -14.485093 -15.307190 -14.127290 0.84098 7620
1.9 -15.473451 -14.532815 -15.295051 -14.178923 0.9837 25654
2.0 -15.446094 -14.340100 -15.283153 -13.792125 2.363 23622

H2O

Score for molecule: 1.435869

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 -70.825791 -72.085718 -70.068565 0.28015 23876
0.6 -74.146204 -72.050796 -73.205037 -71.608318 0.52986 762
0.7 -74.643693 -72.812760 -73.845590 -72.528906 0.64434 762
0.8 -74.883002 -73.313342 -74.229468 -73.105919 0.68261 762
0.9 -74.987693 -73.647690 -74.463993 -73.479487 0.67882 762
1.0 -75.019855 -73.869172 -74.606163 -73.724400 0.65005 762
1.1 -75.012625 -74.011566 -74.689275 -73.882916 0.60213 762
1.2 -74.985126 -74.098195 -74.734667 -73.981439 0.53384 762
1.3 -74.948779 -74.145827 -74.756594 -74.038071 0.43931 762
1.4 -74.910271 -74.164531 -74.764526 -74.088872 0.48088 18796
1.5 -74.873436 -74.140723 -74.764648 -73.901817 1.1961 31750
1.6 -74.840495 -74.180218 -74.760965 -73.975633 1.5724 7366
1.7 -74.812706 -74.208865 -74.756009 -74.030887 2.1391 762
1.8 -74.790571 -74.229410 -74.751236 -74.071846 3.0057 762
1.9 -74.773909 -74.243874 -74.747304 -74.100822 4.3768 762
2.0 -74.761988 -74.271371 -74.744346 -74.162662 5.1618 25400