arxiv: 2604.20908 · v1 · submitted 2026-04-21 · ⚛️ nucl-th

Recognition: unknown

Systematic VQE Benchmarking of the Deuteron, Triton, and Helium-3 within Lattice Pionless Effective Field Theory

P{\i}nar \c{C}ifci , Serkan Akkoyun

Authors on Pith no claims yet

Pith reviewed 2026-05-10 00:32 UTC · model grok-4.3

classification ⚛️ nucl-th

keywords variational quantum eigensolverpionless effective field theorylight nucleideuterontritonhelium-3ground-state energyquantum simulation

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The pith

The variational quantum eigensolver reproduces classical ground-state energies for the deuteron, triton, and helium-3 in lattice pionless effective field theory.

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

The paper benchmarks the variational quantum eigensolver against exact diagonalization for three light nuclear systems modeled on a lattice with a simplified pionless interaction. It fixes the two-body strength using the deuteron, fits the three-body strength using the triton, and applies the same values to helium-3 while including Coulomb forces. In ideal simulations the quantum variational results match the classical energies, with particle-number conserving circuits used for the three-body cases and variance analysis to check convergence. A separate noisy simulation for the triton illustrates hardware effects. A reader would care because the work provides a transparent test of whether quantum algorithms can handle few-body nuclear problems with a small number of adjustable parameters.

Core claim

Using classical exact diagonalization as reference, the VQE algorithm with tailored ansatze yields ground-state energies in good agreement for the deuteron, triton, and isospin-asymmetric helium-3 within the lattice pionless EFT. The two-body low-energy constant is fixed by the deuteron binding energy, the three-body interaction by the triton, and these are used without adjustment for helium-3. Analysis of energy variance confirms convergence, and a noisy simulation illustrates NISQ hardware effects.

What carries the argument

Particle-number conserving variational ansatze applied to the lattice pionless effective field theory Hamiltonian with low-energy constants fitted from the deuteron and triton.

If this is right

The same fitted parameters describe both isospin-symmetric and asymmetric nuclei including Coulomb effects.
VQE serves as a practical method for computing ground states of few-nucleon systems in this framework.
Energy variance acts as an internal diagnostic for the quality of the obtained variational states.
Depolarizing noise increases the deviation from exact results, indicating the need for error mitigation on real devices.

Where Pith is reading between the lines

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

The approach could be tested on four-nucleon systems to check whether the ansatz and parameter transfer remain accurate.
Increasing the lattice volume while keeping the same ansatz might allow study of larger nuclei without changing the calibration procedure.
The method opens a route to quantum computation of other observables such as charge radii once the ground state is obtained.

Load-bearing premise

The chosen variational forms are expressive enough to represent the true ground states and the interaction strengths fitted to the deuteron and triton transfer directly to helium-3.

What would settle it

A clear mismatch between the VQE energy and the exact diagonalization energy for helium-3 in a noiseless simulation would show that the agreement does not hold.

Figures

Figures reproduced from arXiv: 2604.20908 by P{\i}nar \c{C}ifci, Serkan Akkoyun.

**Figure 2.** Figure 2: Schematic of a particle-number--conserving ansatz layer for three-nucleon systems. The full ansatz operates on 12 qubits (three sites × four modes), with qubits ordered as 𝑞𝑖,𝜎 where 𝜎 ∈ {𝑝 ↑, 𝑝 ↓, 𝑛 ↑, 𝑛 ↓} for each site 𝑖. Three representative qubits are shown for clarity. Fermionic hopping between adjacent sites is encoded via Givens rotations (𝑅𝑋𝑋 + 𝑅𝑌𝑌) acting on qubit pairs sharing the same spin-isos… view at source ↗

read the original abstract

We investigate the performance of quantum algorithms for light nuclear systems by studying the deuteron (2H), triton (3H), and helium-3 (3He) nuclei within a lattice formulation of pionless effective field theory (EFT). We first compute ground-state energies using classical exact diagonalization (ED), serving as a benchmark reference for variational quantum algorithms. We then perform Variational Quantum Eigensolver (VQE) calculations using noiseless classical statevector simulations of quantum circuits, enabling a controlled assessment of algorithmic performance in the absence of hardware-induced noise. We calibrate the two-body low-energy constant using the deuteron system and fit the three-body interaction strength to the triton, then consistently apply the resulting Hamiltonian parameters to the helium-3 nucleus. Our VQE calculations employ physically motivated ansatze targeting the relevant particle-number sector, with explicit particle-number-conserving constructions implemented for the triton and helium-3 systems. The variational optimization includes an analysis of the Hamiltonian energy variance roviding additional insight into convergence behavior and the quality of the variational states. We find that the VQE results are in good agreement with the corresponding classical ED ground-state energies across all three systems, including the isospin-asymmetric helium-3 nucleus with Coulomb interactions. Overall, our study provides a transparent and reproducible benchmark for assessing the applicability of variational quantum algorithms to few-body nuclear systems. Additionally, we perform a noisy VQE simulation with a depolarizing noise model for the triton system to illustrate the impact of realistic Noisy Intermediate-Scale Quantum (NISQ)-era hardware noise on variational energy estimation.

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

Solid incremental benchmark showing VQE matches ED for deuteron, triton, and He-3 in lattice pionless EFT, with particle-number conserving ansatze and a basic noise test.

read the letter

The main thing to know is that this paper runs VQE on deuteron, triton, and helium-3 in a lattice pionless EFT, fits the two-body constant to the deuteron and three-body strength to the triton, then applies the parameters to He-3 including Coulomb, and reports that the variational energies line up with exact diagonalization results. They add a depolarizing noise run for the triton and track energy variance to check variational quality. The agreement holds for the isospin-asymmetric case, and the setup uses the same Hamiltonians for VQE and ED so there is no circularity in the comparison. The particle-number conserving ansatze for the A=3 systems are a practical choice that keeps the circuits in the right sector. This is the kind of transparent, reproducible exercise that fills in the record for these specific nuclei. The soft spots are proportionate and not load-bearing. Most runs are noiseless statevector simulations, so the work mainly tests algorithmic expressivity rather than hardware noise or scaling. The systems are small enough that success is expected once the ansatz is chosen sensibly, and the abstract itself gives few numbers, though the paper supplies the details. No major fitting issues or untested assumptions jump out. This is for people already working on quantum algorithms for nuclear EFTs or few-body problems. A reader who wants concrete examples of ansatz construction and variance checks on realistic nuclear Hamiltonians will get something out of it. It is worth sending to peer review because the comparisons are direct, the methodology is clear, and the claims are supported by the reported agreement.

Referee Report

0 major / 2 minor

Summary. The manuscript benchmarks the Variational Quantum Eigensolver (VQE) for ground-state energies of the deuteron, triton, and helium-3 within a lattice pionless effective field theory. Classical exact diagonalization provides reference energies; two-body low-energy constants are calibrated to the deuteron and three-body strength to the triton, then applied consistently to helium-3 (including Coulomb). VQE employs particle-number-conserving ansatze in noiseless statevector simulations, with Hamiltonian variance analysis and an additional depolarizing-noise simulation for the triton; the central finding is good agreement between VQE and ED results across all systems.

Significance. If the reported agreement holds, the work supplies a transparent, reproducible benchmark for variational quantum algorithms applied to few-body nuclear systems in EFT. Credit is due for the use of identical Hamiltonians for VQE and ED comparisons, explicit particle-number conservation in the ansatze, variance-based assessment of variational quality, and the controlled noiseless-plus-noisy protocol that isolates algorithmic performance from hardware effects.

minor comments (2)

[Abstract] Abstract: the statement of 'good agreement' would be strengthened by inclusion of quantitative metrics (energy differences, uncertainties, or convergence thresholds) even at the abstract level.
[Abstract] Abstract: 'roviding' is a typographical error and should read 'providing'.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the positive assessment of its significance as a transparent benchmark for VQE applied to few-body nuclear systems in lattice pionless EFT. We appreciate the recommendation for minor revision and the specific credit given for our use of identical Hamiltonians for VQE and ED, particle-number-conserving ansatze, variance-based assessment, and the controlled noiseless-plus-noisy protocol.

Circularity Check

0 steps flagged

No significant circularity in the benchmarking procedure

full rationale

The paper fits two- and three-body LECs classically to deuteron and triton data, then applies the identical Hamiltonian (including Coulomb for 3He) to compute VQE energies and compares them directly to independent exact diagonalization (ED) results on the same lattice pionless EFT operator. This is a standard cross-validation benchmark rather than a derivation that reduces to its own inputs. No self-definitional steps, fitted parameters renamed as predictions, or load-bearing self-citations appear in the abstract or described workflow. The variational ansatze are assessed via energy variance and noiseless statevector simulation against the external ED benchmark, keeping the central claim externally falsifiable.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The approach depends on the validity of pionless EFT for these systems and the ability of the chosen ansatze to capture the ground states.

free parameters (2)

two-body low-energy constant
Fitted to reproduce deuteron ground state energy.
three-body interaction strength
Fitted to triton ground state.

axioms (2)

domain assumption Pionless effective field theory accurately describes low-energy nuclear interactions for these light nuclei.
Used as the framework for the Hamiltonian.
domain assumption The lattice discretization is sufficient for the systems studied.
Lattice formulation of the EFT.

pith-pipeline@v0.9.0 · 5612 in / 1366 out tokens · 38899 ms · 2026-05-10T00:32:45.332701+00:00 · methodology

discussion (0)

Reference graph

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