BeH2

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

Final energy-2.8633835654hartree

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): -2.94234

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: 2026-08-01T12:11:17+00:00
Wall time (s): 3528.42

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: 1935
Two-qubit gates: 391
Hamiltonian terms: 119

Scientific provenance

Cohort: primary heron
Reference method: CASCI
Reference energy (Ha): -3.9177491482222147
Energy convention: Qiskit Nature active-space qubit Hamiltonian; nuclear and inactive-space constants excluded
Absolute error (Ha): 1.05437
Signed error (Ha): 1.05437
Total QPU time (s): 520
Calibration time: 2026-08-01T11:56:48+00:00
Mean readout error: 0.0124267578125
Mean two-qubit gate error: 0.003388131786678243

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
Be	0	1.32945
H	0.00130266	2.65895

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	-2.5958163333	60.77	13	[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
2	succeeded	-2.6386080038	91.0444	13	[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
3	succeeded	-2.7400487050	60.8016	13	[1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
4	succeeded	-2.7299363090	151.331	13	[1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]
5	succeeded	-2.8114066731	121.036	13	[1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]
6	succeeded	-2.7491627671	90.8477	13	[1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0]
7	succeeded	-2.7656803398	91.0133	13	[1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0]
8	succeeded	-2.7339945074	121.045	13	[1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0]
9	succeeded	-2.8433185842	91.1154	13	[1.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0]
10	succeeded	-2.8273421723	120.94	13	[1.245865084959357, 1.5828406855871138, -0.05810208119309167, 1.4099964462388033, -0.35763042221252156, -0.26272656954834006, -0.44478162304474267, 1.1833540182761044]
11	succeeded	-2.8732057392	91.0736	13	[1.0795500254905102, 1.188578998124218, -0.01879901752103673, 0.8591939296415583, 0.15774917778183217, 0.18845546493045784, 0.12955127302899663, 1.332785523580804]
12	succeeded	-2.9423391930	120.934	13	[1.498215163138339, 0.9496124616994466, -0.03139801597094748, 0.8601324255215769, 0.1681658595819817, 0.21945133198617353, 0.12106987369941945, 1.4605106044465697]
13	succeeded	-2.9100371214	121.188	13	[1.7579402293824078, 0.683138415273717, -0.06310138811245712, 0.8624940008686803, 0.19437777959314506, 0.2974474927145745, 0.09972778366779152, 1.7819104194072954]
14	succeeded	-2.9004015428	60.7979	13	[1.498215163138339, 0.9496124616994466, -0.1518071833920943, 0.8676378648856189, 0.16066042021793975, 0.21194589262213157, 0.15109163115558735, 1.4530051650825277]
15	succeeded	-2.9270785403	90.9524	13	[1.577613058114076, 0.9882555560208843, 0.10558682932177786, 0.9043280458126265, 0.1261832933977973, 0.1814795221044035, 0.29546775419710597, 1.4413907218446378]
16	succeeded	-2.9075164774	120.953	13	[1.498215163138339, 0.9496124616994466, -0.03139801597094748, 0.8276545796235617, 0.1303388488167069, 0.22212591441980334, 0.12106987369941945, 1.4631851868801995]
17	succeeded	-2.9157767386	151.322	13	[1.526837891346687, 0.9635431935687243, -0.010242430684907607, 0.855381043286245, 0.2494938167081842, 0.1924739108411425, 0.09337086847613432, 1.4403292525285532]
18	succeeded	-2.9214774568	60.7693	13	[1.4872992698158778, 0.923735559540237, -0.028818405611788084, 0.8419294445229908, 0.18404389911079053, 0.2402520475531654, 0.14081724348049313, 1.443233863430753]
19	succeeded	-2.8815952650	60.6951	13	[1.517672533711147, 0.9739734037671444, -0.02472702302075344, 0.9147551615704167, 0.15758818339539085, 0.2898683197329473, 0.09559024331227588, 1.4437726586329154]
20	succeeded	-2.8848933924	90.8819	13	[1.4977623196842327, 0.9698466488581865, -0.03343847569649827, 0.846684532652173, 0.1834527702768874, 0.23807112655002904, 0.13329616226720103, 1.494796093855002]
21	succeeded	-2.8876046001	60.7769	13	[1.4689391642942629, 0.8919007696496519, -0.015444955463858455, 0.9107296022506128, 0.1595198458675232, 0.17179970831176944, 0.10832389431438262, 1.4826422848504108]
22	succeeded	-2.8748705617	90.767	13	[1.537019105170407, 0.9249840739517594, -0.034364435252187193, 0.8512643369792449, 0.1618265282531154, 0.22438225043656349, 0.11450760115317045, 1.4743918674489742]
23	succeeded	-2.8106179827	60.6565	13	[1.4657027042399253, 0.9871707945093621, -0.01860650890160763, 0.8223189511942492, 0.12577716746788087, 0.18728846163806975, 0.10109748274886939, 1.4084656017022563]
24	succeeded	-2.8383030398	30.5807	13	[1.478287609834441, 0.9449716383300563, -0.0432601577904497, 0.8444065202784095, 0.175026083681717, 0.23254741503811416, 0.08669480273982944, 1.4776315069938246]
25	succeeded	-2.8222729085	90.9395	13	[1.4928525186949493, 0.9926444985770813, -0.00907725495896428, 0.8730814930396654, 0.18484922708870172, 0.21491368655776918, 0.19243942420756505, 1.5059094305091525]
26	succeeded	-2.7943708263	90.9248	13	[1.540457099104081, 0.9327418245028942, -0.027951794077090177, 0.848357844371868, 0.15264622624307597, 0.21541977089151948, 0.12343020998764632, 1.4647295555754816]
27	succeeded	-2.8030162128	60.8719	13	[1.4969037917087444, 0.951465028526748, -0.020705965675211786, 0.8579075360571853, 0.16769537035485277, 0.22142551900400903, 0.12213408314644861, 1.465665884480413]
28	succeeded	-2.8519832214	90.9179	13	[1.49738867541438, 0.9519232158218262, -0.05262147749671032, 0.8674730648980069, 0.17234727622477994, 0.21483120950398513, 0.12713184509211342, 1.4542592242964918]
29	succeeded	-2.8034494940	90.8267	13	[1.4964917963877877, 0.9494761724025395, -0.032318260900508544, 0.8595740838988358, 0.16387014915226103, 0.22035975795360888, 0.12229160174332133, 1.4607967004531779]
30	succeeded	-2.8188900048	121.1	13	[1.4988861684028674, 0.9500800724080312, -0.029021398389064056, 0.8593569207895062, 0.17032246154832684, 0.2161506898650116, 0.11618436710279285, 1.4531847578551307]
31	succeeded	-2.8091106907	90.972	13	[1.4973335775751504, 0.9500352444043257, -0.03209729068893043, 0.8571404079282587, 0.16875104221281084, 0.21602104740402256, 0.12238170091976466, 1.4613896525608912]
32	succeeded	-2.7738045254	67.4834	13	[1.5014979569934523, 0.9494249280565916, -0.0336927804178535, 0.8659670792507735, 0.1738610754624318, 0.22310742322392643, 0.12142118520231567, 1.462498835015554]
33	succeeded	-2.8331396150	91.0855	13	[1.4994536508969047, 0.9531951776939118, -0.03228622885697348, 0.8580324633848501, 0.16831205922270376, 0.22154474492232365, 0.12150641391462676, 1.4595956117402513]
34	succeeded	-2.8698879602	60.7598	13	[1.49499264203918, 0.9464302217388009, -0.03247613394360876, 0.8636657488564523, 0.16047337330684122, 0.22143224959487529, 0.12099931810932654, 1.4588557217650444]
35	succeeded	-2.8526976767	90.9414	13	[1.4943741229919996, 0.9517446191807618, -0.03163803040663239, 0.8615017772657075, 0.16948565359483872, 0.218788713537922, 0.12221834461028928, 1.4599932273470184]
36	succeeded	-2.8606643965	60.795	13	[1.4996839787782241, 0.9452112519256914, -0.034258326938746704, 0.8564231798843687, 0.16733876588543561, 0.21316715991657528, 0.12318452122792779, 1.4639581273777131]
37	succeeded	-2.8630623928	90.9619	13	[1.5003026606751628, 0.9506893354265605, -0.030478477459074775, 0.8611825788528561, 0.16729972964949139, 0.21849701984224276, 0.12464361083528296, 1.4587494019961589]
38	succeeded	-2.8540929163	60.9035	13	[1.4995879257007039, 0.9539219158886496, -0.03557878812836831, 0.8540554756160932, 0.16583764152636055, 0.22368411812329975, 0.11972890754961703, 1.4605367490525518]
39	succeeded	-2.8177556611	90.9564	13	[1.4993401115660656, 0.9522002541903102, -0.03166243157476839, 0.8620130493834898, 0.16664034149598472, 0.217417803553165, 0.11910380559852485, 1.4622722208184655]
40	succeeded	-2.8633835654	60.8191	13	[1.5007511981446067, 0.9445286228994973, -0.03317360186055187, 0.8626748963873166, 0.17331018013991345, 0.22489740141567657, 0.12050026866262653, 1.4617982728887362]

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	-2.5693395544	-2.6077887102	-2.5296165427	137
theta_final	EPOCH-F8C28BAB591E00DE	1024	0	12	-2.5615433175	-2.5911338237	-2.5221435244	137

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

Measurement CSV · Measurement JSON