H2O

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

Final energy-4.1470174856hartree

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): -4.20137

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: 2026-09-01T17:16:42+00:00
Wall time (s): 38751.1

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: 2131
Two-qubit gates: 542
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): 1.9988
Signed error (Ha): 1.9988
Total QPU time (s): 540
Calibration time: 2026-09-01T16:48:01+00:00
Mean readout error: 0.00458984375
Mean two-qubit gate error: 0.003041260053504656

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
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

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	-4.1418139214	1433.37	18	[0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
2	succeeded	-4.1447850989	1827.95	18	[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
3	succeeded	-4.1185167070	1706.19	18	[1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
4	succeeded	-4.0918882492	245.295	18	[1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]
5	succeeded	-4.1129813575	1887.92	18	[1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]
6	succeeded	-4.0841549920	11346.1	18	[1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]
7	succeeded	-4.0479381581	336.258	18	[1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0]
8	succeeded	-4.1057717757	762.335	18	[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0]
9	succeeded	-4.0273921051	2893.3	18	[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]
10	succeeded	-4.0515723695	915.479	18	[1.0163888769836034, -0.14489522757654927, -0.2917765614351329, -0.17542795748362547, -0.33443284883008534, -0.5342032193015493, -0.2151956753942509, -0.6475342918099675]
11	succeeded	-4.1812856225	1309.41	18	[1.0044184454580147, -0.03906379069256033, -0.07866303615055509, -0.047295422543460156, -0.0901631822242951, -0.14402132558205138, -0.05801680953987274, 0.45584238011188233]
12	succeeded	-4.0658240418	1615.72	18	[1.0150835422872035, -0.13335467064347467, -0.26853725897294556, -0.16145554193306363, -0.3077960755093428, -0.4916552156902899, -0.19805585660810934, 0.5197673347154113]
13	succeeded	-4.1642903613	186.186	18	[1.0044184454580147, -0.03906379069256033, -0.07866303615055509, -0.047295422543460156, -0.19611339412669568, -0.07769220228137445, -0.05801680953987274, 0.45584238011188233]
14	succeeded	-4.0512745425	700.586	18	[1.0060951444864088, -0.0538876061095411, -0.10851385982541148, -0.06524295404059897, 0.08414204788050449, -0.010190419548529533, -0.0800328622693636, 0.5666869847912037]
15	succeeded	-4.2013699324	1036.52	18	[1.0044184454580147, -0.03906379069256033, -0.048984994423859646, -0.047295422543460156, -0.0901631822242951, -0.14402132558205138, -0.0982562657895355, 0.45584238011188233]
16	succeeded	-4.1269073793	793.254	18	[1.0045995061083581, -0.040664560785771256, 0.03823060897220608, -0.04923351141325751, -0.10013200445924268, -0.17555910727231708, -0.06434750423790825, 0.46781208717941575]
17	succeeded	-4.0937884139	1127.19	18	[1.0044184454580147, -0.03906379069256033, -0.04960336099333132, -0.09693248799663333, -0.09087195092193319, -0.1451534707087725, -0.09871233330539135, 0.45002969977064267]
18	succeeded	-4.0673198983	852.904	18	[1.0045333454125573, -0.04007962936647502, -0.07378767181719076, 0.038493496757567816, -0.09813310474372722, -0.1666606657001608, -0.1358508521051478, 0.4499575621128387]
19	succeeded	-4.0595081082	794.452	18	[1.0044184454580147, -0.08877163865477042, -0.0495160139540465, -0.04886469041777146, -0.09077183417834962, -0.14499355015397225, -0.09864791173218433, 0.4508507668256585]
20	succeeded	-4.0467055334	124.292	18	[1.0044912488143034, 0.034417143910013284, -0.06533869270014064, -0.10538438219903629, -0.0959445362025566, -0.15953448038894935, -0.12254773710628944, 0.44611516757141595]
21	succeeded	-4.0322927988	1097.89	18	[1.0544161321903878, -0.03903867926819972, -0.0489344273680965, -0.04726501956912645, -0.08998888798644716, -0.1437429182925468, -0.09821897077288261, 0.4554989715484986]
22	succeeded	-4.0731679992	855.73	18	[0.9716312731677998, -0.01806022190844009, -0.0343885228600315, -0.03061762119073276, -0.04623285370206548, -0.07631042526980565, -0.09228440522641489, 0.49382056447760153]
23	succeeded	-4.0955684862	1193.1	18	[1.0048512317854912, -0.046422303708327374, -0.058405336400731124, -0.054273647587134086, -0.098341402998308, -0.15708473092910258, -0.10520410575374167, 0.5008136840735431]
24	succeeded	-3.9599681544	184.42	18	[0.9550093847000153, -0.10294928471175599, -0.05149038643999219, -0.07776849942420272, -0.08630408771849839, -0.14157747637702237, -0.10735136986501978, 0.40645698715287065]
25	succeeded	-4.1323434764	1550.81	18	[1.0498644308142755, -0.048171670376989204, -0.046161036337451604, -0.05017727311074663, -0.0807052188038884, -0.13013440246829497, -0.09855131307810115, 0.4485593599859375]
26	succeeded	-4.0039048745	154.096	18	[1.0044191957699016, -0.039070424253340154, -0.0499104670307454, -0.04597163085470397, -0.0797704521317494, -0.15074008519282153, -0.098938835018942, 0.4556856599318358]
27	succeeded	-4.0522055825	369.682	18	[1.0043428649467991, -0.03608384774431101, -0.04840174112352433, -0.039869712466737775, -0.11155437682899982, -0.1342227290214975, -0.09852947812529306, 0.4532037200537547]
28	succeeded	-4.0054098540	520.265	18	[1.0048568414006067, -0.041483282180530115, -0.04981201568948079, -0.048555108107554625, -0.09204088285962922, -0.146947743366611, -0.09886622362489206, 0.453787783130392]
29	succeeded	-4.0611570216	734.389	18	[1.0012428471547723, -0.03954385369611739, -0.04703607887773546, -0.051270384968500025, -0.0873903257098375, -0.13657851275458613, -0.09689353570116757, 0.45811070273321786]
30	succeeded	-4.1470174856	183.676	18	[1.0036326541589553, -0.042597311825256806, -0.04873572104128628, -0.04400739971613145, -0.089952545752935, -0.14310485896178773, -0.09807241773245773, 0.45616711109223373]

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	-4.0773611159	-4.2009955451	-3.9926942826	204
theta_final	EPOCH-F50BF1CDD6F82CA5	1024	0	12	-4.0688841735	-4.1400576790	-4.0261055111	204

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

Measurement CSV · Measurement JSON