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arxiv: 2509.10758 · v1 · submitted 2025-09-13 · 🪐 quant-ph · physics.chem-ph

Moments-based quantum computation of the electric dipole moment of molecular systems

Michael A. Jones , Harish J. Vallury , Manolo C. Per , Harry M. Quiney , Lloyd C. L. Hollenberg This is my paper

Pith reviewed 2026-05-18 17:32 UTC · model grok-4.3

classification 🪐 quant-ph physics.chem-ph
keywords quantum computationquantum chemistryelectric dipole momentwater moleculequantum computed momentsLanczos cluster expansionnoise mitigationvariational quantum eigensolver
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The pith

Moments-based quantum computation estimates the electric dipole moment of water to within 2 percent of exact results on noisy hardware.

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

This paper shows how the quantum computed moments method, built on a Lanczos cluster expansion, can be adapted to calculate the electric dipole moment of the water molecule. On an IBM Quantum superconducting device with noise mitigation, the results match full configuration interaction calculations to within 0.03 debye. Standard direct measurement via VQE produces larger errors of about 0.07 debye, even in the absence of noise. The work extends moments-based techniques from energy estimation to other ground-state molecular properties.

Core claim

The quantum computed moments (QCM) method, based on the Lanczos cluster expansion, is applied to estimate the dipole moment of the water molecule on a quantum device. Noise-mitigated QCM results agree with FCI calculations to within 0.03 ± 0.007 debye (2% ± 0.5%), outperforming direct expectation value determination via VQE, which shows errors on the order of 0.07 debye (5%) even when performed without noise. This demonstrates that moments-based energy estimation techniques can be adapted to noise-robust evaluation of non-energetic ground-state properties of chemical systems.

What carries the argument

The quantum computed moments (QCM) method based on the Lanczos cluster expansion, which estimates property expectation values through moment expansions of the Hamiltonian and operator instead of direct measurement.

If this is right

  • The same moments expansion can be applied to other non-energy ground-state properties of molecules.
  • Noise-robust property calculations become feasible on near-term quantum devices without requiring full error correction.
  • QCM offers a practical alternative to VQE for chemical properties when device noise is present.
  • The approach may reduce the resource overhead for obtaining accurate molecular descriptors in quantum chemistry.

Where Pith is reading between the lines

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

  • The method could be tested on larger molecules where classical exact methods become intractable.
  • Combining QCM with additional error suppression techniques might further reduce the observed discrepancy.
  • Similar moment expansions might apply to other observables such as polarizabilities or transition moments.

Load-bearing premise

The Lanczos cluster expansion can be adapted to compute the dipole operator expectation value on noisy hardware without introducing systematic biases that the chosen noise mitigation cannot correct.

What would settle it

Repeating the QCM dipole calculation for a different molecule or on hardware with higher noise levels and checking whether the agreement with FCI stays within 2 percent or deviates substantially.

Figures

Figures reproduced from arXiv: 2509.10758 by Harish J. Vallury, Harry M. Quiney, Lloyd C. L. Hollenberg, Manolo C. Per, Michael A. Jones.

Figure 1
Figure 1. Figure 1: Details of the application of the method to the electric dipole moment of the water [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Three methods for evaluating the second moment, [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Results of evaluating the dipole moment using statevector simulation (green) [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
read the original abstract

With rapid progress being made in the development of platforms for quantum computation, there has been considerable interest in whether present-day and near-term devices can be used to solve problems of relevance. A commonly cited application area is the domain of quantum chemistry. While most experimental demonstrations of quantum chemical calculations on quantum devices have focused on the ground-state electronic energy of the system, other properties of the ground-state, such as the electric dipole moment, are also of interest. Here we employ the quantum computed moments (QCM) method, based on the Lanczos cluster expansion, to estimate the dipole moment of the water molecule on an IBM Quantum superconducting quantum device. The noise-mitigated results agree with full configuration interaction (FCI) calculations to within 0.03 $\pm$ 0.007 debye (2% $\pm$ 0.5%), compared to direct expectation value determination (i.e. VQE) with errors on the order of 0.07 debye (5%), even when the VQE calculation is performed without noise. This demonstrates that moments-based energy estimation techniques can be adapted to noise-robust evaluation of non-energetic ground-state properties of chemical systems.

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

1 major / 2 minor

Summary. The manuscript applies the quantum computed moments (QCM) method, based on the Lanczos cluster expansion, to estimate the electric dipole moment of the water molecule on an IBM Quantum superconducting device. Noise-mitigated QCM results are reported to agree with full configuration interaction (FCI) to within 0.03 ± 0.007 debye (2% ± 0.5%), outperforming direct expectation-value evaluation via VQE (errors ~0.07 debye or 5%), even when the VQE reference is performed without noise.

Significance. If the central numerical claim holds, the work shows that moments-based techniques originally developed for Hamiltonian energies can be repurposed for non-commuting observables such as the dipole moment, yielding improved noise robustness on near-term hardware relative to standard variational approaches. This is a concrete, falsifiable demonstration with direct comparison to both FCI benchmarks and experimental device output.

major comments (1)
  1. [§2] §2 (Theory / Operator mapping): The manuscript must explicitly derive or state the modified Lanczos cluster expansion (or auxiliary resolvent) used for the dipole operator μ. Because μ does not commute with H, the moment hierarchy differs from the energy case; without the precise definition of the operators whose moments are measured, it is impossible to confirm that the reported 0.03 D improvement is free of method-specific systematic bias that survives the chosen noise mitigation.
minor comments (2)
  1. [Results] Figure 3 or equivalent results table: clarify whether the quoted ±0.007 debye uncertainty is purely statistical (shot noise) or includes device calibration and mitigation-parameter uncertainties.
  2. [Abstract / §3] Abstract and §3: the phrase 'even when the VQE calculation is performed without noise' should be accompanied by the precise VQE ansatz depth and optimizer settings used for that reference.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive overall assessment. We address the single major comment below and will incorporate the requested clarification in a revised version.

read point-by-point responses

  1. Referee: [§2] §2 (Theory / Operator mapping): The manuscript must explicitly derive or state the modified Lanczos cluster expansion (or auxiliary resolvent) used for the dipole operator μ. Because μ does not commute with H, the moment hierarchy differs from the energy case; without the precise definition of the operators whose moments are measured, it is impossible to confirm that the reported 0.03 D improvement is free of method-specific systematic bias that survives the chosen noise mitigation.

    Authors: We agree that an explicit derivation of the adapted Lanczos procedure for the dipole operator is required for full transparency. In the revised manuscript we will insert a new subsection in §2 that derives the modified cluster expansion for a non-commuting observable. We define the auxiliary Krylov operators generated by repeated application of the dipole operator μ to the reference state, together with the corresponding three-term recurrence that accounts for the non-vanishing commutator [H, μ]. The moments that are actually measured on the device are then stated precisely as the expectation values of these auxiliary operators. This addition removes any ambiguity about the operator hierarchy and allows the reader to verify that the reported improvement is not an artifact of an incompletely specified method. revision: yes

Circularity Check

0 steps flagged

No significant circularity; QCM dipole adaptation validated against independent FCI benchmark

full rationale

The paper adapts the Lanczos-based quantum computed moments (QCM) method—previously used for Hamiltonian energy moments—to estimate the ground-state expectation value of the electric dipole operator on noisy quantum hardware. The central result is obtained by direct computation on the device followed by noise mitigation, then compared to external full configuration interaction (FCI) values as an independent benchmark. No step reduces the reported dipole moment to a fitted parameter, self-defined quantity, or load-bearing self-citation chain; the adaptation is presented as an extension whose accuracy is tested against an external, non-fitted reference rather than internal consistency alone. This is the most common honest finding for a paper whose claims rest on hardware output versus classical benchmark.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the method relies on standard quantum chemistry approximations and device noise models assumed from prior work.

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Reference graph

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