BeH2

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

Final energy-2.7455179952hartree

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: 30
Best energy (Ha): -2.81439

Execution

Mode: hardware
Provider: IBM Quantum
Compute resource: ibm_pittsburgh
Resource type: quantum processor
Processor family: Heron
Processor model: ibm_pittsburgh
Processor revision: 3
Qubits: 156
Connectivity: Not recorded
Runtime execution: single-job
Shots: 1024
Precision: 0.03125
Resilience: 0
Submitted: 2026-09-02T06:18:03+00:00
Wall time (s): 13192.3

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: 1979
Two-qubit gates: 451
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): 1.17223
Signed error (Ha): 1.17223
Total QPU time (s): 420
Calibration time: 2026-09-02T05:45:27+00:00
Mean readout error: 0.0046875
Mean two-qubit gate error: 0.0021978633927446575

Software

Qiskit: 2.5.2
Qiskit Aer: 0.17.2
Qiskit Algorithms: 0.4.0
Qiskit Ibm Runtime: 0.49.0
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

30 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	-2.7288386244	487.973	14	[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
2	succeeded	-2.7430347122	61.8576	14	[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
3	succeeded	-2.7306581012	639.752	14	[1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
4	succeeded	-2.7268257331	214.688	14	[1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]
5	succeeded	-2.8143868586	884.943	14	[1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]
6	succeeded	-2.7733785570	153.341	14	[1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0]
7	succeeded	-2.7559675165	760.873	14	[1.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0]
8	succeeded	-2.7372860743	760.518	14	[1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0]
9	succeeded	-2.7514819235	93.0956	14	[1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0]
10	succeeded	-2.6957942297	638.232	14	[1.0986585952259686, -0.08601377177819043, -0.11264759149890526, 1.4958762301792576, -0.2849955188453086, -0.4059970809762643, -0.5358275568814759, -0.4371706198825655]
11	succeeded	-2.7139882117	153.11	14	[1.0164965913127235, -0.01438226478940572, -0.018835675442811613, 1.082914899530295, -0.04765377603016129, -0.0678863093852489, 0.47965454399595314, -0.07309880131188416]
12	succeeded	-2.7813476375	640.927	14	[1.1249261371178225, 0.0, 0.0, 1.0, 0.0, 0.0, -0.004296541029594351, 0.0]
13	succeeded	-2.6937235569	1009.95	14	[0.8205425300009102, -0.008148953243478673, -0.010672243957424289, 1.0469793630804112, -0.02700050363632854, -0.03846420359749053, -0.154866765141863, -0.04141758775597507]
14	succeeded	-2.7201925396	642.2	14	[1.0000869062535165, -0.04993603210591799, 0.0, 1.0, 0.0, 0.0, 0.0025268844096688753, 0.0]
15	succeeded	-2.7231940613	184.8	14	[0.9895366833763554, 0.08814275369850735, -0.0007376813785655802, 1.0032472834634916, -0.0018663149777939376, -0.0026587029727225256, 0.04573332740772933, -0.002862845279266128]
16	succeeded	-2.7854000250	641.524	14	[0.9999745500113686, -3.748924458661074e-05, -0.04999450341302844, 1.0, 0.0, 0.0, -0.0007399833371818697, 0.0]
17	succeeded	-2.7176119311	185.091	14	[0.9919656420702783, 0.02932785804633655, 0.011869526652554767, 1.00129077895188, -0.00074185087874167, -0.0010568211476064495, -0.09449768187606869, -0.0011379666944726788]
18	succeeded	-2.7467846448	643.337	14	[1.0000032892136692, -0.0018899707758498398, -2.1993534742363163e-18, 1.049964175698105, 0.0, 0.0, 9.56371078522034e-05, 0.0]
19	succeeded	-2.7805038143	62.8335	14	[0.988852204266632, -0.06295105787474753, 0.026385752513264086, 0.9350304645021815, -0.001895189986858532, -0.002699837547191927, 0.031245962353877645, -0.002907138276092983]
20	succeeded	-2.7713610832	63.0558	14	[1.0000020619149452, -0.001184769182235554, -1.1588020951830388e-19, 1.00263252779334, -0.04991655557913467, 0.0, 5.995219582719688e-05, 0.0]
21	succeeded	-2.6650283397	612.708	14	[0.9925935962927241, -0.045731629701087004, 0.01754618150930002, 1.0780581349211917, 0.03171677003030293, -0.0017953567791875243, 0.020973988931014615, -0.0019332090619480645]
22	succeeded	-2.7397047856	184.885	14	[1.000002562481081, -0.001472392749191159, 8.813930419178583e-20, 0.9979976808038661, -7.056262636789792e-05, -0.04993808406955585, 7.450664632201953e-05, 0.0]
23	succeeded	-2.6895637386	641.096	14	[0.9939577097370922, -0.030623572907928748, 0.014287251100352774, 0.9194677137613633, 0.018069260769578332, 0.04155460292331606, 0.016743706186599056, -0.0015741455360466798]
24	succeeded	-2.7113294149	216.01	14	[1.000003004528373, -0.0017263915911895332, -7.356748906652425e-20, 1.0016712815799946, 0.0001292219441803253, -1.6162302043916857e-05, 8.735960413329083e-05, -0.04994198423867188]
25	succeeded	-2.7309198236	641.53	14	[0.994796719725553, -0.03005426582686826, 0.012318399866396733, 1.0703626185831092, 0.023038806722126156, 0.03032024447787403, 0.01462108141906458, 0.04799110384865597]
26	succeeded	-2.7462368656	123.545	14	[0.9983529881286567, -0.010213537654882003, 0.00390204157083045, 0.9937588400138415, 0.005809784100315537, -0.045598189953345414, 0.00466653835235465, 0.014285233479611057]
27	succeeded	-2.7381505269	703.519	14	[0.9878270317120098, -0.0017569420979052194, -9.597746779912211e-20, 1.0020603521978, 0.0001504679474955145, 0.0006630778203605375, 0.0005076713456870146, 0.0001300128874609926]
28	succeeded	-2.7796928530	276.245	14	[1.0216145915827863, -0.001107142983586684, 0.0017910814562646224, 1.007836757348836, 0.0031459272797475886, 0.0058844759917844255, 0.0011911893508530316, 0.0067836626079714035]
29	succeeded	-2.7376665763	641.49	14	[1.0001501616718678, -0.0019284074190408977, -5.72462114739778e-05, 0.9979152440530715, -5.94137359446271e-05, 0.0011057249857483159, 0.0039601821990103096, 3.3205455650169295e-06]
30	succeeded	-2.7455179952	215.045	14	[1.0011579382390337, 0.004110572030920186, 0.00037043875662328476, 0.9963829205686368, 7.657774673647784e-05, -0.0004257029645651462, -0.008244414607803794, 0.0006200231748066761]

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-F50BF1CDD6F82CA5	1024	0	12	-2.7326631222	-2.7711155220	-2.7064353531	150
theta_final	EPOCH-F50BF1CDD6F82CA5	1024	0	12	-2.7259627882	-2.7543609475	-2.6739934962	150

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

Measurement CSV · Measurement JSON