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arxiv: 2604.05380 · v1 · submitted 2026-04-07 · 🪐 quant-ph · physics.chem-ph

Recognition: no theorem link

Molecular Excited States using Quantum Subspace Methods: Accuracy, Resource Reduction, and Error-Mitigated Hardware Implementation of q-sc-EOM

Srivathsan Poyyapakkam Sundar , Prince Frederick Kwao , Alexey Galda , Ayush Asthana
Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:54 UTC · model grok-4.3

classification 🪐 quant-ph physics.chem-ph
keywords quantum computingexcited statesquantum chemistryq-sc-EOMerror mitigationvariational quantum eigensolvermolecular potential energy surfaceshardware implementation
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The pith

The q-sc-EOM algorithm on quantum hardware, with readout mitigation and symmetry projection, produces reasonably accurate excited-state energies where gate noise dominates the remaining error.

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

The paper shows how to make a quantum subspace method for molecular excited states practical on current hardware. It combines q-sc-EOM with ground-state techniques such as ADAPT-VQE, reduces measurement cost from O(N^12) to O(N^5) by adding the Davidson algorithm and basis rotation grouping, and runs the full workflow on real superconducting processors. With M3 readout correction and symmetry projection applied, the computed excited-state energies for bond-breaking molecules match classical EOM-CCSD benchmarks within acceptable error. The dominant remaining inaccuracy traces to gate noise rather than the subspace construction or measurement reduction steps.

Core claim

The hardware implementation of the q-sc-EOM algorithm, augmented by mitigation of M3 readout error and symmetry projection, produces reasonably accurate excited-state energies with gate noise identified as the predominant source of error.

What carries the argument

q-sc-EOM (quantum subspace equation-of-motion) operator, restricted to a Davidson-generated subspace and measured via basis-rotation grouping.

If this is right

  • Excited-state potential energy surfaces become computable on near-term quantum devices for bond-breaking regimes where classical methods are expensive.
  • Measurement overhead drops to O(N^5), removing the primary scaling barrier for larger active spaces.
  • M3 readout mitigation plus symmetry projection is sufficient to reach chemical accuracy once gate noise is controlled.
  • The combination of ADAPT-VQE ground states with q-sc-EOM excited states yields consistent full potential surfaces on hardware.
  • Gate noise is now the clearest target for hardware or compilation advances.

Where Pith is reading between the lines

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

  • If gate fidelities improve by another factor of ten, the same workflow could reach molecules with 20–30 orbitals where classical EOM-CCSD already becomes prohibitive.
  • The measurement-grouping technique could be ported to other equation-of-motion or response methods on quantum computers.
  • Symmetry projection may mask small symmetry-breaking errors that only appear at higher precision, so future runs should track both projected and unprojected energies.

Load-bearing premise

The Davidson algorithm together with basis rotation grouping keeps the accuracy of the full q-sc-EOM operator while cutting the measurement cost to O(N^5) without adding uncontrolled approximations to the subspace.

What would settle it

A classical simulation of the unreduced q-sc-EOM on a small molecule such as H2 or LiH that shows large energy deviations from the Davidson-reduced version on the same geometry would falsify the claim that the reduction preserves accuracy.

Figures

Figures reproduced from arXiv: 2604.05380 by Alexey Galda, Ayush Asthana, Prince Frederick Kwao, Srivathsan Poyyapakkam Sundar.

Figure 1
Figure 1. Figure 1: FIG. 1. Potential energy surface of ground and excited states as a function of bond distance in NH [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Potential energy surface of ground and excited [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Potential energy surface of H [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Number of BRG groups as a function of [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Left: absolute q-sc-EOM excitation-energy errors for linear H [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Eigen energies of ground and excited states of H [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Mean absolute energy error (Hartree) relative to FCI for the four roots obtained from q-sc-EOM for H [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Mean absolute energy error (Hartree) relative [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Root-wise q-sc-EOM error comparison on H [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Mean absolute energy error (Hartree) relative [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
read the original abstract

Problems in quantum chemical simulations, especially achieving accurate excited-state potential energy surfaces, are among the primary applications to achieve quantum utility. On near-term quantum hardware, variants of the variational quantum eigensolver (VQE) algorithms are the primary choice for chemistry simulation. In this study, a combination of leading ground and excited state quantum algorithms for general excited states, namely, ADAPT-VQE/LUCJ and q-sc-EOM, are utilized to calculate accurate excited state potential energy surfaces in challenging bond-breaking scenarios and compared with the classical scalable EOM-CCSD method. This work investigates avenues toward quantum utility in excited-state quantum chemistry using the q-sc-EOM approach. We assess its accuracy while mitigating major scaling bottlenecks through the Davidson algorithm and basis rotation grouping, reducing the measurement scaling from O(N$^{12}$) to O(N$^{5}$), and implementing the method on quantum hardware with various error mitigation strategies to reduce gate and measurement errors in excited states. The hardware implementation of the q-sc-EOM algorithm, augmented by mitigation of M3 readout error and symmetry projection, produces reasonably accurate excited-state energies with gate noise identified as the predominant source of error. This paves the way for accurate and scalable, generally applicable quantum excited-state methods with potential for quantum utility while identifying critical problems that require advancements.

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.

Referee Report

2 major / 2 minor

Summary. The paper claims to advance quantum excited-state calculations by combining q-sc-EOM with ADAPT-VQE for accurate potential energy surfaces in bond-breaking scenarios. It reduces the measurement scaling of q-sc-EOM from O(N^{12}) to O(N^5) using the Davidson algorithm and basis rotation grouping, implements the method on quantum hardware with error mitigation (M3 readout and symmetry projection), and reports reasonably accurate mitigated excited-state energies where gate noise is the dominant error, benchmarked against EOM-CCSD.

Significance. This work has potential significance in demonstrating a path to quantum utility for excited-state quantum chemistry on near-term devices. The resource reduction and hardware implementation with mitigation strategies, if the approximations hold, could enable more scalable simulations. The identification of gate noise as the main error source is useful for guiding future hardware and algorithm development.

major comments (2)
  1. [Abstract] The reduction of measurement scaling to O(N^5) via Davidson algorithm and basis rotation grouping is presented as preserving accuracy for the q-sc-EOM subspace, but no quantitative comparison of the approximated eigenvalues to the full operator or error bounds are provided. This is particularly concerning for bond-breaking regimes, as it underpins the hardware accuracy claims.
  2. [Hardware Implementation and Results] The statement that mitigated hardware energies are 'reasonably accurate' lacks supporting quantitative data such as mean absolute deviations, error bars on the reported energies, or tables directly comparing q-sc-EOM, mitigated hardware, and EOM-CCSD results. This makes the central claim difficult to evaluate without additional details.
minor comments (2)
  1. [Abstract] Specify the full list of error mitigation strategies used beyond M3 and symmetry projection for better context.
  2. [Figures] Include error bars on all hardware data points and ensure clear distinction between different methods in plots of potential energy surfaces.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable feedback on our manuscript. We agree that the major comments highlight areas where additional quantitative support will strengthen the presentation of our results on the q-sc-EOM method, its resource reduction, and hardware implementation. We will revise the manuscript to address these points directly.

read point-by-point responses

  1. Referee: [Abstract] The reduction of measurement scaling to O(N^5) via Davidson algorithm and basis rotation grouping is presented as preserving accuracy for the q-sc-EOM subspace, but no quantitative comparison of the approximated eigenvalues to the full operator or error bounds are provided. This is particularly concerning for bond-breaking regimes, as it underpins the hardware accuracy claims.

    Authors: We agree that explicit quantitative validation of the approximation is necessary to support the claims, particularly in challenging bond-breaking regimes. In the revised manuscript, we will add a dedicated section or appendix with direct numerical comparisons of the eigenvalues from the approximated q-sc-EOM operator (via Davidson algorithm and basis rotation grouping) against the full operator for the studied molecules. This will include deviation metrics and error analysis to confirm accuracy preservation. revision: yes

  2. Referee: [Hardware Implementation and Results] The statement that mitigated hardware energies are 'reasonably accurate' lacks supporting quantitative data such as mean absolute deviations, error bars on the reported energies, or tables directly comparing q-sc-EOM, mitigated hardware, and EOM-CCSD results. This makes the central claim difficult to evaluate without additional details.

    Authors: We acknowledge that the qualitative description 'reasonably accurate' requires quantitative backing for rigorous evaluation. In the revision, we will expand the results section with tables and supplementary figures providing direct comparisons of energies from classical q-sc-EOM, error-mitigated hardware runs, and EOM-CCSD references. These will include mean absolute deviations, error bars derived from multiple hardware executions, and specific numerical values for the excited states across the potential energy surfaces. revision: yes

Circularity Check

0 steps flagged

Minor self-citation of q-sc-EOM framework but no load-bearing circularity in accuracy claims or scaling reductions.

full rationale

The paper combines established VQE/EOM methods with classical EOM-CCSD benchmarks for validation. Scaling reduction via Davidson diagonalization and basis rotation grouping is presented as an applied optimization to achieve O(N^5) measurements from O(N^12), without redefining the target excited-state energies or fitting them to the reduced operator. Hardware results are assessed against external references after error mitigation, with no equations or steps reducing predictions to self-referential inputs by construction. Any self-citation of the q-sc-EOM method is not load-bearing for the central hardware accuracy claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard quantum mechanics and established quantum chemistry algorithms rather than new postulates; no free parameters, ad-hoc axioms, or invented entities are introduced in the abstract description.

axioms (1)
  • domain assumption Standard assumptions of the variational quantum eigensolver and equation-of-motion coupled-cluster frameworks hold for the chosen molecular systems.
    Invoked implicitly when comparing q-sc-EOM results to EOM-CCSD and when claiming accuracy on hardware.

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