Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE

Abel Carreras; David Casanova; Rom\'an Or\'us

arxiv: 2506.03995 · v1 · submitted 2025-06-04 · 🪐 quant-ph · physics.chem-ph

Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE

Abel Carreras , David Casanova , Rom\'an Or\'us This is my paper

Pith reviewed 2026-05-19 11:14 UTC · model grok-4.3

classification 🪐 quant-ph physics.chem-ph

keywords variational quantum eigensolverADAPT-VQEmolecular energyquantum noiseNISQbenzeneIBM quantumquantum chemistry

0 comments

The pith

Current quantum noise levels prevent VQE from producing accurate molecular ground-state energies on today's hardware.

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

The paper investigates the practical limits of variational quantum eigensolvers for computing molecular energies on noisy quantum devices. By applying optimizations to ADAPT-VQE and testing on benzene using an IBM quantum computer, it finds that noise prevents accurate results needed for useful chemical insights. A sympathetic reader would care because this clarifies why quantum computers have not yet transformed molecular modeling and what hardware progress is required. The study also outlines steps to reduce circuit depth and improve optimization for future attempts.

Core claim

The noise levels in today's devices prevent meaningful evaluations of molecular Hamiltonians with sufficient accuracy to produce reliable quantum chemical insights. Using benzene as a benchmark, optimizations to the Hamiltonian, ansatz, and COBYLA optimizer were implemented on IBM hardware, but quantum noise in state preparation and energy measurement still dominated, leading to an extrapolation of future hardware requirements.

What carries the argument

ADAPT-VQE algorithm enhanced with Hamiltonian simplification, ansatz optimization, and modified COBYLA, limited by quantum noise effects.

Load-bearing premise

Quantum noise is the main source of error rather than classical optimization problems or Hamiltonian simplifications.

What would settle it

Achieving chemical accuracy for the benzene ground state energy using the optimized VQE on current quantum hardware would falsify the claim that noise prevents meaningful evaluations.

read the original abstract

Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the Noisy Intermediate-Scale Quantum (NISQ) era. In this study, we investigate the capabilities and limitations of VQE algorithms implemented on current quantum hardware for determining molecular ground-state energies, focusing on the adaptive derivative-assembled pseudo-Trotter ansatz VQE (ADAPT-VQE). To address the significant computational challenges posed by molecular Hamiltonians, we explore various strategies to simplify the Hamiltonian, optimize the ansatz, and improve classical parameter optimization through modifications of the COBYLA optimizer. These enhancements are integrated into a tailored quantum computing implementation designed to minimize the circuit depth and computational cost. Using benzene as a benchmark system, we demonstrate the application of these optimizations on an IBM quantum computer. Despite these improvements, our results highlight the limitations imposed by current quantum hardware, particularly the impact of quantum noise on state preparation and energy measurement. The noise levels in today's devices prevent meaningful evaluations of molecular Hamiltonians with sufficient accuracy to produce reliable quantum chemical insights. Finally, we extrapolate the requirements for future quantum hardware to enable practical and scalable quantum chemistry calculations using VQE algorithms. This work provides a roadmap for advancing quantum algorithms and hardware toward achieving quantum advantage in molecular modeling.

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 runs optimized ADAPT-VQE on benzene on IBM hardware and finds noise blocks chemical accuracy, but skips the controls needed to confirm noise as the main culprit over optimization or simplifications.

read the letter

The main thing to take from this paper is that even with ADAPT-VQE, Hamiltonian simplifications, and a modified COBYLA optimizer, the IBM hardware execution on benzene falls short of useful accuracy for molecular energies, and the authors use that to sketch basic hardware targets for the future. They actually carried out the run on physical qubits rather than staying in simulation, which gives a real data point for the NISQ quantum chemistry crowd. The adaptive ansatz and circuit-depth reductions are practical steps that address known pain points, and reporting the outcome on a molecule of this size adds to the set of hardware benchmarks that exist so far. That part is worth noting because it moves past pure theory and shows the scale of the gap on current devices. The soft spot is exactly the one the stress-test flags: no direct comparison of the same ansatz and optimizer on a noiseless simulator versus the hardware run, and no side-by-side with exact classical results. Without that breakdown it is hard to tell how much of the error trace comes from decoherence, how much from the optimizer hitting plateaus, and how much from the Hamiltonian approximations themselves. The extrapolation to future device specs therefore rests on an assumption that noise dominates, which the data as described does not fully test. Minor details like error bars and raw circuit depths are also thin in the summary, though the full text may fill some of that in. This is the kind of paper that people working on near-term VQE implementations will want to see for the concrete numbers and the hardware roadmap it offers. It has enough experimental content and a clear practical question to justify sending it out for peer review rather than rejecting at the desk, even if the authors need to add the missing controls to make the central claim tighter.

Referee Report

2 major / 2 minor

Summary. The paper implements ADAPT-VQE with Hamiltonian simplifications and a modified COBYLA optimizer to compute the ground-state energy of benzene on IBM quantum hardware. It reports that, despite reductions in circuit depth, current noise levels prevent chemically accurate results and extrapolates the hardware improvements required for practical VQE-based quantum chemistry.

Significance. If the dominant error source is isolated and the extrapolation is validated, the work supplies a concrete hardware benchmark on a chemically relevant system (benzene) with an adaptive ansatz, which could guide error-mitigation priorities and hardware roadmaps in the NISQ era.

major comments (2)

[Results / benzene benchmark] Results section on benzene execution: the manuscript reports hardware energies but provides no direct comparison of the identical ansatz and optimizer on a noiseless simulator versus hardware versus classical exact diagonalization. Without this ablation, the claim that quantum noise is the primary limiter (abstract and conclusion) cannot be separated from possible contributions of barren plateaus in COBYLA optimization or accuracy loss from Hamiltonian simplifications.
[Discussion / future hardware requirements] Extrapolation paragraph (final section): the projected hardware requirements for future VQE calculations rest on the assumption that observed deviations scale linearly with current noise models; this is load-bearing for the roadmap claim yet is not supported by any sensitivity analysis or alternative error budgets that include classical optimization failure.

minor comments (2)

[Abstract] Abstract states the central conclusion but supplies no error bars, circuit depths, or raw measurement counts for the benzene hardware run, reducing verifiability.
[Methods] Notation for the modified COBYLA optimizer and the precise form of the Hamiltonian simplifications should be defined explicitly with equations rather than descriptive text only.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below, indicating where revisions will be made to strengthen the manuscript.

read point-by-point responses

Referee: [Results / benzene benchmark] Results section on benzene execution: the manuscript reports hardware energies but provides no direct comparison of the identical ansatz and optimizer on a noiseless simulator versus hardware versus classical exact diagonalization. Without this ablation, the claim that quantum noise is the primary limiter (abstract and conclusion) cannot be separated from possible contributions of barren plateaus in COBYLA optimization or accuracy loss from Hamiltonian simplifications.

Authors: We agree that an explicit ablation study would better isolate the dominant error source. In the revised manuscript we will add a direct comparison of the same ADAPT-VQE ansatz and modified COBYLA optimizer executed on a noiseless simulator, on the IBM hardware, and against classical exact diagonalization of the simplified Hamiltonian. This addition will allow readers to quantify the separate contributions of quantum noise, optimization behavior, and Hamiltonian truncation. Our original focus was on end-to-end hardware performance for a chemically relevant molecule, but we acknowledge that the requested comparison clarifies the central claim. revision: yes
Referee: [Discussion / future hardware requirements] Extrapolation paragraph (final section): the projected hardware requirements for future VQE calculations rest on the assumption that observed deviations scale linearly with current noise models; this is load-bearing for the roadmap claim yet is not supported by any sensitivity analysis or alternative error budgets that include classical optimization failure.

Authors: The extrapolation is derived from the measured error scaling between simulator and hardware runs under the noise levels present in the device. We will revise the final section to include a sensitivity analysis that varies the assumed error model and explicitly discusses possible contributions from classical optimization difficulties. We will also state the linear-scaling assumption more clearly and note its limitations, thereby strengthening the roadmap discussion without overstating its generality. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental hardware demonstration with independent empirical results

full rationale

The paper reports direct execution of ADAPT-VQE on IBM quantum hardware for the benzene molecule after applying Hamiltonian simplifications and optimizer modifications. The central claim that current noise levels prevent reliable molecular energy estimates is grounded in observed deviations between hardware runs and reference values, not in any mathematical derivation, fitted parameter renamed as prediction, or self-citation chain that reduces to the paper's own inputs. No equations or sections exhibit self-definitional loops, uniqueness theorems imported from the authors' prior work, or ansatzes smuggled via citation. The extrapolation to future hardware requirements is an assumption-based scaling argument rather than a construction that forces the conclusion from the data by definition. This is a standard non-circular experimental study.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The central claim rests on the unstated premise that observed deviations are dominated by hardware noise rather than algorithmic or modeling choices.

pith-pipeline@v0.9.0 · 5766 in / 935 out tokens · 41186 ms · 2026-05-19T11:14:16.615751+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The noise levels in today's devices prevent meaningful evaluations of molecular Hamiltonians with sufficient accuracy to produce reliable quantum chemical insights.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

we reduce the number of interacting elements... by discarding one- and two-electron terms with negligible contributions, determined by setting an energy threshold

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages · 2 internal anchors

[1]

Feynman, R. P. Simulating physics with computers 21, 467–488 (1982). URL https://doi.org/10.1007/BF02650179

work page doi:10.1007/bf02650179 1982
[2]

D., Love, P

Aspuru-Guzik, A., Dutoi, A. D., Love, P. J. & Head-Gordon, M. Simulate d quantum computation of molecular energies 309, 1704–1707 (2005)

work page 2005
[3]

Cao, Y. et al. Quantum chemistry in the age of quantum computing 119, 10856– 10915 (2019)

work page 2019
[4]

Alexeev, Y. et al. Quantum-centric supercomputing for materials science: A perspective on challenges and future directions. Future Gener. Comput. Syst. 160, 666–710 (2024). URL https://www.sciencedirect.com/science/article/pii/ S0167739X24002012

work page 2024
[5]

Peruzzo, A. et al. A variational eigenvalue solver on a photonic quantum processor 5, 4213 (2014)

work page 2014
[6]

Tilly, J. et al. The variational quantum eigensolver: A review of methods and best practices 986, 1–128 (2022). The Variational Quantum Eigensolver: a review of methods and best practices

work page 2022
[7]

A., Peng, B., Govind, N

Fedorov, D. A., Peng, B., Govind, N. & Alexeev, Y. Vqe method: a short survey and recent developments 6, 2 (2022)

work page 2022
[8]

Quantum computing in the NISQ era and beyond

Preskill, J. Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018). URL https://doi.org/10.22331/q-2018-08-06-79

work page internal anchor Pith review doi:10.22331/q-2018-08-06-79 2018
[9]

R., Economou, S

Grimsley, H. R., Economou, S. E., Barnes, E. & Mayhall, N. J. An adaptiv e variational algorithm for exact molecular simulations on a quantum computer 10, 3007 (2019). URL https://doi.org/10.1038/s41467-019-10988-2https://www. nature.com/articles/s41467-019-10988-2

work page doi:10.1038/s41467-019-10988-2https://www 2019
[10]

Blum, V. et al. Roadmap on methods and software for electronic structure based simulations in chemistry and materials 6, 042501 (2024)

work page 2024
[11]

It is worth noting that an energy threshold of 10 − 2 Hartrees for individual Hamil- tonian terms corresponds to even smaller overall contributions to th e ground-state energy, as the one- and two-electron terms are scaled by the one- and two-p article density matrices, respectively

work page
[12]

Vaquero-Sabater, N., Carreras, A., Or´ us, R., Mayhall, N. J. & Casanova, D. Physically motivated improvements of variational quantum eigensolvers 20, 5133– 5144 (2024). URL https://doi.org/10.1021/acs.jctc.4c00329

work page doi:10.1021/acs.jctc.4c00329 2024
[13]

R., Barron, G

Grimsley, H. R., Barron, G. S., Barnes, E., Economou, S. E. & Mayhall , N. J. Adaptive, problem-tailored variational quantum eigensolver mitigate s rough 21 parameter landscapes and barren plateaus 9, 19 (2023)

work page 2023
[14]

Tang, H. L. et al. Qubit-ADAPT-VQE: An Adaptive Algorithm for Constructing Hardware-Eﬃcient Ans¨ atze on a Quantum Processor 2, 020310 (2021). URL https://link.aps.org/doi/10.1103/PRXQuantum.2.020310

work page doi:10.1103/prxquantum.2.020310 2021
[15]

Claudino, D., Wright, J., McCaskey, A. J. & Humble, T. S. Benchmark ing adap- tive variational quantum eigensolvers 8, 606863. URL https://www.frontiersin. org/articles/10.3389/fchem.2020.606863/full

work page doi:10.3389/fchem.2020.606863/full 2020
[16]

& Mishra, S

Singh, H., Majumder, S. & Mishra, S. Benchmarking of diﬀerent opt imizers in the variational quantum algorithms for applications in quantum chemistry . J. Comp. Phys. 159, 044117

work page
[17]

Powell, M. J. D. A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation , 51–67 (Springer Netherlands, Dordrecht, 1994)

work page 1994
[18]

R., Romero, J., Babbush, R

McClean, J. R., Romero, J., Babbush, R. & Aspuru-Guzik, A. The the ory of variational hybrid quantum-classical algorithms 18, 023023 (2016)

work page 2016
[19]

B., Puigvert, V

Mansky, M. B., Puigvert, V. R., Castillo, S. L. & Linnhoﬀ-Popien, C. D ecom- position algorithm of an arbitrary pauli exponential through a quantum circu it. 2305.04807[quant-ph]

work page arXiv
[20]

& Cincio, L

Giurgica-Tiron, T., Hindy, Y., LaRose, R., Mari, A. & Cincio, L. Digital ze ro noise extrapolation for quantum error mitigation 2, 010317 (2021)

work page 2021
[21]

URL https://docs.quantum

IBM Quantum Documentation: Build noise models. URL https://docs.quantum. ibm.com/guides/build-noise-models

work page
[22]

Kim, S. et al. Pubchem 2025 update. Nucleic Acids Research 53, D1516–D1525 (2024). URL https://doi.org/10.1093/nar/gkae1059

work page doi:10.1093/nar/gkae1059 2025
[23]

Sun, Q. et al. Pyscf: the python-based simulations of chemistry framework 8, e1340 (2018). URL https://wires.onlinelibrary.wiley.com/doi/abs/10.1002/wcms. 1340

work page doi:10.1002/wcms 2018
[24]

& Wigner, E

Jordan, P. & Wigner, E. ¨Uber das paulische ¨ aquivalenzverbot. Zeitschrift f¨ ur Physik 47, 631–651 (1928). URL https://doi.org/10.1007/BF01331938

work page doi:10.1007/bf01331938 1928
[25]

Harris, C. R. et al. Array programming with NumPy. Nature 585, 357–362 (2020). URL https://doi.org/10.1038/s41586-020-2649-2

work page doi:10.1038/s41586-020-2649-2 2020
[26]

Virtanen, P. et al. SciPy 1.0: Fundamental algorithms for scientiﬁc computing in python. Nature Methods 17, 261–272 (2020). 22

work page 2020
[27]

McClean, J. R. et al. Openfermion: The electronic structure package for quantum computers (2019). 1710.07629. 23 Supporting Information: Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE Abel Carreras, ∗,† Rom´ an Or´ us,†,‡,¶ and David Casanova ‡,¶ †Multiverse Computing, Donostia, 20014, Euskadi, Spain ‡Donostia International Phys...

work page internal anchor Pith review Pith/arXiv arXiv 2019

[1] [1]

Feynman, R. P. Simulating physics with computers 21, 467–488 (1982). URL https://doi.org/10.1007/BF02650179

work page doi:10.1007/bf02650179 1982

[2] [2]

D., Love, P

Aspuru-Guzik, A., Dutoi, A. D., Love, P. J. & Head-Gordon, M. Simulate d quantum computation of molecular energies 309, 1704–1707 (2005)

work page 2005

[3] [3]

Cao, Y. et al. Quantum chemistry in the age of quantum computing 119, 10856– 10915 (2019)

work page 2019

[4] [4]

Alexeev, Y. et al. Quantum-centric supercomputing for materials science: A perspective on challenges and future directions. Future Gener. Comput. Syst. 160, 666–710 (2024). URL https://www.sciencedirect.com/science/article/pii/ S0167739X24002012

work page 2024

[5] [5]

Peruzzo, A. et al. A variational eigenvalue solver on a photonic quantum processor 5, 4213 (2014)

work page 2014

[6] [6]

Tilly, J. et al. The variational quantum eigensolver: A review of methods and best practices 986, 1–128 (2022). The Variational Quantum Eigensolver: a review of methods and best practices

work page 2022

[7] [7]

A., Peng, B., Govind, N

Fedorov, D. A., Peng, B., Govind, N. & Alexeev, Y. Vqe method: a short survey and recent developments 6, 2 (2022)

work page 2022

[8] [8]

Quantum computing in the NISQ era and beyond

Preskill, J. Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018). URL https://doi.org/10.22331/q-2018-08-06-79

work page internal anchor Pith review doi:10.22331/q-2018-08-06-79 2018

[9] [9]

R., Economou, S

Grimsley, H. R., Economou, S. E., Barnes, E. & Mayhall, N. J. An adaptiv e variational algorithm for exact molecular simulations on a quantum computer 10, 3007 (2019). URL https://doi.org/10.1038/s41467-019-10988-2https://www. nature.com/articles/s41467-019-10988-2

work page doi:10.1038/s41467-019-10988-2https://www 2019

[10] [10]

Blum, V. et al. Roadmap on methods and software for electronic structure based simulations in chemistry and materials 6, 042501 (2024)

work page 2024

[11] [11]

It is worth noting that an energy threshold of 10 − 2 Hartrees for individual Hamil- tonian terms corresponds to even smaller overall contributions to th e ground-state energy, as the one- and two-electron terms are scaled by the one- and two-p article density matrices, respectively

work page

[12] [12]

Vaquero-Sabater, N., Carreras, A., Or´ us, R., Mayhall, N. J. & Casanova, D. Physically motivated improvements of variational quantum eigensolvers 20, 5133– 5144 (2024). URL https://doi.org/10.1021/acs.jctc.4c00329

work page doi:10.1021/acs.jctc.4c00329 2024

[13] [13]

R., Barron, G

Grimsley, H. R., Barron, G. S., Barnes, E., Economou, S. E. & Mayhall , N. J. Adaptive, problem-tailored variational quantum eigensolver mitigate s rough 21 parameter landscapes and barren plateaus 9, 19 (2023)

work page 2023

[14] [14]

Tang, H. L. et al. Qubit-ADAPT-VQE: An Adaptive Algorithm for Constructing Hardware-Eﬃcient Ans¨ atze on a Quantum Processor 2, 020310 (2021). URL https://link.aps.org/doi/10.1103/PRXQuantum.2.020310

work page doi:10.1103/prxquantum.2.020310 2021

[15] [15]

Claudino, D., Wright, J., McCaskey, A. J. & Humble, T. S. Benchmark ing adap- tive variational quantum eigensolvers 8, 606863. URL https://www.frontiersin. org/articles/10.3389/fchem.2020.606863/full

work page doi:10.3389/fchem.2020.606863/full 2020

[16] [16]

& Mishra, S

Singh, H., Majumder, S. & Mishra, S. Benchmarking of diﬀerent opt imizers in the variational quantum algorithms for applications in quantum chemistry . J. Comp. Phys. 159, 044117

work page

[17] [17]

Powell, M. J. D. A Direct Search Optimization Method That Models the Objective and Constraint Functions by Linear Interpolation , 51–67 (Springer Netherlands, Dordrecht, 1994)

work page 1994

[18] [18]

R., Romero, J., Babbush, R

McClean, J. R., Romero, J., Babbush, R. & Aspuru-Guzik, A. The the ory of variational hybrid quantum-classical algorithms 18, 023023 (2016)

work page 2016

[19] [19]

B., Puigvert, V

Mansky, M. B., Puigvert, V. R., Castillo, S. L. & Linnhoﬀ-Popien, C. D ecom- position algorithm of an arbitrary pauli exponential through a quantum circu it. 2305.04807[quant-ph]

work page arXiv

[20] [20]

& Cincio, L

Giurgica-Tiron, T., Hindy, Y., LaRose, R., Mari, A. & Cincio, L. Digital ze ro noise extrapolation for quantum error mitigation 2, 010317 (2021)

work page 2021

[21] [21]

URL https://docs.quantum

IBM Quantum Documentation: Build noise models. URL https://docs.quantum. ibm.com/guides/build-noise-models

work page

[22] [22]

Kim, S. et al. Pubchem 2025 update. Nucleic Acids Research 53, D1516–D1525 (2024). URL https://doi.org/10.1093/nar/gkae1059

work page doi:10.1093/nar/gkae1059 2025

[23] [23]

Sun, Q. et al. Pyscf: the python-based simulations of chemistry framework 8, e1340 (2018). URL https://wires.onlinelibrary.wiley.com/doi/abs/10.1002/wcms. 1340

work page doi:10.1002/wcms 2018

[24] [24]

& Wigner, E

Jordan, P. & Wigner, E. ¨Uber das paulische ¨ aquivalenzverbot. Zeitschrift f¨ ur Physik 47, 631–651 (1928). URL https://doi.org/10.1007/BF01331938

work page doi:10.1007/bf01331938 1928

[25] [25]

Harris, C. R. et al. Array programming with NumPy. Nature 585, 357–362 (2020). URL https://doi.org/10.1038/s41586-020-2649-2

work page doi:10.1038/s41586-020-2649-2 2020

[26] [26]

Virtanen, P. et al. SciPy 1.0: Fundamental algorithms for scientiﬁc computing in python. Nature Methods 17, 261–272 (2020). 22

work page 2020

[27] [27]

McClean, J. R. et al. Openfermion: The electronic structure package for quantum computers (2019). 1710.07629. 23 Supporting Information: Limitations of Quantum Hardware for Molecular Energy Estimation Using VQE Abel Carreras, ∗,† Rom´ an Or´ us,†,‡,¶ and David Casanova ‡,¶ †Multiverse Computing, Donostia, 20014, Euskadi, Spain ‡Donostia International Phys...

work page internal anchor Pith review Pith/arXiv arXiv 2019