arxiv: 2604.11478 · v1 · submitted 2026-04-13 · 🪐 quant-ph

Recognition: unknown

Accuracy-Cost Trade-offs for Reference VQE Calculations of H₂ on IBM Quantum Hardware

Julen Larrucea , Marita Oliv , Jeanette Lorenz

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:17 UTC · model grok-4.3

classification 🪐 quant-ph

keywords variational quantum eigensolverquantum chemistryIBM Quantum hardwarehydrogen moleculeaccuracy-cost trade-offstapered mappingsresilience levelssession execution

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The pith

Tapered mappings deliver the most consistent accuracy gains for VQE ground-state calculations of H2 on IBM quantum processors.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes a hardware-validated reference dataset for variational ground-state energy calculations of the hydrogen molecule on multiple IBM Quantum processors available in 2026. Using a fixed workflow, the authors measure how shot count, backend selection, optimization choices, and execution modes affect energy accuracy relative to exact diagonalization. Tapered mappings for circuit simplification produce the steadiest accuracy improvements across the tested setups. Resilience level 1 raises accuracy but at a marked cost increase, while session-based runs show no systematic accuracy benefit over single-job runs despite substantially higher billed time. The dataset and analysis supply a concrete baseline for new users to anticipate trade-offs in quantum-chemistry applications on present hardware.

Core claim

Across the configurations studied, circuit simplification through tapered mappings provides the most consistent accuracy gains, resilience level 1 improves accuracy at a substantial cost premium, and session-based execution yields no systematic accuracy advantage over single-job execution despite markedly higher billed time.

What carries the argument

The standardized benchmarking workflow that systematically varies shot count, backend, optimization strategy including tapered mappings, resilience settings, and session versus single-job execution to quantify accuracy-cost trade-offs for VQE on H2.

If this is right

Tapered mappings should be applied early in similar VQE workflows to obtain accuracy improvements without increasing shot counts.
Resilience level 1 can be chosen when accuracy is prioritized over cost, but the premium must be budgeted in advance.
Single-job execution remains sufficient for accuracy in this H2 case, making it preferable when minimizing billed time.
The released dataset lets practitioners estimate expected energy errors and run costs before launching their own calculations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Extending the workflow to slightly larger molecules would test whether the accuracy advantage of tapered mappings persists as circuit depth increases.
The lack of accuracy benefit from sessions implies that hardware drift during the experiment is not the dominant error source in these VQE runs.
Future reductions in hardware noise could shrink the cost gap for resilience level 1 and change the observed trade-off.

Load-bearing premise

The standardized workflow and selected hardware configurations are representative of typical VQE usage in quantum chemistry and that observed variability generalizes beyond the tested backends and periods.

What would settle it

Repeating the full set of VQE runs for H2 on an additional IBM backend or with a different small molecule such as LiH and checking whether tapered mappings still produce the largest accuracy gains would test the central claim.

Figures

Figures reproduced from arXiv: 2604.11478 by Jeanette Lorenz, Julen Larrucea, Marita Oliv.

**Figure 2.** Figure 2: Cross-backend comparison at PT, COBYLA, 1024 shot [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: Distribution of per-iteration quantum execution [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: Backend comparison at fixed optimization depth (it [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: Energy error and billed time for different numbers o [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: Cell-wise early-convergence distributions ( [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

**Figure 7.** Figure 7: Mapper comparison on ibm_aachen (left) and ibm_brussels (right) at COBYLA, 1024 shots, resilience=0, session mode. Eerr = |E − Eexact| (reported as Eerr × 10 in a.u.); btime denotes billed time; bars span minimum to maximum value. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗

**Figure 8.** Figure 8: Energy error and billed time vs. number of shots for [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗

**Figure 9.** Figure 9: Energy-improvement for resilience level 1 (left) [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗

**Figure 10.** Figure 10: Resilience impact on btime at PT, COBYLA, 1024 shots, session mode. Eerr = |E − Eexact| (reported as Eerr × 10 in a.u.); btime denotes billed time and qtime denotes quantum execution time [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗

**Figure 11.** Figure 11: Session vs single-job comparison of Eerr across backends for workflow with 1024 shots and PT mapper without error mitigation. Eerr = |E − Eexact| (reported as Eerr × 10 in a.u.). substantially higher billed time than single-job execution (Sections 3.6). Revisiting common best practices Several workflow choices are often recommended as broadly beneficial, including the use of runtime sessions, or increased… view at source ↗

**Figure 12.** Figure 12: Session vs single-job timing comparison across b [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗

**Figure 13.** Figure 13: Shot sweep on ibm_brussels for PT, COBYLA, resilience=0, session mode. Eerr = |E − Eexact| (reported as Eerr × 10 in a.u.); btime denotes billed time and the vertical bars spread minimum to maximum value. 2 2 [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗

**Figure 14.** Figure 14: Shot sweep on ibm_kingston for PT, COBYLA, resilience=0, session mode. Eerr = |E − Eexact| (reported as Eerr × 10 in a.u.); btime denotes billed time and the vertical bars spread minimum to maximum value [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗

**Figure 15.** Figure 15: Cross-backend comparison at PT, COBYLA, 1024 sho [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗

**Figure 16.** Figure 16: Compact multi-backend shot-sweep view with per- [PITH_FULL_IMAGE:figures/full_fig_p025_16.png] view at source ↗

**Figure 17.** Figure 17: Quantum time as function of number of shots aggreg [PITH_FULL_IMAGE:figures/full_fig_p025_17.png] view at source ↗

read the original abstract

We present a hardware-validated reference dataset for variational ground-state energy calculations of the hydrogen molecule H\(_2\) on several IBM Quantum processors available in 2026. Using a standardized workflow, we benchmark the impact of shot count, backend choice, optimization strategy, and runtime variability on the achievable energy accuracy relative to exact diagonalization. The resulting dataset and analysis provide a transparent baseline for assessing the current capabilities and limitations of IBM Quantum hardware for quantum-chemistry applications, and are meant to ease the entry for new users by providing a comprehensive overview of choices and their effects as well as runtime efforts and costs that can be expected. Across the configurations studied here, circuit simplification through tapered mappings provides the most consistent accuracy gains, resilience level 1 improves accuracy at a substantial cost premium, and session-based execution yields no systematic accuracy advantage over single-job execution despite markedly higher billed time.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper gives a narrow but honest empirical benchmark of VQE accuracy-cost trade-offs for H2 on 2026 IBM hardware, with clear observations from a standardized workflow.

read the letter

The paper's main contribution is new measured data on how different practical choices affect VQE results for the hydrogen molecule on recent IBM processors. It tests shot counts, backends, optimization methods, tapered mappings, resilience levels, and session versus single-job execution, then compares energies to exact diagonalization. The headline findings—that tapered mappings give the most consistent accuracy lift, resilience level 1 buys accuracy at high cost, and sessions add billed time without systematic accuracy benefit—are presented as direct observations from their runs. This is useful because it supplies a transparent, hardware-specific reference set that new users can consult when estimating what accuracy and runtime to expect on similar IBM devices. The standardized workflow and explicit cost tracking are the parts that work well; they make the dataset reproducible enough for others to check or extend. The scope stays tightly on one trivial molecule and one vendor's 2026 backends, so the ordering of gains may shift for larger molecules or different hardware where circuit depth and noise behave differently. Variability across runs is acknowledged but the paper does not appear to include formal statistical tests or full raw datasets in the sections visible, which keeps the support for the claims descriptive rather than definitive. This work is mainly for practitioners onboarding to IBM quantum chemistry or for groups that need a current baseline to cite when discussing hardware limitations. It does not open new directions but fills a small, practical gap with honest measurements. I would send it to peer review so the dataset and workflow can be vetted and archived properly.

Referee Report

2 major / 3 minor

Summary. The manuscript presents a hardware-validated reference dataset for variational quantum eigensolver (VQE) ground-state energy calculations of the H₂ molecule on several 2026 IBM Quantum processors. Using a standardized workflow, it benchmarks the effects of shot count, backend choice, optimization strategy, and runtime variability (including single-job vs. session execution) on energy accuracy relative to exact diagonalization. The central descriptive findings are that tapered mappings yield the most consistent accuracy gains, resilience level 1 improves accuracy at a substantial cost premium, and session-based execution provides no systematic accuracy advantage despite higher billed time. The work positions the dataset and analysis as a transparent baseline to assist new users with accuracy-cost trade-offs in quantum chemistry applications.

Significance. If the empirical observations hold under the stated scope, the paper supplies a useful, reproducible reference point for current IBM Quantum hardware performance in small-molecule VQE calculations. The explicit scoping of claims to the tested configurations, the standardized workflow, and the focus on both accuracy and billed-time costs are strengths that could ease entry for practitioners and support future benchmarking studies. No parameter-free derivations or machine-checked proofs are present, but the direct hardware measurements against exact diagonalization provide falsifiable, configuration-specific data.

major comments (2)

[§4] §4 (Results) and associated figures/tables: The headline claim of 'no systematic accuracy advantage' for session-based execution over single-job execution is presented without statistical tests, confidence intervals, or quantitative error-bar analysis to support the absence of a difference, despite the manuscript noting runtime variability; visual or qualitative comparison alone is insufficient to substantiate this load-bearing observation.
[Methods] Methods section: The standardized workflow is outlined at a high level, but the manuscript does not include raw data tables, complete error-bar details, the full list of tested configurations, or explicit criteria used to avoid post-hoc selection; these omissions prevent independent verification of the three headline claims on accuracy gains from tapered mappings, resilience level 1, and session execution.

minor comments (3)

[Abstract] Abstract: The number of backends, total configurations, and specific shot counts or resilience levels tested could be stated explicitly to give readers immediate context for the scope of the findings.
[Figures] Figure captions and axis labels: Ensure all panels clearly indicate the metric (e.g., energy error in Hartree), error representation (standard deviation, etc.), and backend identifiers so that the accuracy-cost plots are self-contained.
[References] References: Include the exact IBM backend names and calibration dates used in 2026 to allow precise reproduction of the hardware conditions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address each major comment point by point below, indicating the revisions we will make to improve clarity, reproducibility, and statistical rigor.

read point-by-point responses

Referee: [§4] §4 (Results) and associated figures/tables: The headline claim of 'no systematic accuracy advantage' for session-based execution over single-job execution is presented without statistical tests, confidence intervals, or quantitative error-bar analysis to support the absence of a difference, despite the manuscript noting runtime variability; visual or qualitative comparison alone is insufficient to substantiate this load-bearing observation.

Authors: We agree that formal statistical support would strengthen the claim. In the revised manuscript we will add quantitative error bars (derived from the observed runtime variability) to the relevant figures in §4. We will also include a statistical comparison between single-job and session results, using a paired test appropriate to the data distribution (e.g., Wilcoxon signed-rank test) together with 95 % confidence intervals on the mean energy difference. The text will explicitly discuss the limitations imposed by runtime variability and state that the conclusion of “no systematic advantage” is now supported by both visual inspection and the statistical analysis. revision: yes
Referee: [Methods] Methods section: The standardized workflow is outlined at a high level, but the manuscript does not include raw data tables, complete error-bar details, the full list of tested configurations, or explicit criteria used to avoid post-hoc selection; these omissions prevent independent verification of the three headline claims on accuracy gains from tapered mappings, resilience level 1, and session execution.

Authors: We accept that additional methodological detail is required for independent verification. We will expand the Methods section with a more granular description of the workflow. In addition, we will deposit a Supplementary Information file containing (i) raw data tables for every configuration, (ii) the exact formulas and values used for all error bars, (iii) the complete enumerated list of tested configurations together with all circuit and runtime parameters, and (iv) the explicit, a-priori selection criteria employed to avoid post-hoc bias. Cross-references to this supplementary material will be inserted in both the Methods and Results sections so that readers can directly verify the three headline claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper is a purely empirical benchmarking study that reports hardware measurements of VQE energies for H2 against exact diagonalization. All central claims (accuracy gains from tapered mappings, cost trade-offs for resilience levels, and lack of session advantage) are direct observational comparisons from a standardized experimental workflow on specific IBM backends. No equations, derivations, fitted parameters, or self-citations are invoked as load-bearing steps that reduce any result to its own inputs by construction. The work is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper is an empirical benchmarking study and introduces no new theoretical entities or derivations. It relies on standard quantum-chemistry assumptions.

axioms (1)

domain assumption Exact diagonalization yields the true ground-state energy of H2
Invoked implicitly when accuracy is measured relative to exact diagonalization; standard in quantum-chemistry benchmarks.

pith-pipeline@v0.9.0 · 5455 in / 1333 out tokens · 83485 ms · 2026-05-10T16:17:00.911862+00:00 · methodology

discussion (0)

Reference graph

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