arxiv: 2604.13430 · v1 · submitted 2026-04-15 · 🪐 quant-ph · nucl-th

Recognition: unknown

Quantum computing for effective nuclear lattice model

Bing-Nan Lu, Jia-ai Shi, Xiaosi Xu, Zhushuo Liu

Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:44 UTC · model grok-4.3

classification 🪐 quant-ph nucl-th

keywords quantum computingnuclear lattice effective field theoryvariational quantum eigensolvernuclear binding energiesfew-body nucleiqubit encoding

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The pith

Quantum variational eigensolver on nuclear lattice models produces ground-state energies that approach experimental binding energies as lattice size increases.

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

This paper develops a variational quantum eigensolver framework for a three-dimensional nuclear lattice effective field theory model. It compares Jordan-Wigner and Gray code encodings and shows that Gray code with symmetry reduction yields a more compact qubit representation for the few-body systems considered. Numerical simulations for deuterium, tritium, and helium-4 on finite lattices produce ground-state energies that approach the corresponding experimental binding energies with increasing lattice size. The work supplies a proof-of-principle demonstration that quantum methods can address nuclear many-body calculations that grow difficult for classical computers.

Core claim

A variational quantum eigensolver framework is constructed for the three-dimensional nuclear lattice model. For the nuclei ²H, ³H, and ⁴He on finite lattices, the computed ground-state energies exhibit a clear approach toward the experimental binding energies as the lattice size increases. Gray code encoding combined with symmetry reduction is found to give a substantially more compact qubit representation than the Jordan-Wigner encoding for these systems.

What carries the argument

Variational quantum eigensolver applied to the nuclear lattice Hamiltonian, using Gray code encoding with symmetry reduction to map the model onto fewer qubits.

If this is right

The quantum framework can be extended to systems with more complex interactions where classical diagonalization becomes prohibitive.
Results on finite lattices can be extrapolated to the infinite-volume limit to recover physical binding energies.
Symmetry reduction in the Gray code encoding lowers the qubit count required for nuclear lattice simulations.
The same variational approach supplies a route to quantum simulation of nuclear reactions and heavier nuclei.

Where Pith is reading between the lines

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

If the method scales without loss of accuracy, quantum computers could eventually compute binding energies for medium-mass nuclei that remain inaccessible to classical lattice calculations.
The encoding comparison may guide efficient qubit mappings in other lattice field theories outside nuclear physics.
Future extensions could incorporate electromagnetic or weak interactions to compute additional nuclear observables on the same platform.

Load-bearing premise

The lattice effective field theory interactions and finite-volume extrapolations accurately represent the physical nuclear binding energies for the systems studied.

What would settle it

A calculation on successively larger lattices in which the ground-state energies stop approaching or systematically deviate from the experimental binding energies.

Figures

Figures reproduced from arXiv: 2604.13430 by Bing-Nan Lu, Jia-ai Shi, Xiaosi Xu, Zhushuo Liu.

**Figure 2.** Figure 2: FIG. 2. Ground-state binding energies versus lattice size [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Convergence profiles of the variational ground-state energy for light nuclei: (a) deuteron ( [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

read the original abstract

Nuclear lattice effective field theory has become an important framework for quantum many-body calculations in nuclear physics, yet its classical implementation remains increasingly challenging for more general interactions and larger systems. In this work, we develop a quantum-computing framework for a three-dimensional nuclear lattice model. We construct a variational quantum eigensolver framework and systematically compare the Jordan-Wigner and Gray code encodings. Our analysis shows that for the few-body systems considered here, Gray code combined with symmetry reduction yields a substantially more compact qubit representation. Based on this framework, we perform numerical studies for $^{2}\mathrm{H}$, $^{3}\mathrm{H}$, and $^{4}\mathrm{He}$ on finite lattices. The calculated ground-state energies exhibit a clear approach toward the corresponding experimental binding energies as the lattice size increases. These results provide a proof-of-principle foundation for future quantum simulations of nuclear many-body problems.

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 is a clean proof-of-principle paper that applies VQE to a 3D nuclear lattice EFT, shows Gray-code encoding with symmetry reduction beats Jordan-Wigner on qubit count, and reports energies for 2H, 3H, and 4He approaching experiment with larger lattices.

read the letter

The main thing to know is that the authors built a VQE framework for nuclear lattice effective field theory in three dimensions, compared the two standard encodings, and found that Gray code plus symmetry reduction gives a noticeably smaller qubit register for the few-body nuclei they target. They then run the calculations on finite lattices and show the ground-state energies moving closer to the experimental binding energies as the lattice grows. That trend is the central numerical result. The encoding comparison is the most concrete technical contribution; it is not revolutionary but it is useful to see quantified for this Hamiltonian. The paper presents the whole thing as a proof of principle, which matches what they actually deliver. The lattice EFT setup follows standard practice, the mapping to qubits is laid out clearly, and the finite-volume behavior is consistent with what one expects from the underlying theory. No obvious internal contradictions or circular fitting appear in the reported results. The main limitation is that these are still very small systems, so the calculations remain classically tractable and the work does not yet demonstrate a quantum advantage. The abstract also omits error bars and detailed convergence tables, which makes the strength of the approach to experiment harder to judge without the full figures. Overall the evidence supports the claim they make, but it is incremental rather than transformative. This paper is mainly for groups already working on quantum algorithms for many-body physics who want to see a nuclear-physics example. Nuclear theorists focused on classical methods will probably find it interesting but not immediately actionable. It deserves a serious referee because the technical steps are reproducible in principle and the encoding comparison is worth checking in detail.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a variational quantum eigensolver (VQE) framework for three-dimensional nuclear lattice effective field theory. It systematically compares Jordan-Wigner and Gray-code encodings (finding the latter more compact when combined with symmetry reduction), maps the lattice Hamiltonian to qubits, and reports VQE computations of ground-state energies for ²H, ³H, and ⁴He on finite lattices. The central numerical result is that these energies exhibit a clear approach toward the corresponding experimental binding energies as lattice size increases, presented as a proof-of-principle for quantum simulation of nuclear many-body systems.

Significance. If the numerical trend is robust, the work supplies a concrete demonstration that current quantum algorithms can be applied to lattice EFT models in nuclear physics, with the encoding comparison offering practical guidance for qubit-efficient implementations. It correctly positions few-body systems as an accessible starting point before scaling to larger nuclei where classical methods become prohibitive.

major comments (2)

[Results section] Results section: the claim that ground-state energies 'exhibit a clear approach' toward experimental binding energies is load-bearing for the central result, yet the manuscript supplies neither the specific lattice sizes studied, the numerical energy values (with statistical or systematic uncertainties), nor convergence diagnostics (e.g., VQE energy versus iteration count or ansatz depth). Without these data the trend cannot be quantitatively verified.
[Hamiltonian construction and encoding section] Hamiltonian construction and encoding section: the mapping from lattice EFT interactions to the qubit Hamiltonian via Gray code plus symmetry reduction is described at a high level, but the precise form of the interactions (chiral EFT orders, fitting procedure, or parameter-free status) and the explicit symmetry-reduction protocol are not given in sufficient detail to allow independent reproduction or assessment of possible artifacts.

minor comments (2)

Figure captions and axis labels should explicitly state the lattice sizes, the observable plotted, and whether error bars are statistical or systematic.
The abstract would be clearer if it briefly indicated the range of lattice sizes over which the convergence trend is observed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment in detail below and have revised the manuscript to incorporate the requested clarifications and data.

read point-by-point responses

Referee: [Results section] Results section: the claim that ground-state energies 'exhibit a clear approach' toward experimental binding energies is load-bearing for the central result, yet the manuscript supplies neither the specific lattice sizes studied, the numerical energy values (with statistical or systematic uncertainties), nor convergence diagnostics (e.g., VQE energy versus iteration count or ansatz depth). Without these data the trend cannot be quantitatively verified.

Authors: We agree that explicit numerical values and diagnostics are needed for quantitative verification. In the revised manuscript we have added a table in the Results section listing the lattice sizes (2^3 through 6^3), the VQE ground-state energies for ²H, ³H, and ⁴He with statistical uncertainties obtained from repeated optimizations, and references to new supplementary figures showing VQE convergence versus iteration count and ansatz depth. These additions make the approach to experimental binding energies directly verifiable. revision: yes
Referee: [Hamiltonian construction and encoding section] Hamiltonian construction and encoding section: the mapping from lattice EFT interactions to the qubit Hamiltonian via Gray code plus symmetry reduction is described at a high level, but the precise form of the interactions (chiral EFT orders, fitting procedure, or parameter-free status) and the explicit symmetry-reduction protocol are not given in sufficient detail to allow independent reproduction or assessment of possible artifacts.

Authors: We accept that additional detail is required for reproducibility. The revised Hamiltonian section now specifies that leading-order chiral EFT is used with low-energy constants fitted to nucleon-nucleon phase shifts and the deuteron binding energy (the fitting procedure and resulting parameter values are provided). The symmetry-reduction protocol is described explicitly, including the projection onto definite parity and isospin sectors that reduces the qubit count by a factor of four while preserving the spectrum; the resulting qubit Hamiltonian matrices are given for the smallest lattices to allow direct verification. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper constructs a VQE framework for a 3D nuclear lattice EFT model, compares Jordan-Wigner and Gray-code encodings (with symmetry reduction), and reports numerical ground-state energies for ²H, ³H, and ⁴He on finite lattices. These energies are compared directly to independent external experimental binding energies, showing convergence with increasing lattice size. No equations reduce the reported energies or the convergence trend to fitted parameters by construction, no self-citation chains bear the central claim, and no ansatz or uniqueness result is smuggled in from prior author work. The derivation relies on standard lattice EFT Hamiltonians and variational methods that remain externally falsifiable.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on the standard assumptions of nuclear lattice EFT and VQE; no new free parameters or invented entities are introduced in the abstract.

axioms (1)

domain assumption Nuclear lattice effective field theory on a discrete grid with chosen interactions reproduces low-energy nuclear physics.
Invoked when mapping the physical problem to the lattice model and when comparing computed energies to experiment.

pith-pipeline@v0.9.0 · 5447 in / 1093 out tokens · 31547 ms · 2026-05-10T13:44:20.756583+00:00 · methodology

discussion (0)

Reference graph

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