arxiv: 2510.02124 · v2 · submitted 2025-10-02 · ⚛️ nucl-th

A low-circuit-depth quantum computing approach to the nuclear shell model

Chandan Sarma , Paul Stevenson This is my paper

Pith reviewed 2026-05-18 10:42 UTC · model grok-4.3

classification ⚛️ nucl-th

keywords quantum computingnuclear shell modelvariational quantum eigensolverSlater determinant mappingNISQ deviceserror mitigationnuclear ground states

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The pith

Mapping each nuclear Slater determinant to one qubit produces low-depth VQE circuits that recover shell-model ground states to within 4 percent after mitigation.

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

The paper introduces a qubit mapping for variational quantum eigensolver calculations of the nuclear shell model in which each Slater determinant is assigned its own qubit instead of mapping individual single-particle orbitals. This choice yields shallower circuits that run on current noisy quantum hardware. The authors test the approach on seven nuclei ranging from lithium isotopes in the p-shell to 210Po and 210Pb, executing the circuits on both a noisy simulator and real IBM hardware. With zero-noise extrapolation applied, the resulting energies deviate by less than 4 percent from exact shell-model values across all cases. The mapping is shown to be especially practical for lighter nuclei and two-nucleon systems.

Core claim

By representing the nuclear many-body basis so that each valid Slater determinant corresponds to one qubit, the Hamiltonian and the variational ansatz can be realized with far fewer entangling operations than in standard orbital-to-qubit encodings, thereby making ground-state energy calculations for nuclei up to mass 210 feasible on present-day NISQ processors.

What carries the argument

The Slater-determinant qubit mapping, which encodes the nuclear configuration space by placing one qubit per many-body basis state so that the variational ansatz requires only low-depth circuits.

If this is right

The method enables simulation of 22-qubit and 29-qubit systems for 210Po and 210Pb respectively.
Post-mitigation energies agree with shell-model predictions to better than 4 percent for every nucleus studied.
The approach proves especially effective for lighter nuclei and two-nucleon systems.
It supplies a concrete route for near-term quantum simulations of nuclear structure on NISQ devices.

Where Pith is reading between the lines

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

The reduced circuit depth could make quantum simulation competitive for nuclei whose Slater-determinant spaces are too large for exact classical diagonalization.
The same encoding might be tested on other fermionic many-body problems where basis states can be enumerated.
Combining the mapping with adaptive or hardware-efficient ansatze could extend the reachable mass range without increasing depth.

Load-bearing premise

The chosen variational ansatz together with the Slater-determinant mapping is expressive enough to reach the true ground state with the low-depth circuits that are actually executed.

What would settle it

Exact classical diagonalization of the identical nuclear Hamiltonians to obtain the precise ground-state energies, followed by direct comparison with the mitigated VQE results; any systematic deviation larger than a few percent that persists after mitigation would show the ansatz fails to capture the ground state.

Figures

Figures reproduced from arXiv: 2510.02124 by Chandan Sarma, Paul Stevenson.

**Figure 2.** Figure 2: FIG. 2. Single excitation Givens rotation in terms of basic [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Double excitation Givens rotation in terms of basic quantum gates. Adapted from [ [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Double excitation ansatz for [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Single excitation ansatz for [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Convergence of binding energies of (a) [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Histograms of single excitation circuits for [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Comparison of the performance of single and double excitation circuits in reproducing the g.s binding energy of [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. Zero noise extrapolation performed on the noisy simulated results for [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. Zero noise extrapolation performed on the hardware results for all seven nuclei considered in this work with using a [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11. The best error mitigated results from noisy simulator and quantum hardware are compared with the shell model [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗

read the original abstract

In this work, we introduce a new qubit mapping strategy for the Variational Quantum Eigensolver (VQE) applied to nuclear shell model calculations, where each Slater determinant (SD) is mapped to a qubit, rather than assigning qubits to individual single-particle states. While this approach may increase the total number of qubits required in some cases, it enables the construction of simpler quantum circuits that are more compatible with current noisy intermediate-scale quantum (NISQ) devices. We apply this method to seven nuclei: Four lithium isotopes $^{6-9}$Li from the \textit{p}-shell, $^{18}$F from the \textit{sd}-shell, and two heavier nuclei ($^{210}$Po, and $^{210}$Pb). We run circuits representing their ground states on a noisy simulator (IBM's \textit{FakeFez} backend) and quantum hardware ($ibm\_pittsburgh$). For heavier nuclei, we demonstrate the feasibility of simulating $^{210}$Po and $^{210}$Pb as 22- and 29-qubit systems, respectively. Additionally, we employ Zero-Noise Extrapolation (ZNE) via two-qubit gate folding to mitigate errors in both simulated and hardware-executed results. Post-mitigation, the best results show less than 4 \% deviation from shell model predictions across all nuclei studied. This SD-based qubit mapping proves particularly effective for lighter nuclei and two-nucleon systems, offering a promising route for near-term quantum simulations in nuclear physics.

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 SD-to-qubit mapping is a workable alternative encoding for nuclear VQE on NISQ hardware, but the paper does not show that the low-depth ansatz actually reaches the ground state in the mapped space.

read the letter

The main takeaway is that this paper maps each Slater determinant directly to one qubit for VQE nuclear shell-model work instead of the usual single-particle-state encoding. That choice trades more qubits for simpler circuits, and they run it on lithium isotopes, 18F, and then 210Po and 210Pb as 22- and 29-qubit systems. After zero-noise extrapolation on both a noisy simulator and real IBM hardware, the energies stay within 4% of classical shell-model results. That is the concrete result they deliver. The approach looks practical for near-term devices on these sizes, and the heavier cases are a step beyond the lighter nuclei that most prior VQE nuclear papers have stayed with. The mapping itself is presented as distinct from earlier work, and the comparisons are to independent classical predictions rather than fitted quantities, so there is no obvious circularity. What is missing is any real check on the variational side. The abstract and the reported numbers give no circuit depth, no parameter count, and no direct comparison of the converged VQE energy to exact diagonalization inside the same Slater-determinant space. With one qubit per determinant the Hilbert space is 2^N dimensional, so even a modest-depth hardware-efficient ansatz spans only a tiny fraction of it. For the heavier nuclei where configuration mixing matters, the observed agreement could come from the ansatz staying close to a restricted manifold rather than from the mapping being accurate. That is the load-bearing assumption that is not tested. The paper is aimed at people who want to run nuclear-structure calculations on current quantum hardware and are willing to try different encodings. It has enough new mapping idea plus actual hardware numbers to be worth a referee's time, though any review will need the ansatz details and convergence checks filled in. I would send it to peer review rather than desk-reject.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a Slater-determinant-to-qubit mapping for the Variational Quantum Eigensolver (VQE) in nuclear shell-model calculations, assigning one qubit per selected SD rather than per single-particle orbital. This encoding is used to construct low-depth circuits for the ground states of seven nuclei (^{6-9}Li, ^{18}F, ^{210}Po with 22 qubits, and ^{210}Pb with 29 qubits). Circuits are executed on IBM's FakeFez noisy simulator and ibm_pittsburgh hardware; zero-noise extrapolation via two-qubit gate folding is applied for error mitigation. The central numerical result is that post-mitigation energies deviate by less than 4% from classical shell-model predictions across all cases.

Significance. If the numerical results hold after the requested verification, the work provides a concrete demonstration that an SD-based encoding can enable hardware-executable circuits for nuclei up to 29 qubits, extending NISQ-era quantum simulations beyond the lightest systems. The explicit use of ZNE on both simulator and real hardware, together with the reported feasibility for two heavier nuclei, supplies a useful benchmark for the community. The approach is noted as especially promising for lighter nuclei and two-nucleon systems.

major comments (2)

[Abstract and numerical results] Abstract and Section on numerical results: the central claim that post-mitigation energies lie within 4% of shell-model predictions assumes the low-depth variational ansatz reaches a state whose energy is close to the true ground state of the Hamiltonian in the chosen SD subspace. With one qubit per SD, the Hilbert space dimension is 2^N (N=22 or 29), yet no circuit depth, layer count, parameter number, or optimization convergence diagnostics are supplied. A hardware-efficient ansatz with modest depth spans only an exponentially small fraction of this space, so the observed agreement could arise from the ansatz being confined to a restricted variational manifold rather than from faithful ground-state preparation.
[Methods / Results] Methods / Results section: no direct comparison is reported between the converged VQE energy and the exact lowest eigenvalue obtained by classical diagonalization of the Hamiltonian matrix constructed within the identical truncated set of Slater determinants. Such a benchmark is required to establish that the variational minimum has been reached and that the <4% deviation is not an artifact of limited ansatz expressivity.

minor comments (2)

[Abstract] Abstract: the qualitative statement that the mapping 'proves particularly effective for lighter nuclei and two-nucleon systems' would be strengthened by quantitative metrics such as gate-count reduction or achieved circuit depth relative to standard orbital-to-qubit mappings.
[Throughout] Throughout: clarify whether the 'shell model predictions' used for comparison are full-space diagonalizations or the exact energies within the same small SD subspace employed for the quantum calculation; this distinction affects interpretation of the reported deviations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important aspects of variational convergence and benchmarking that we will clarify in the revision. Below we respond point by point to the major comments.

read point-by-point responses

Referee: [Abstract and numerical results] Abstract and Section on numerical results: the central claim that post-mitigation energies lie within 4% of shell-model predictions assumes the low-depth variational ansatz reaches a state whose energy is close to the true ground state of the Hamiltonian in the chosen SD subspace. With one qubit per SD, the Hilbert space dimension is 2^N (N=22 or 29), yet no circuit depth, layer count, parameter number, or optimization convergence diagnostics are supplied. A hardware-efficient ansatz with modest depth spans only an exponentially small fraction of this space, so the observed agreement could arise from the ansatz being confined to a restricted variational manifold rather than from faithful ground-state preparation.

Authors: We agree that explicit circuit-depth, layer-count, parameter-count, and convergence diagnostics were not included and that these details are necessary to assess ansatz expressivity. In the revised manuscript we will add a dedicated subsection in Methods describing the hardware-efficient ansatz (number of layers, entangling gates, and total variational parameters) together with optimization convergence plots for each nucleus. We note that the SD-to-qubit mapping was deliberately chosen to permit shallow circuits whose action remains within the physically relevant manifold spanned by the selected determinants; the close post-ZNE agreement with classical shell-model energies across seven nuclei (including two-nucleon systems) provides empirical support that the variational minimum lies near the ground state. Nevertheless, we will expand the discussion to address the referee’s concern about possible restriction to a sub-manifold. revision: yes
Referee: [Methods / Results] Methods / Results section: no direct comparison is reported between the converged VQE energy and the exact lowest eigenvalue obtained by classical diagonalization of the Hamiltonian matrix constructed within the identical truncated set of Slater determinants. Such a benchmark is required to establish that the variational minimum has been reached and that the <4% deviation is not an artifact of limited ansatz expressivity.

Authors: We acknowledge that a direct classical diagonalization benchmark within the identical truncated SD subspace was not presented. For the lighter nuclei (^{6-9}Li and ^{18}F) the selected SD spaces are small enough that exact diagonalization is feasible; we will add these comparisons in the revised Results section, confirming that the VQE energies converge to the exact subspace ground-state energies within the reported precision. For the heavier systems (^{210}Po, 22 qubits; ^{210}Pb, 29 qubits) the 2^{22}–2^{29} dimensional matrices cannot be diagonalized classically on current hardware, which is precisely the regime where the quantum approach becomes advantageous. In those cases we will instead report the classical shell-model energies obtained in the full (untruncated) valence space and discuss the truncation error separately. We believe these additions will satisfy the referee’s request while respecting computational limits. revision: partial

Circularity Check

0 steps flagged

No circularity detected; results benchmarked against independent classical shell-model calculations

full rationale

The paper defines a new Slater-determinant-to-qubit mapping, constructs variational circuits for ground-state preparation, executes them on simulators and hardware, applies standard ZNE mitigation, and reports energies that deviate by less than 4% from separate classical shell-model diagonalizations. No equation or parameter is fitted to the target nuclei and then re-used to generate the reported 'prediction'; the shell-model reference values are computed externally and independently. No self-citations, uniqueness theorems, or ansatzes from prior author work are invoked as load-bearing justifications. The derivation chain therefore remains self-contained and externally falsifiable.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Review performed from abstract only; full paper likely contains additional variational parameters and explicit mapping definitions not visible here.

free parameters (1)

VQE ansatz parameters
Variational parameters are optimized during the algorithm; their number and initialization are not stated in the abstract.

axioms (1)

domain assumption The nuclear shell-model Hamiltonian can be represented as a qubit operator under the Slater-determinant mapping.
This mapping is the central technical step required to run the VQE.

pith-pipeline@v0.9.0 · 5796 in / 1310 out tokens · 36287 ms · 2026-05-18T10:42:18.305162+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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

Improved quasiparticle nuclear Hamiltonians for quantum computing
nucl-th 2026-04 unverdicted novelty 5.0

Brillouin-Wigner perturbation theory plus Hartree-Fock mean-field approximation upgrades quasiparticle nuclear Hamiltonians, yielding <0.2% and ~2% ground-state energy errors versus exact shell-model results in the sd...

Reference graph

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