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arxiv: 2504.11689 · v1 · pith:OQZPOCTVnew · submitted 2025-04-16 · 🪐 quant-ph · nucl-th

Advancing quantum simulations of nuclear shell model with noise-resilient protocols

Nifeeya Singh , Pooja Siwach , P. Arumugam This is my paper

Pith reviewed 2026-05-25 08:38 UTC · model grok-4.3

classification 🪐 quant-ph nucl-th
keywords nuclear shell modelquantum simulationvariational quantum eigensolverNISQ devicesGray code encodingnoise mitigation38Ar6Li
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The pith

Noise-resilient quantum protocols compute nuclear shell-model energies for 38Ar and 6Li with improved accuracy on NISQ hardware.

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

The paper develops variational quantum algorithms tailored to the nuclear shell model to address the exponential growth of Hilbert space in many-body nuclear calculations. It combines an optimized ansatz based on Givens rotations, qubit-ADAPT-VQE with variational quantum deflation, Gray code encoding to map basis states to fewer qubits, generalized fermionic operator transformations, and zero-noise extrapolation to mitigate device noise. These elements are applied to compute ground and excited state energies, with results shown for noiseless simulations, noisy runs, and mitigated cases, outperforming standard Jordan-Wigner approaches in accuracy for the chosen nuclei. A sympathetic reader would care because the work shows concrete steps toward making quantum computers usable for realistic nuclear physics problems despite current hardware limitations.

Core claim

By employing Gray code encoding to reduce qubit requirements and generalizing transformations of fermionic operators, together with a Givens-rotation ansatz in VQE, qubit-ADAPT-VQE combined with VQD, and zero-noise extrapolation, the ground and excited state energy levels of 38Ar and 6Li are obtained with better accuracy under noisy conditions than with conventional encodings and methods.

What carries the argument

Gray code encoding of basis states combined with zero-noise extrapolation applied to VQE variants (including qubit-ADAPT-VQE and VQD) to achieve noise resilience while lowering qubit and gate counts.

If this is right

  • Fewer qubits and gates become available for larger nuclei or more complex interactions.
  • Ground and excited state energies can be extracted reliably enough to compare with experimental nuclear data.
  • The same protocol stack applies to both Jordan-Wigner and Gray code mappings, allowing direct benchmarking.
  • Noise mitigation extends the usable range of current NISQ devices for many-body fermionic problems.

Where Pith is reading between the lines

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

  • If hardware noise continues to decrease, the same encoding and mitigation stack could handle nuclei beyond mass 38 without classical pre-processing.
  • The approach may transfer to other fermionic many-body systems such as molecular Hamiltonians where Gray code locality helps.
  • Testing the full pipeline on actual quantum hardware rather than simulators would reveal whether the reported accuracy gains survive real gate errors.

Load-bearing premise

The Gray code mapping of nuclear basis states to qubits and the generalized fermionic operator transformations correctly capture the many-body states without major approximation errors.

What would settle it

A direct comparison showing that the mitigated quantum energies for 38Ar and 6Li deviate from exact classical shell-model diagonalization by more than the accuracy gain reported after applying the protocols.

Figures

Figures reproduced from arXiv: 2504.11689 by Nifeeya Singh, P. Arumugam, Pooja Siwach.

Figure 1
Figure 1. Figure 1: FIG. 1. Quantum circuit to prepare superposition of states [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Quantum circuit to prepare superposition of states [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The decomposition of double excitation circuit in terms of single- and two-qubit gates. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Level scheme of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Level scheme of [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: and 7. From Table X, it is evident that the GC encoding yields the extrapolated energies closer to the exact value. However, the JW shows a greater deviation, suggesting it is more sensitive to noise due to increased circuit depth and gate errors. For 0+ state, the JW scheme results in a significantly large deviation. Overall the results show that GC has better accuracy, where extrapolated values are much … view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Quantum circuit to prepare ansatz given in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Quantum circuit for 0 [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Quantum circuit for 1 [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Quantum circuit for 2 [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Quantum circuit for 0 [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Quantum circuit for 1 [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Quantum circuit for 0 [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Quantum circuit for 1 [PITH_FULL_IMAGE:figures/full_fig_p017_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Quantum circuit for 2 [PITH_FULL_IMAGE:figures/full_fig_p017_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Quantum circuit for 0 [PITH_FULL_IMAGE:figures/full_fig_p017_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19. Quantum circuit for 1 [PITH_FULL_IMAGE:figures/full_fig_p017_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20. Quantum circuit for 2 [PITH_FULL_IMAGE:figures/full_fig_p019_20.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22. Quantum circuit for 0 [PITH_FULL_IMAGE:figures/full_fig_p019_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: FIG. 23. Quantum circuit for 1 [PITH_FULL_IMAGE:figures/full_fig_p019_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: FIG. 24. Quantum circuit for 2 [PITH_FULL_IMAGE:figures/full_fig_p019_24.png] view at source ↗
read the original abstract

Some of the computational limitations in solving the nuclear many-body problem could be overcome by utilizing quantum computers. The nuclear shell-model calculations providing deeper insights into the properties of atomic nuclei, is one such case with high demand for resources as the size of the Hilbert space grows exponentially with the number of particles involved. Quantum algorithms are being developed to overcome these challenges and advance such calculations. To develop quantum circuits for the nuclear shell-model, leveraging the capabilities of noisy intermediate-scale quantum (NISQ) devices. We aim to minimize resource requirements (specifically in terms of qubits and gates) and strive to reduce the impact of noise by employing relevant mitigation techniques. We achieve noise resilience by designing an optimized ansatz for the variational quantum eigensolver (VQE) based on Givens rotations and incorporating qubit-ADAPT-VQE in combination with variational quantum deflation (VQD) to compute ground and excited states incorporating the zero-noise extrapolation mitigation technique. Furthermore, the qubit requirements are significantly reduced by mapping the basis states to qubits using Gray code encoding and generalizing transformations of fermionic operators to efficiently represent manybody states. By employing the noise-resilient protocols, we achieve the ground and excited state energy levels of 38Ar and 6Li with better accuracy. These energy levels are presented for noiseless simulations, noisy conditions, and after applying noise mitigation techniques. Results are compared for Jordan Wigner and Gray code encoding using VQE, qubit-ADAPT-VQE, and VQD. Our work highlights the potential of noise-resilient protocols to leverage the full potential of NISQ devices in scaling the nuclear shell model calculations.

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 manuscript develops quantum circuits for nuclear shell-model calculations on NISQ devices by combining Gray-code encoding of many-body basis states with generalized fermionic operator transformations to reduce qubit count, an optimized Givens-rotation ansatz, qubit-ADAPT-VQE, VQD for excited states, and zero-noise extrapolation. It applies these protocols to compute ground- and excited-state energies of 38Ar and 6Li and asserts that the noise-resilient combination yields higher accuracy than standard Jordan-Wigner implementations under both noiseless and noisy conditions.

Significance. If the Gray-code mapping is shown to reproduce the exact shell-model Hamiltonian and the reported energy improvements are statistically robust, the work would provide a concrete route to lowering qubit and gate overhead for nuclear many-body problems, thereby extending the reach of variational algorithms on current hardware.

major comments (2)
  1. [qubit mapping and operator transformations section] The section on qubit mapping and operator transformations asserts that Gray-code encoding together with the generalized fermionic creation/annihilation transformations correctly represents the many-body states, yet supplies no explicit verification (e.g., a side-by-side comparison of two-body matrix elements or the full Hamiltonian matrix for the 6Li valence space against the standard second-quantized shell-model operator). Because all subsequent VQE/VQD/ZNE results rest on this equivalence, the absence of such a check is load-bearing for the central accuracy claim.
  2. [results section] Results section (tables/figures presenting energies for 38Ar and 6Li): the manuscript states that the noise-resilient protocols achieve “better accuracy,” but the abstract and the provided description contain no numerical values, error bars, or direct quantitative comparison between Gray-code and Jordan-Wigner runs under identical shot budgets and noise models. Without these data the improvement cannot be assessed.
minor comments (2)
  1. Figure captions and axis labels should explicitly state the number of shots, the noise model parameters, and whether the plotted energies are variational minima or extrapolated values.
  2. The manuscript would benefit from a short table listing the exact valence-space dimensions, the number of qubits required under each encoding, and the circuit depth for the ansatz used for each nucleus.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and will revise the manuscript to incorporate the requested clarifications and data.

read point-by-point responses

  1. Referee: [qubit mapping and operator transformations section] The section on qubit mapping and operator transformations asserts that Gray-code encoding together with the generalized fermionic creation/annihilation transformations correctly represents the many-body states, yet supplies no explicit verification (e.g., a side-by-side comparison of two-body matrix elements or the full Hamiltonian matrix for the 6Li valence space against the standard second-quantized shell-model operator). Because all subsequent VQE/VQD/ZNE results rest on this equivalence, the absence of such a check is load-bearing for the central accuracy claim.

    Authors: We agree that an explicit verification is necessary to substantiate the equivalence. In the revised manuscript we will add a side-by-side comparison of the two-body matrix elements (and, space permitting, the full Hamiltonian matrix) for the 6Li valence space between the Gray-code mapped operators and the standard second-quantized shell-model operators. revision: yes

  2. Referee: [results section] Results section (tables/figures presenting energies for 38Ar and 6Li): the manuscript states that the noise-resilient protocols achieve “better accuracy,” but the abstract and the provided description contain no numerical values, error bars, or direct quantitative comparison between Gray-code and Jordan-Wigner runs under identical shot budgets and noise models. Without these data the improvement cannot be assessed.

    Authors: The full manuscript contains tables and figures reporting the energies under noiseless, noisy, and mitigated conditions with comparisons between encodings. To make the claimed improvements quantitatively assessable, we will augment the results section with explicit numerical values, error bars obtained from repeated runs, and direct side-by-side error metrics (relative to exact diagonalization) for Gray-code versus Jordan-Wigner under matched shot budgets and noise models. We will also update the abstract to include representative numerical gains. revision: yes

Circularity Check

0 steps flagged

No circularity; computational demonstration on standard techniques

full rationale

The paper applies established methods (VQE, qubit-ADAPT-VQE, VQD, Gray-code encoding, ZNE) to compute nuclear shell-model energies for 38Ar and 6Li. No derivation chain, equation, or central claim reduces by construction to fitted inputs or self-citations. The work is a numerical demonstration whose results are externally falsifiable against known shell-model benchmarks; the encoding and operator mappings are presented as implementation choices rather than self-defining the target energies. This matches the default expectation of a self-contained application paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient detail to enumerate free parameters, axioms, or invented entities; work appears to rest on standard quantum-computing and nuclear-physics assumptions not enumerated here.

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discussion (0)

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Reference graph

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