H2O

BeyondH2 hardware VQE and fixed-parameter remeasurement · hardware · ibm_aachen

Final energy-4.0072314163hartree

Shots1024

Runtime executionsingle-job

Resilience0

MappingPT

Active space4e4o

Parity mapping with full symmetry tapering · Shots and precision · Resilience settings

Method

Mapper: PT
Ansatz: UCC
Optimizer: COBYLA
Maximum iterations: 40
Best energy (Ha): -4.19782

Execution

Mode: hardware
Provider: IBM Quantum
Compute resource: ibm_aachen
Resource type: quantum processor
Processor family: Heron
Processor model: ibm_aachen
Processor revision: 3
Qubits: 156
Connectivity: Not recorded
Runtime execution: single-job
Shots: 1024
Precision: 0.03125
Resilience: 0
Submitted: 2026-08-01T13:37:34+00:00
Wall time (s): 3791.95

Molecular system

Charge: 0
Multiplicity: 1
Basis: sto3g
Active space: 4e4o
Active electrons: 4
Spatial orbitals: 4
Active orbital indices: Not recorded
Geometry units: angstrom

Circuit

Logical qubits: 5
Physical qubits: 5
Parameters: 8
Depth: 2275
Two-qubit gates: 602
Hamiltonian terms: 155

Scientific provenance

Cohort: primary heron
Reference method: CASCI
Reference energy (Ha): -6.145813933438759
Energy convention: Qiskit Nature active-space qubit Hamiltonian; nuclear and inactive-space constants excluded
Absolute error (Ha): 2.13858
Signed error (Ha): 2.13858
Total QPU time (s): 720
Calibration time: 2026-08-01T11:56:48+00:00
Mean readout error: 0.0124267578125
Mean two-qubit gate error: 0.00305796024114062

Software

Qiskit: 1.4.3
Qiskit Aer: 0.17.1
Qiskit Algorithms: 0.3.1
Qiskit Ibm Runtime: 0.40.1
Qiskit Nature: 0.7.2

Molecular geometry (angstrom)

Atom	x	z
H	0	0
O	0	0.968544
H	0.941424	1.19631

Dataset publication

Data and analysis code for "The winner's curse in hardware VQE: drift-differenced remeasurement of finite-shot selection bias" version 1.1 · CC BY 4.0

Associated articles

The winner's curse in hardware VQE: drift-differenced remeasurement of finite-shot selection bias DOI 10.48550/arXiv.2609.27704 arXiv 2609.27704 published preprint

Compute access

Fraunhofer Quantum Now and EQeS · IBM Quantum · allocation: Fraunhofer Quantum Now

Optimization trajectory

40 recorded objective evaluations. Charts use cumulative time so convergence cost remains comparable across calculations.

Download trajectory CSV · Download trajectory JSON

Energy (Ha)

Signed reference error (mHa)

Cumulative quantum time (s)

Cumulative wall time (s)

Attempt	Outcome	Energy (Ha)	Elapsed (s)	Quantum (s)	Parameters
1	succeeded	-4.0948291659	271.651	18	[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
2	succeeded	-4.0297939326	90.837	18	[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
3	succeeded	-4.0546287813	90.9167	18	[0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
4	succeeded	-4.0620706723	90.9223	18	[0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]
5	succeeded	-4.0230027231	90.7482	18	[0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]
6	succeeded	-4.0985394415	90.7523	18	[0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]
7	succeeded	-3.9936507215	60.7461	18	[0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0]
8	succeeded	-4.1111292956	90.8914	18	[0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0]
9	succeeded	-4.0902898356	90.9046	18	[0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0]
10	succeeded	-4.0317344482	120.787	18	[-0.42257400733656625, -0.26120668373806755, -0.21285212980581852, -0.46670068257258107, 1.0241079485728033, -0.6815266823728863, 1.0818040439930914, -0.13540681974437221]
11	succeeded	-4.1153553600	90.7762	18	[0.16957631496144107, 0.20815356960607967, 0.21971344367893464, 0.15902717806532138, 1.2763622687345586, -0.1629290725452619, 1.0195564713208893, -0.032371010743763244]
12	succeeded	-4.1128008487	120.883	18	[0.15800711356248098, 0.23971788054420706, 0.2642029348956945, 0.1356629090638085, 1.3841912281671538, 0.05021266998897109, 1.0414227058354988, -0.06856527609888374]
13	succeeded	-4.0975843714	90.7137	18	[0.13174993598666662, 0.20991029250521787, 0.22147016657807284, 0.19158338834268127, 1.2781189916336968, -0.1629290725452619, 1.0195564713208893, -0.032371010743763244]
14	succeeded	-4.1327163853	91.1553	18	[0.26126540452859726, 0.19063438918116868, 0.20408971793671266, 0.12865924857167652, 1.2700271632700135, -0.156503491443426, 1.022763115693348, -0.03767883533691547]
15	succeeded	-4.1032104517	60.7317	18	[0.2731470907789806, 0.20004537758420185, 0.21492988013483239, 0.0355802124543175, 1.287870949883217, -0.18197463965169028, 1.0251809271816072, -0.04168093778058213]
16	succeeded	-4.1260812834	90.9136	18	[0.2580385041223675, 0.1472124994606158, 0.2209594572011729, 0.13058528751334966, 1.2868969025344739, -0.16209283623130885, 1.022763115693348, -0.03767883533691547]
17	succeeded	-4.1471746087	91.0218	18	[0.31666003360290185, 0.19622027758751223, 0.16801939097357355, 0.1925311231282613, 1.2423336932239153, -0.12964565781774914, 1.0256549984799097, -0.04246564821422117]
18	succeeded	-4.0911620602	90.8632	18	[0.3618842315733681, 0.16044755480666706, 0.1448686175368699, 0.2673034063380334, 1.2327725109355125, -0.11029359994286936, 1.0303464364628405, -0.0502311896995574]
19	succeeded	-4.1064249616	121.11	18	[0.31666003360290185, 0.19622027758751223, 0.19024171849862473, 0.1925311231282613, 1.220111365698864, -0.12964565781774912, 1.0256549984799097, -0.08135441675654848]
20	succeeded	-4.1394338604	121.021	18	[0.33130476293721567, 0.20413988024349236, 0.22381147019869144, 0.19168467034936845, 1.2030632437988535, -0.11043563984237381, 1.0258258620100056, 0.02607716342143366]
21	succeeded	-4.1115781111	30.6405	18	[0.31482293970663194, 0.19633799391267304, 0.16676971368300633, 0.1908909061695983, 1.2397148160519171, -0.13332403476067214, 1.0753677542882583, -0.04168324215321918]
22	succeeded	-4.0311382131	90.9102	18	[0.33952041767985724, 0.2373228993114891, 0.1250723448763926, 0.14604015230294756, 1.2646180300887797, -0.1324703778096355, 0.9775656959059419, -0.011401738995865492]
23	succeeded	-4.0652975122	60.6499	18	[0.3327875224379131, 0.2176137391153877, 0.190540123761257, 0.20771093452971906, 1.2680055054353088, -0.14880497925881936, 1.0272647908230392, -0.046453236027238706]
24	succeeded	-4.1808863472	91.0309	18	[0.3127715545717932, 0.19303550981950485, 0.19075750162959682, 0.16584124339052297, 1.1768640193700466, -0.1129820940815071, 1.0081996378875935, -0.10472898786233562]
25	succeeded	-4.1094688177	151.325	18	[0.2938417140370512, 0.15239569175029077, 0.22769579350960473, 0.14333096353213676, 1.1074116999079908, -0.08896782277736923, 1.029921253183798, -0.1204381489573908]
26	succeeded	-4.1335987461	60.859	18	[0.31444005070677156, 0.1883009086961865, 0.18351442338438248, 0.17014990553978407, 1.1560385079711697, -0.15666912257869015, 1.0041433589042157, -0.09801622853859747]
27	succeeded	-4.1148106929	121.063	18	[0.34246769133177263, 0.23447219821799944, 0.2585896156788398, 0.18193576811425038, 1.2051022852038147, -0.12163265413261475, 1.0096513701707606, -0.1455526515943932]
28	succeeded	-4.1394427705	60.7347	18	[0.3176945827376201, 0.2084250862394242, 0.16854904325062703, 0.13927150414318967, 1.1833754816504631, -0.09182544555645011, 0.9850684182017629, -0.1008946923525995]
29	succeeded	-4.0548708499	60.7394	18	[0.3223286198547143, 0.18537769433024917, 0.19032539486697375, 0.16478983825468563, 1.1788189930609185, -0.11277900563873604, 1.0073859008961248, -0.10540193745751916]
30	succeeded	-4.0678824238	60.6971	18	[0.2928932573388092, 0.20243527192078517, 0.19033570760239782, 0.17656704812367277, 1.175090178831443, -0.11006701693397983, 1.0043766797935918, -0.10459564409414929]
31	succeeded	-4.1286087267	61.3025	18	[0.31499603634680545, 0.19492060880442744, 0.1891074562255724, 0.16798660901812335, 1.1745156928374805, -0.11165722574679997, 1.0095612800231457, -0.10495002230552461]
32	succeeded	-4.1027905287	151.115	18	[0.3102305228098267, 0.19489628337048637, 0.1902251230025696, 0.16020727919267433, 1.1795586302819632, -0.11537691962002748, 1.0149122097704983, -0.1047599907937358]
33	succeeded	-4.1066203330	120.887	18	[0.31299407187672945, 0.1938544117345354, 0.19082980165382674, 0.165594002736175, 1.1770042132641263, -0.1138339974107193, 1.0074727571200772, -0.109518537027701]
34	succeeded	-4.0992239349	60.7344	18	[0.31502362335167033, 0.1973914135017087, 0.19829736475994697, 0.164515861352205, 1.1765153531354997, -0.11372370099782367, 1.0058487153374869, -0.10138986672764837]
35	succeeded	-4.1978177445	90.8654	18	[0.3135139086223477, 0.1946166413796872, 0.1896643407240717, 0.16802760972187433, 1.1805502466866113, -0.11436035741289943, 1.0078219384579028, -0.10414315814855529]
36	succeeded	-4.1210400082	90.9927	18	[0.30671706310855695, 0.19146092657405214, 0.18796696616236785, 0.17136738287766165, 1.1818323169825782, -0.11300318391821286, 1.004965596802006, -0.0998811306734409]
37	succeeded	-4.1399248391	60.7938	18	[0.3136659482761548, 0.19456636246255637, 0.1880157689931596, 0.16726435935222136, 1.1785005569252065, -0.11816390299479072, 1.0064422206377248, -0.10309329733845925]
38	succeeded	-4.1354572586	120.998	18	[0.3165050155082506, 0.20033427981733512, 0.18866079338810235, 0.1720227602420454, 1.1865202763384775, -0.1137873232886926, 1.0097098168647625, -0.10550692071158767]
39	succeeded	-4.0492359104	120.93	18	[0.31383474793439126, 0.19602310546778579, 0.18747308186760955, 0.1652883662771982, 1.181148674605288, -0.11220957896426212, 1.0055027114698805, -0.10364208614917197]
40	succeeded	-4.0072314163	60.7113	18	[0.30801456977990777, 0.1902711594094897, 0.19222678698930154, 0.17413139575598124, 1.1814741534684223, -0.11414049100822841, 1.0094206078304826, -0.10224736406950365]

Independent fixed-parameter remeasurements

These measurements reevaluate saved parameter vectors without running the optimizer. They are kept separate from the optimization trajectory.

Vector	Epoch	Shots	Resilience	Measurements	Mean energy (Ha)	Minimum (Ha)	Maximum (Ha)	Allocated QPU time (s)
theta_best	EPOCH-F8C28BAB591E00DE	1024	0	12	-4.1430837906	-4.2201869480	-4.0356506330	183
theta_final	EPOCH-F8C28BAB591E00DE	1024	0	12	-4.1627628933	-4.2241620149	-4.0786624911	183

Means below combine the displayed measurements descriptively. Inspect epochs and replicates in the download before drawing statistical conclusions.

Measurement CSV · Measurement JSON