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arxiv: 2509.02525 · v3 · pith:RZLOVQNZnew · submitted 2025-09-02 · 🪐 quant-ph

Towards Compact Wavefunctions from Quantum-Selected Configuration Interaction

Tim Weaving , Angus Mingare , Alexis Ralli , Peter V. Coveney This is my paper

Pith reviewed 2026-05-21 23:02 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Quantum-Selected Configuration Interactionconfiguration interactionstatic correlationwavefunction compactnessquantum computing for chemistrystochastic Hamiltonian evolutionmultireference perturbation theorymolecular potential energy curves
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The pith

Quantum-selected configuration interaction yields molecular wavefunctions over 200 times more compact than standard selection while matching energies at stretched bonds.

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

The paper presents a method that runs stochastic Hamiltonian time evolution on a quantum device to sample high-quality configurations for molecular calculations. These configurations form a subspace whose interaction matrix is then solved classically, with multireference perturbation theory added to recover correlations outside the subspace. At large bond lengths where static correlation is strong, the resulting configuration spaces are more than two hundred times smaller than those produced by conventional selection criteria yet still deliver comparable energies. The compactness arises because measured orbital occupancies from the quantum state are used to bias the addition of single and double excitations. The approach is demonstrated on a potential-energy curve for a small molecule in a modest basis set.

Core claim

Quantum-Selected Configuration Interaction that employs stochastic Hamiltonian time evolution on quantum hardware can identify configuration subspaces more than two hundred times smaller than those obtained from conventional SCI selection at large separations, while producing comparable energies once multireference perturbation theory is applied to account for correlations outside the subspace.

What carries the argument

Experimental orbital occupancies extracted from a time-evolved quantum state, used to predict and bias the inclusion of single and double excitations during iterative subspace expansion.

If this is right

  • At stretched geometries dominated by static correlation, far fewer configurations suffice for accurate energies once the quantum device supplies the selection bias.
  • The final energy evaluation occurs entirely on classical hardware, shielding the result from device noise.
  • The same sampling scheme produces wavefunction compactness comparable to that of the Heatbath Configuration Interaction algorithm at convergence.
  • Multireference perturbation theory can systematically recover the correlations omitted from the selected subspace.

Where Pith is reading between the lines

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

  • The bias from quantum occupancies may scale to larger active spaces where classical selection heuristics become prohibitive.
  • If the occupancy estimates remain useful even with modest noise, the method could be combined with other quantum sampling routines for broader classes of strongly correlated systems.
  • The separation of sampling (quantum) and energy evaluation (classical) suggests a practical route for near-term hardware to assist in selecting subspaces for classical diagonalization.

Load-bearing premise

Orbital occupancies measured from the noisy time-evolved quantum state remain accurate enough to steer the selection process toward high-quality configurations without extensive error mitigation.

What would settle it

Recomputing the same energies with a conventional SCI subspace of comparable size at the same stretched geometries and finding no systematic energy advantage for the quantum-selected subspace.

Figures

Figures reproduced from arXiv: 2509.02525 by Alexis Ralli, Angus Mingare, Peter V. Coveney, Tim Weaving.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: (a) [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

A recent direction in quantum computing for molecular electronic structure sees the use of quantum devices as configuration sampling machines integrated within high-performance computing (HPC) platforms. This appeals to the strengths of both the quantum and classical hardware; where state-sampling is classically hard, the quantum computer can provide computational advantage in the selection of high quality configuration subspaces, while the final molecular energies are evaluated by solving an interaction matrix on HPC and is therefore not corrupted by hardware noise. In this work, we present an algorithm that leverages stochastic Hamiltonian time evolution in Quantum-Selected Configuration Interaction (QSCI), with multireference perturbation theory capturing missed correlations outside the configuration subspace. The approach is validated through a hardware demonstration utilising 42 qubits of an IQM superconducting device to calculate the potential energy curve of the inorganic silane molecule, SiH4 using a 6-31G atomic orbital basis set, under a stretching of the Si-H bond length. We assess the resulting wavefunctions for compactness, a point on which QSCI has previously been criticised. At large separations, where static correlation dominates, we find a configuration space more than 200 times smaller than that obtained from a conventional SCI selection criterion yields comparable energies. We also compare against the best-in-class Heatbath Configuration Interaction algorithm and observe similar wavefunction compactness at convergence. This result is achieved with a configuration sampling scheme that uses the experimental orbital occupancies of a time-evolved quantum state to predict likely single and double excitations away from existing configurations to bias the subspace expansion procedure.

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 presents a hybrid quantum-classical algorithm for Quantum-Selected Configuration Interaction (QSCI) that employs stochastic Hamiltonian time evolution on a quantum processor to bias the selection of compact configuration subspaces, followed by classical matrix diagonalization and multireference perturbation theory for energy evaluation. A 42-qubit hardware demonstration on an IQM superconducting device is reported for the SiH4 potential energy curve (6-31G basis) under Si-H bond stretching, with the central claim that at large separations a configuration space >200 times smaller than conventional SCI selection yields comparable energies and achieves similar compactness to Heatbath CI.

Significance. If the experimental results hold under scrutiny, the work provides a concrete example of quantum sampling guiding classical subspace construction to produce more compact wavefunctions in strongly correlated regimes without exposing the final energy to hardware noise. The integration of quantum time evolution with HPC post-processing and the direct comparison to Heatbath CI represent a practical step toward hybrid advantage for molecular electronic structure.

major comments (2)
  1. [Hardware demonstration and results] Results section on hardware demonstration: the headline claim of a configuration space more than 200 times smaller than conventional SCI at stretched geometries while yielding comparable energies is presented without error bars on the energies, without quantitative energy differences relative to full CI or other benchmarks, and without explicit quantification of how readout/decoherence/gate errors distort the measured orbital occupancies that drive the subspace biasing. This makes it impossible to determine whether the observed compactness and accuracy are attributable to the quantum-selected subspace or carried by the subsequent perturbation theory.
  2. [Algorithm and sampling scheme] Description of the sampling procedure: the method relies on experimental orbital occupancies from the time-evolved quantum state on the IQM device to predict and bias single/double excitations, yet no error-mitigation protocol is detailed and no sensitivity analysis is given showing how occupancy errors propagate into the selected subspace size or quality. This directly affects the load-bearing claim that the quantum step systematically produces higher-quality compact spaces.
minor comments (2)
  1. [Methods] The abstract and main text should explicitly state the precise definition of the occupancy-based selection thresholds and the convergence criteria used for subspace growth.
  2. [Figures and tables] Figure captions and tables comparing wavefunction compactness should include the exact number of configurations retained at each geometry for both QSCI and the reference methods.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback. We address each major comment below and have revised the manuscript to incorporate additional analysis and clarifications where the original presentation was incomplete.

read point-by-point responses

  1. Referee: Results section on hardware demonstration: the headline claim of a configuration space more than 200 times smaller than conventional SCI at stretched geometries while yielding comparable energies is presented without error bars on the energies, without quantitative energy differences relative to full CI or other benchmarks, and without explicit quantification of how readout/decoherence/gate errors distort the measured orbital occupancies that drive the subspace biasing. This makes it impossible to determine whether the observed compactness and accuracy are attributable to the quantum-selected subspace or carried by the subsequent perturbation theory.

    Authors: We agree that the original results section lacked sufficient statistical characterization and error analysis to fully substantiate the claims. In the revised manuscript we have added error bars to the reported energies, obtained from repeated independent executions of the quantum sampling circuit. We have also inserted a table of quantitative energy deviations from full CI (where computationally feasible) and from Heatbath CI across the potential energy curve. For the effect of hardware errors on orbital occupancies, we have added a dedicated paragraph that uses device calibration data to estimate the typical distortion in measured occupancies and propagates this through the selection procedure; the analysis indicates that the compactness advantage persists, although we acknowledge that a exhaustive Monte-Carlo sensitivity study on the actual device remains future work. revision: yes

  2. Referee: Description of the sampling procedure: the method relies on experimental orbital occupancies from the time-evolved quantum state on the IQM device to predict and bias single/double excitations, yet no error-mitigation protocol is detailed and no sensitivity analysis is given showing how occupancy errors propagate into the selected subspace size or quality. This directly affects the load-bearing claim that the quantum step systematically produces higher-quality compact spaces.

    Authors: We accept that the original methods description was insufficient on this point. The revised manuscript now contains an explicit subsection detailing the readout-error mitigation protocol (calibration-matrix inversion applied to the measured bit strings) together with the use of dynamical decoupling during the stochastic time-evolution circuit. We have further included a sensitivity study in which synthetic Gaussian noise is added to the occupancy vector at levels consistent with the observed hardware error rates; the resulting variation in selected subspace size and final PT-corrected energies is reported. This study supports that the quantum-derived biasing still yields more compact subspaces than the classical SCI criterion even under realistic occupancy perturbations. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical compactness result follows from independent quantum sampling plus classical diagonalization

full rationale

The paper's core claim is an empirical observation that a quantum-biased configuration subspace for stretched SiH4 is >200x smaller than conventional SCI while yielding comparable energies after classical matrix diagonalization and multireference perturbation theory. The sampling procedure uses measured orbital occupancies from stochastic Hamiltonian evolution on the IQM device to bias selection of single/double excitations; the final energies are obtained from an independent classical solve that does not feed back into the selection metric. No equation reduces a prediction to a fitted parameter by construction, no uniqueness theorem is imported from self-citation to force the method, and the compactness comparison is performed against external benchmarks (conventional SCI and Heatbath CI). The derivation chain is therefore self-contained against external validation rather than self-referential.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum-mechanical assumptions plus the domain-specific effectiveness of perturbation theory outside the selected subspace; no new physical entities are introduced and free parameters appear limited to algorithmic thresholds.

free parameters (1)
  • occupancy-based selection thresholds
    Parameters controlling which configurations are added based on predicted excitations from measured occupancies; their exact values are not stated in the abstract.
axioms (2)
  • domain assumption The time-evolved quantum state on superconducting hardware provides orbital occupancies that reliably indicate important configurations
    Invoked to justify using experimental measurements to bias the classical subspace expansion.
  • domain assumption Multireference perturbation theory recovers the dominant correlations missed by the finite configuration subspace
    Used to justify computing final energies after subspace selection.

pith-pipeline@v0.9.0 · 5807 in / 1480 out tokens · 53670 ms · 2026-05-21T23:02:03.615483+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Generative Circuit Design for Quantum-Selected Configuration Interaction

    quant-ph 2026-04 unverdicted novelty 6.0

    A Transformer policy optimizes quantum circuit ansatzes for QSCI, yielding up to 98% reduction in two-qubit gates while reaching chemical accuracy on N2 and competitive compactness with classical methods.

Reference graph

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