Size-Consistent Quantum Chemistry on Quantum Computers

David A. Mazziotti; Michael Rose; Noah Garrett

arxiv: 2512.18395 · v1 · submitted 2025-12-20 · 🪐 quant-ph · physics.chem-ph· physics.comp-ph

Size-Consistent Quantum Chemistry on Quantum Computers

Noah Garrett , Michael Rose , David A. Mazziotti This is my paper

Pith reviewed 2026-05-16 20:35 UTC · model grok-4.3

classification 🪐 quant-ph physics.chem-phphysics.comp-ph

keywords size consistencyquantum chemistryquantum computershybrid quantum-classical algorithmsmolecular simulationH2 moleculesunitary circuitsnoise effects

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The pith

Quantum hardware maintains size-consistent molecular energies for up to 118 non-interacting H2 molecules.

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

The paper examines whether simulations on quantum computers keep the energy of many separate molecules adding up correctly as the number of molecules grows. This property, called size consistency, is essential for any reliable method to handle large chemical systems. By running calculations on groups of non-interacting H2 molecules with special shallow circuits, the work shows that the energies stay accurate even for dozens of molecules. A sympathetic reader would care because it indicates that noise in real quantum devices does not yet destroy this basic scaling behavior at practical sizes.

Core claim

By simulating systems composed of increasing numbers of non-interacting H₂ molecules using optimally shallow unitary circuits on quantum hardware, molecular energies remain size-consistent within chemical accuracy for an estimated 118 and 71 H₂ subsystems for one- and two-qubit unitary designs, respectively.

What carries the argument

Optimally shallow unitary circuits used to represent the wavefunctions of each H2 molecule in hybrid quantum-classical algorithms.

If this is right

Molecular energies scale linearly with the number of non-interacting H2 subsystems on current quantum devices.
Size consistency holds within chemical accuracy for system sizes relevant to chemistry.
The approach supports scalable, noise-resilient simulation of strongly correlated molecules and materials.
Both one-qubit and two-qubit unitary designs preserve size consistency at these scales.

Where Pith is reading between the lines

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

Tests on molecules larger than H2 could show whether the result extends to systems with stronger electron correlation.
Reduced hardware noise would likely push the limit of preserved size consistency to even more subsystems.
Modular assembly of large-molecule calculations from consistent small-unit results may become practical.

Load-bearing premise

Noise on the quantum hardware does not create unexpected interactions between separate H2 molecules that would break the linear scaling of total energy.

What would settle it

A measurement on the same quantum hardware showing that the energy per H2 molecule deviates from the isolated-molecule value by more than chemical accuracy once the number of subsystems reaches around 100.

Figures

Figures reproduced from arXiv: 2512.18395 by David A. Mazziotti, Michael Rose, Noah Garrett.

**Figure 1.** Figure 1: Energy per H2 as system size (N) increases. Energies are calculated with single-qubit (left) and two-qubit (right) representations per subsystem. The energies for the single-qubit representation are simulated using the selective sample procedure (N=2,4,8,16; n=8,4,2,1; k=3) with the exception of N=1, which is generated using the random sample procedure (s=50). The energies for the two-qubit representation … view at source ↗

**Figure 2.** Figure 2: (a) Average double-excitation population per H2 subsystem as system size increases. (b) Average single-excitation population per H2 as system size increases. The CISD result overlaps exactly with the FCI line. The populations for both figures are represented as single-qubit: × (orange), two-qubit: + (blue), four-qubit: ◦ (green), CISD: − (purple), and FCI: − (black). 9 [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗

**Figure 3.** Figure 3: Average energy error per H2 subsystem as system size increases. The energy errors are represented as single-qubit: × (orange), two-qubit: + (blue), Hartree-Fock: · · · (red), and FCI: − (black). The average error per H2 for each set of energies is shown in [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

read the original abstract

Hybrid quantum-classical algorithms have begun to leverage quantum devices to efficiently represent many-electron wavefunctions, enabling early demonstrations of molecular simulations on real hardware. A key prerequisite for scalable quantum chemistry, however, is size consistency: the energy of non-interacting subsystems must scale linearly with system size. While many algorithms are theoretically size-consistent, noise on quantum devices may couple nominally independent subsystems and degrade this fundamental property. Here, we systematically evaluate size consistency on quantum hardware by simulating systems composed of increasing numbers of non-interacting H$_{2}$ molecules using optimally shallow unitary circuits. We find that molecular energies remain size-consistent within chemical accuracy for an estimated 118 and 71 H$_{2}$ subsystems for one- and two-qubit unitary designs, respectively, demonstrating that current quantum devices preserve size consistency over chemically relevant system sizes and supporting the feasibility of scalable, noise-resilient simulation of strongly correlated molecules and materials.

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

The paper tests size consistency on real hardware for non-interacting H2 stacks with shallow circuits and reports extrapolated limits of 118 and 71 subsystems before chemical accuracy breaks, but those limits rest on a simple additive noise fit whose validity at scale is untested.

read the letter

The main thing to know is that this work checks whether current quantum devices preserve size-consistent energies when simulating many separate H2 molecules, using shallow one- and two-qubit unitary circuits, and finds the property holds within chemical accuracy out to estimated limits of 118 and 71 subsystems respectively. Those numbers come from hardware runs on small stacks followed by extrapolation. The focus on a real-device constraint rather than ideal scaling is the practical contribution. They do well by choosing optimally shallow circuits that fit NISQ constraints and by directly measuring energy additivity as the number of non-interacting molecules grows. The specific extrapolated thresholds are new empirical points that build on earlier discussions of size consistency in quantum algorithms. This gives people working on hybrid quantum-classical chemistry a concrete benchmark for how far present hardware can go before noise starts to couple subsystems. The soft spot is the extrapolation step itself. The headline figures are projections from fitting observed per-molecule errors on small systems to a noise model, not direct measurements at the quoted scales. The abstract supplies no error bars, no description of the fit range or functional form, and no checks for correlated noise or calibration drift that could appear only at larger sizes. If the dominant error channel is not strictly additive and independent, the real breakdown point would be lower. Without the full methods and raw data it is difficult to judge how conservative the model is. Readers who run variational quantum algorithms on molecular systems will find the hardware numbers useful as a reference point. The paper deserves a serious referee because the question is central to scaling claims and the approach is straightforward, even though the extrapolation needs clearer validation and more detail on the fitting procedure before publication.

Referee Report

2 major / 2 minor

Summary. The paper evaluates size consistency of hybrid quantum-classical simulations on quantum hardware by computing energies of increasing numbers of non-interacting H₂ molecules using optimally shallow one- and two-qubit unitary circuits. It reports that energies remain within chemical accuracy up to extrapolated limits of 118 and 71 H₂ subsystems, respectively, and concludes that current devices preserve size consistency at chemically relevant scales.

Significance. If the extrapolation and underlying noise model are validated, the result would provide concrete evidence that hardware noise does not destroy size consistency at scales relevant to molecular simulation, strengthening the case for scalable quantum chemistry on near-term devices. The work directly addresses a key prerequisite for practical quantum advantage in chemistry.

major comments (2)

[Abstract] Abstract: the headline limits of 118 and 71 H₂ subsystems are extrapolations obtained by fitting energy deviations on small numbers of molecules to a noise model and projecting forward; the manuscript must detail the functional form of the fit, the exact range of system sizes actually executed on hardware, the statistical methods used to obtain error bars, and any cross-validation or tests for correlated noise or crosstalk that could invalidate the additive assumption.
[Results] Results section (presumably §4 or equivalent): without explicit reporting of the raw hardware data points, circuit depths, measurement statistics, and data-exclusion criteria for the H₂ subsystems, the central claim that size consistency holds within chemical accuracy cannot be independently assessed from the presented text.

minor comments (2)

[Abstract] Clarify the precise numerical threshold adopted for 'chemical accuracy' (e.g., 1.6 mHa or another value) and how it is applied per molecule versus total energy.
[Methods] Provide a brief description or reference for the construction of the 'optimally shallow unitary circuits' to allow readers to reproduce the ansatz choice.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important aspects of clarity and reproducibility. We address each major comment below and will revise the manuscript accordingly to strengthen the presentation of our results.

read point-by-point responses

Referee: [Abstract] Abstract: the headline limits of 118 and 71 H₂ subsystems are extrapolations obtained by fitting energy deviations on small numbers of molecules to a noise model and projecting forward; the manuscript must detail the functional form of the fit, the exact range of system sizes actually executed on hardware, the statistical methods used to obtain error bars, and any cross-validation or tests for correlated noise or crosstalk that could invalidate the additive assumption.

Authors: We agree that the extrapolation procedure requires more explicit documentation. The functional form is a linear fit of the per-molecule energy deviation versus the number of H₂ subsystems, derived from an additive noise model. Hardware executions were performed for system sizes from 1 to the maximum feasible on the device (specifically up to 8 subsystems). Error bars were computed using bootstrap resampling of the shot-level measurement outcomes. We will add cross-validation by holding out subsets of the data for fit validation and include explicit checks for correlated noise via separate two-qubit crosstalk measurements on non-adjacent qubits. These details will be incorporated into the abstract and expanded in the Methods and Results sections. revision: yes
Referee: [Results] Results section (presumably §4 or equivalent): without explicit reporting of the raw hardware data points, circuit depths, measurement statistics, and data-exclusion criteria for the H₂ subsystems, the central claim that size consistency holds within chemical accuracy cannot be independently assessed from the presented text.

Authors: We acknowledge the need for greater transparency in the raw data and experimental parameters. In the revised manuscript we will add a dedicated table in the Results section listing the measured energies for each system size, the circuit depths (one-qubit and two-qubit unitary designs), the number of measurement shots per circuit, and the data-exclusion criteria (runs with variance exceeding a predefined threshold were discarded). This will enable independent verification of the size-consistency claims within chemical accuracy. revision: yes

Circularity Check

0 steps flagged

No significant circularity: results from direct hardware simulations

full rationale

The paper reports size-consistency findings from quantum hardware simulations of increasing numbers of non-interacting H2 molecules using optimally shallow unitary circuits. The abstract presents the 118 and 71 subsystem estimates as outcomes of these simulations, with the term 'estimated' referring to projection from observed energy deviations rather than any self-referential definition or tautological reduction. No equations, derivations, or load-bearing steps are shown that equate predictions to inputs by construction, smuggle ansatzes via self-citation, or rename known results. The central claim relies on external hardware benchmarks and noise considerations independent of the target figures, satisfying the default expectation of self-contained derivations without enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions from quantum computing and chemistry with no free parameters, invented entities, or ad-hoc axioms introduced in the abstract.

axioms (1)

domain assumption Quantum mechanics governs electron behavior in molecules and noise on quantum devices can couple independent subsystems
Standard background assumption invoked to frame the size-consistency test.

pith-pipeline@v0.9.0 · 5452 in / 1230 out tokens · 31513 ms · 2026-05-16T20:35:36.971766+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.

unitary circuits that preserve these properties in the absence of noise... FCI wavefunctions

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

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Nielsen, M. A.; Chuang, I. L. Quantum Computation and Quantum Information; Cambridge University Press, 2000 mcitethebibliography main-arXiv.tex0000664000000000000000000010421615121526764012330 0ustar rootroot [journal=jpclck,manuscript=letter] achemso chemformula [T1] fontenc dsfont hyperref * [1] #1 Noah Garrett Michael Rose David A. Mazziotti Department...

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A.; Binkley, J

Pople, J. A.; Binkley, J. S.; Seeger, R. Theoretical models incorporating electron correlation. Int. J. Quantum Chem. 1976, 10, 1--19

work page 1976

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J.; Shavitt, I

Bartlett, R. J.; Shavitt, I. Determination of the size-consistency error in the single and double excitation configuration interaction model. Int. J. Quantum Chem. 1977, 12, 165--173

work page 1977

[3] [3]

Bartlett, R. J. Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules. Annu. Rev. Phys. Chem. 1981, 32, 359--401

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On the importance of size-consistency corrections in semiempirical MNDOC calculations

Cremer, D.; Thiel, W. On the importance of size-consistency corrections in semiempirical MNDOC calculations. J. Comput. Chem. 1987, 8, 48--50

work page 1987

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Deleuze, M.; Pickup, B. T. Size consistency and size extensivity of linear-response properties using the perturbed electron propagator. J. Chem. Phys. 1995, 102, 8967--8977

work page 1995

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Sheppard, M. G. Size consistency in perturbation theories. J. Chem. Phys. 1984, 80, 1225--1229

work page 1984

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Mahapatra, U. S.; Datta, B.; Mukherjee, D. A state-specific multi-reference coupled cluster formalism with molecular applications. Mol. Phys. 1998, 94, 157--171

work page 1998

[9] [9]

S.; Datta, B.; Mukherjee, D

Mahapatra, U. S.; Datta, B.; Mukherjee, D. A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications. J. Chem. Phys. 1999, 110, 6171--6188

work page 1999

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R.; Mukherjee, D

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work page 2005

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Thermodynamic limit and size-consistent design

Hirata, S. Thermodynamic limit and size-consistent design. Theor. Chem. Acc. 2011, 129, 727--746

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K.; Mukherjee, D

Sen, A.; Sen, S.; Samanta, P. K.; Mukherjee, D. Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications. J. Comput. Chem. 2015, 36, 670--688

work page 2015

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E.; Surj\'an, P

Mih\'alka, Z. E.; Surj\'an, P. R.; Szabados, A. Half-Projection of the Strongly Orthogonal Unrestricted Geminals’ Product Wave Function. J. Chem. Theory Comput. 2020, 16, 892--903

work page 2020

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