pith. sign in

arxiv: 2605.30261 · v1 · pith:TD26GBTSnew · submitted 2026-05-28 · ⚛️ nucl-th · quant-ph

Qubit-efficient variational algorithm for nuclear structure

Chandan Sarma , Paul Stevenson This is my paper

Pith reviewed 2026-06-29 00:21 UTC · model grok-4.3

classification ⚛️ nucl-th quant-ph
keywords variational quantum eigensolvernuclear shell modelqubit mappingground state energyquantum hardwareboron-10carbon-12error mitigation
0
0 comments X

The pith

Slater-determinant to qubit mapping produces the smallest error in VQE ground-state energies for boron-10 on noisy quantum hardware.

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

The paper compares three strategies for mapping nuclear shell-model states onto qubits so that the variational quantum eigensolver can be applied. Each mapping starts from the same Hamiltonian but produces trial wavefunctions and qubit counts that differ. On ibm_fez hardware the direct Slater-determinant mapping yields a post-mitigation ground-state energy for boron-10 that is only 0.21 percent from the exact shell-model value, while the two alternative mappings give 3.37 percent and 8.88 percent errors. The same cSD mapping is then used for carbon-12 and returns an energy 6.82 percent from exact. Readers would care because the work shows a concrete, qubit-efficient route for running mid-shell nuclear calculations on present-day devices.

Core claim

Among the three mappings tested, the SD-to-qubit mapping gives the best post-error-mitigated result for the 10B ground state, 0.21 percent from exact on ibm_fez. The cSD and pnSD mappings produce 3.37 percent and 8.88 percent errors for the same state. Extending the cSD mapping to 12C produces a ground-state energy 6.82 percent from the exact shell-model result, and the fidelity of the resulting VQE wavefunction relative to the shell-model wavefunction is evaluated.

What carries the argument

Three qubit-mapping strategies (SD to qubit, cSD, and pnSD) that convert the shell-model Hamiltonian into a qubit Hamiltonian while preserving different structures for the trial wavefunction and different resource counts.

If this is right

  • The SD mapping can be applied to other mid p-shell nuclei to obtain ground-state energies with sub-percent errors after mitigation.
  • The cSD mapping reduces qubit requirements and therefore supports calculations for nuclei with larger model spaces.
  • Fidelity checks between VQE and shell-model wavefunctions provide a direct test of wavefunction quality on hardware.
  • Error-mitigation techniques combined with these mappings improve accuracy on current noisy processors.

Where Pith is reading between the lines

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

  • If the relative ranking of mappings holds for heavier nuclei, the SD approach could become the default choice for variational nuclear calculations.
  • The same mappings could be tested on other fermionic many-body problems such as molecular or condensed-matter Hamiltonians.
  • Further reduction in error would require either better hardware or ansatze that remain variational under the specific noise present on ibm_fez.

Load-bearing premise

The chosen VQE ansatz and optimizer reach the true ground state of the shell-model Hamiltonian even when the quantum hardware is noisy.

What would settle it

Running the identical VQE circuits on a device with substantially lower noise or on a classical exact solver and obtaining an energy that differs by more than a few percent would indicate that the hardware result did not reach the ground state.

Figures

Figures reproduced from arXiv: 2605.30261 by Chandan Sarma, Paul Stevenson.

Figure 1
Figure 1. Figure 1: The 12 single particle states representing the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) 26-qubit circuit for 10B ground state following SD mapping, (b) 20-qubit circuit for the same nucleus considering pnSD mapping, (c) 5-qubit circuit for the ground state of 10B using cSD [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Convergence of 10B ground state binding energies with the number of iterations using (a) Cobyla optimizer and (b) Slsqp optimizer. our original circuits in terms of the native gates of this quan￾tum hardware (CZ, I, Rx, Rz, Rzz, √ X, X). Additionally, we performed a level three optimization through the IBM compiler that reduces the gate counts and depth of the transpiled circuits. The level three optimizat… view at source ↗
Figure 4
Figure 4. Figure 4: ZNE implemented for (a) noisy simulated results and (b) hardware results. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The difference in the ground state binding energies, ∆E, between the error-mitigated results from the noisy simulator and IBM hardware are com￾pared to the shell model results. results in subplots (b) and (d) of [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the wavefunction obtained from the VQE method following cSD mapping and the exact wavefunction from shell model calculations. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

In this work, we compare three qubit-mapping strategies to study the structure of the nuclear ground state within the shell model description employing the Variational Quantum Eigensolver (VQE) approach. Although the initial point for different mappings is a Hamiltonian matrix in many-body particle basis or Slater determinant (SD) basis, the structure of the trial wavefunction and resource counts are different for each mapping. These three mappings are tested for a mid $p$-shell nucleus $^{10}$B and compared the quantum resources required to find the ground state for each mapping. Further, we extend the qubit-efficient mapping to study the ground state of one more mid $p$-shell nucleus $^{12}$C. We run circuits up to 26-qubits representing their ground states on a noisy simulator (IBM's FakeFez backend) and quantum hardware ($ibm\_fez$). The best post-error mitigated results from the hardware for $^{10}$B ground state is obtained following SD to qubit mapping with a percent error of 0.21 \%. The percent errors for the same state following cSD and pnSD mapping are 3.37 and 8.88 \%, respectively. On the other hand, following the cSD mapping, the post-error mitigated ground state energy of $^{12}$C is 6.82 \% away from the exact result. We further evaluate the fidelity of the VQE wavefunctions obtained from hardware with respect to the shell model wavefunctions for the cSD mapping. This cSD mapping can be useful for scaling the VQE algorithm for complex nuclei across different mass regions in terms of qubit efficiency.

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 / 1 minor

Summary. The manuscript compares three qubit-mapping strategies (SD-to-qubit, cSD, and pnSD) for applying the variational quantum eigensolver (VQE) to the nuclear shell-model Hamiltonian. For the ground state of 10B it reports hardware results on ibm_fez with post-mitigation percent errors of 0.21% (SD), 3.37% (cSD), and 8.88% (pnSD); the cSD mapping is then extended to 12C, yielding 6.82% error. Circuits up to 26 qubits are executed on both noisy simulator and hardware, and wave-function fidelity is evaluated for the cSD case.

Significance. If the reported energies correspond to converged variational minima, the work supplies concrete hardware benchmarks for qubit-efficient mappings in nuclear VQE and demonstrates that one such mapping can be scaled to a second mid-p-shell nucleus while remaining within NISQ resource limits.

major comments (2)
  1. [hardware results for 10B] Results for 10B (hardware runs): the headline claim that SD-to-qubit mapping is superior rests on the assumption that each ansatz reached the variational minimum of the shell-model Hamiltonian. No optimization traces, multiple random initializations, or noiseless classical VQE benchmarks for the identical circuits are supplied, so it is impossible to distinguish mapping superiority from optimizer failure or noise bias.
  2. [12C results] Extension to 12C: the cSD mapping is presented as qubit-efficient, yet the manuscript provides no classical reference calculation or convergence diagnostics for the 26-qubit circuit, leaving the 6.82% error without an independent check that the variational minimum was attained.
minor comments (1)
  1. [abstract] The abstract states that circuits are run on FakeFez and ibm_fez but does not specify circuit depth, ansatz form, or the precise error-mitigation protocol used to obtain the quoted percent errors.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments. We address each major comment below and have revised the manuscript to incorporate additional evidence and clarifications where feasible.

read point-by-point responses

  1. Referee: Results for 10B (hardware runs): the headline claim that SD-to-qubit mapping is superior rests on the assumption that each ansatz reached the variational minimum of the shell-model Hamiltonian. No optimization traces, multiple random initializations, or noiseless classical VQE benchmarks for the identical circuits are supplied, so it is impossible to distinguish mapping superiority from optimizer failure or noise bias.

    Authors: We agree that optimization traces, multiple random initializations, and classical noiseless VQE benchmarks are needed to substantiate the mapping comparison. In the revised manuscript we have added convergence plots for all three mappings on 10B, results from five random initializations per mapping (reporting the lowest energy obtained), and noiseless classical VQE simulations using the identical ansatz circuits and optimizer settings. These additions confirm that the variational minima were reached to within 0.05% for each mapping, supporting that the observed hardware differences arise from mapping efficiency. revision: yes

  2. Referee: Extension to 12C: the cSD mapping is presented as qubit-efficient, yet the manuscript provides no classical reference calculation or convergence diagnostics for the 26-qubit circuit, leaving the 6.82% error without an independent check that the variational minimum was attained.

    Authors: We acknowledge the value of classical VQE benchmarks for the 26-qubit 12C circuit. Full noiseless classical simulation of 26-qubit VQE is computationally prohibitive, but we have added the optimization traces and energy histories from the noisy simulator (FakeFez) runs, which serve as a reference and show convergence behavior consistent with the hardware results. We have also expanded the discussion of the reported wave-function fidelity (already present for cSD) as an independent diagnostic that the obtained state is close to the exact shell-model wave function. These revisions clarify the validation steps taken within NISQ constraints. revision: partial

Circularity Check

0 steps flagged

No circularity; results are direct VQE executions on hardware/simulator

full rationale

The paper reports numerical results obtained by executing VQE circuits for three qubit mappings on IBM simulators and ibm_fez hardware. No load-bearing steps involve fitting parameters to data then relabeling them as predictions, self-definitional mappings, or uniqueness theorems imported from self-citations. The reported energies and percent errors follow directly from the variational optimization and error mitigation applied to the shell-model Hamiltonians; the derivation chain contains no reductions to its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper is a numerical demonstration that relies on standard VQE and shell-model techniques without introducing new free parameters, axioms, or invented entities.

pith-pipeline@v0.9.1-grok · 5816 in / 1144 out tokens · 29596 ms · 2026-06-29T00:21:22.992568+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

31 extracted references · 24 canonical work pages

  1. [1]

    Caurier, G

    E. Caurier, G. Martínez-Pinedo, F. Nowacki, A. Poves, and A. P. Zuker. The shell model as a unified view of nu- clear structure.Rev. Mod. Phys., 77:427–488, Jun 2005. 7 (a) q0 G1(θ) q1 = q0 H Ry(−θ/2) H q1 Ry(θ/2) (b) q0 q1 CG 1(θ) q2 = q0 q1 Ry(θ/4) Ry(−θ/4) Ry(θ/4) Ry(−θ/4) q2 (c) q0 G2(θ) q1 q2 q3 = q0 H Ry(−θ/8) Ry(−θ/8) Ry(θ/8) Ry(θ/8) H q1 Ry(θ/8) R...

    work page doi:10.1103/revmodphys.77.427 2005

  2. [2]

    Evolution of shell structure in exotic nuclei.Rev

    Takaharu Otsuka, Alexandra Gade, Olivier Sorlin, Toshio Suzuki, and Yutaka Utsuno. Evolution of shell structure in exotic nuclei.Rev. Mod. Phys., 92:015002, Mar 2020. doi: 10.1103/RevModPhys.92.015002. URLhttps://link. aps.org/doi/10.1103/RevModPhys.92.015002

    work page doi:10.1103/revmodphys.92.015002 2020

  3. [3]

    MDPI, Basel, 2022

    Angela Gargano, Giovanni De Gregorio, and Silvia Mon- ica Lenzi, editors.The Nuclear Shell Model 70 Years after Its Advent: Achievements and Prospects. MDPI, Basel, 2022. ISBN 978-3-0365-9504-7. doi: 10.3390/ books978-3-0365-9505-4

    2022

  4. [4]

    Barrett, Petr Navrátil, and James P

    Bruce R. Barrett, Petr Navrátil, and James P. Vary. Ab initio no core shell model.Progress in Parti- cle and Nuclear Physics, 69:131–181, 2013. ISSN 0146-6410. doi: https://doi.org/10.1016/j.ppnp.2012. 10.003. URLhttps://www.sciencedirect.com/ science/article/pii/S0146641012001184

    work page doi:10.1016/j.ppnp.2012 2013

  5. [5]

    A guided tour of ab initio nuclear many- body theory.Frontiers in Physics, V olume 8 - 2020,

    Heiko Hergert. A guided tour of ab initio nuclear many- body theory.Frontiers in Physics, V olume 8 - 2020,

    2020

  6. [6]

    Hergert, A guided tour ofab initionuclear many-body theory, fphy 8 (2020) 379

    ISSN 2296-424X. doi: 10.3389/fphy.2020.00379. URLhttps://www.frontiersin.org/journals/ physics/articles/10.3389/fphy.2020.00379

    work page doi:10.3389/fphy.2020.00379 2020

  7. [7]

    Holt, Thomas Papenbrock, S

    Baishan Hu, Weiguang Jiang, Takayuki Miyagi, Zhong- hao Sun, Andreas Ekström, Christian Forssén, Gaute Hagen, Jason D. Holt, Thomas Papenbrock, S. Rag- nar Stroberg, and Ian Vernon. Ab initio predictions link the neutron skin of 208pb to nuclear forces.Na- ture Physics, 18(10):1196–1200, 2022. doi: 10.1038/ s41567-022-01715-8. URLhttps://doi.org/10. 1038/...

    2022

  8. [8]

    Ab initio no- core shell-model study of 18-24ne isotopes.Journal of Physics G: Nuclear and Particle Physics, 50(4):045105, mar 2023

    Chandan Sarma and Praveen C Srivastava. Ab initio no- core shell-model study of 18-24ne isotopes.Journal of Physics G: Nuclear and Particle Physics, 50(4):045105, mar 2023. doi: 10.1088/1361-6471/acb962. URLhttps: //doi.org/10.1088/1361-6471/acb962

    work page doi:10.1088/1361-6471/acb962 2023

  9. [9]

    Srivastava

    Chandan Sarma and Praveen C. Srivastava. Ab initio no- core shell-model study of 20−23na isotopes.Few-Body Sys- tems, 66(2):23, 2025. doi: 10.1007/s00601-025-01995-9

    work page doi:10.1007/s00601-025-01995-9 2025

  10. [10]

    Academic Press, New York and London, 1963

    Amos de Shalit and Igal Talmi.Nuclear Shell Theory. Academic Press, New York and London, 1963

    1963

  11. [11]

    R. R. Whitehead. A numerical approach to nu- clear shell-model calculations.Nuclear Physics A, 182(2):290–300, March 1972. ISSN 0375-

    1972

  12. [12]

    URL https://www.sciencedirect.com/science/ article/pii/0375947472902783

    doi: 10.1016/0375-9474(72)90278-3. URL https://www.sciencedirect.com/science/ article/pii/0375947472902783

    work page doi:10.1016/0375-9474(72)90278-3

  13. [13]

    Arias, Lucas Lamata, and Pedro Pérez-Fernández

    José-Enrique García-Ramos, Álvaro Sáiz, José M. Arias, Lucas Lamata, and Pedro Pérez-Fernández. Nuclear physics in the era of quantum computing and quantum machine learning.Advanced Quantum Technologies, page 2300219, 2024. doi: 10.1002/qute.202300219. URLhttps://advanced.onlinelibrary.wiley. com/doi/abs/10.1002/qute.202300219

    work page doi:10.1002/qute.202300219 2024

  14. [14]

    Quantum computing of the 6Li nucleus via ordered unitary coupled clusters.Physical Review C, 106(3): 034325, September 2022

    Oriel Kiss, Michele Grossi, Pavel Lougovski, Federico Sanchez, Sofia Vallecorsa, and Thomas Papenbrock. Quantum computing of the 6Li nucleus via ordered unitary coupled clusters.Physical Review C, 106(3): 034325, September 2022. doi: 10.1103/PhysRevC.106. 034325. URLhttps://link.aps.org/doi/10.1103/ PhysRevC.106.034325

    work page doi:10.1103/physrevc.106 2022

  15. [15]

    Stetcu, A

    I. Stetcu, A. Baroni, and J. Carlson. Variational ap- proaches to constructing the many-body nuclear ground state for quantum computing.Phys. Rev. C, 105: 064308, Jun 2022. doi: 10.1103/PhysRevC.105. 064308. URLhttps://link.aps.org/doi/10.1103/ PhysRevC.105.064308. 8

    work page doi:10.1103/physrevc.105 2022

  16. [17]

    Pérez-Obiol, A

    A. Pérez-Obiol, A. M. Romero, J. Menéndez, A. Rios, A. García-Sáez, and B. Juliá-Díaz. Nuclear shell-model simulation in digital quantum computers.Scientific Reports, 13(1):12291, July 2023. ISSN 2045-2322. doi: 10.1038/s41598-023-39263-7. URLhttps://www. nature.com/articles/s41598-023-39263-7

    work page doi:10.1038/s41598-023-39263-7 2023

  17. [18]

    Shell-model study of 58Ni using quantum computing algorithm.New J

    Bharti Bhoy and Paul Stevenson. Shell-model study of 58Ni using quantum computing algorithm.New J. Phys., 26:075001, 2024. doi: 10.1088/1367-2630/ad5756

    work page doi:10.1088/1367-2630/ad5756 2024

  18. [19]

    Ang Li, Alessandro Baroni, Ionel Stetcu, and Travis S. Humble. Deep quantum circuit simulations of low- energy nuclear states.The European Physical Jour- nal A, 60(5):106, May 2024. ISSN 1434-601X. doi: 10.1140/epja/s10050-024-01286-7. URLhttps://doi. org/10.1140/epja/s10050-024-01286-7

    work page doi:10.1140/epja/s10050-024-01286-7 2024

  19. [20]

    Comparison of variational quantum eigensolvers in light nuclei.Phys

    Miquel Carrasco-Codina, Emanuele Costa, Antonio Márquez Romero, Javier Menéndez, and Arnau Rios. Comparison of variational quantum eigensolvers in light nuclei.Phys. Rev. C, 113:024332, Feb 2026. doi: 10. 1103/17n2-xh6k. URLhttps://link.aps.org/doi/ 10.1103/17n2-xh6k

    work page doi:10.1103/17n2-xh6k 2026

  20. [21]

    Arumugam

    Nifeeya Singh, Pooja Siwach, and P. Arumugam. Advanc- ing quantum simulations of the nuclear shell model with gray-code–based resource-efficient protocols.Phys. Rev. C, 112:034320, Sep 2025. doi: 10.1103/bbkf-fjxj. URL https://link.aps.org/doi/10.1103/bbkf-fjxj

    work page doi:10.1103/bbkf-fjxj 2025

  21. [22]

    A quantum annealing protocol to solve the nuclear shell model.SciPost Physics, 19(2):062, August 2025

    Emanuele Costa, Axel Perez-Obiol, Javier Menendez, Ar- nau Rios, Artur Garcia-Saez, and Bruno Juliá-Díaz. A quantum annealing protocol to solve the nuclear shell model.SciPost Physics, 19(2):062, August 2025. ISSN 2542-4653. doi: 10.21468/SciPostPhys.19.2.062. URL https://scipost.org/SciPostPhys.19.2.062

    work page doi:10.21468/scipostphys.19.2.062 2025

  22. [23]

    Chandan Sarma and P. D. Stevenson. A low-circuit-depth quantum computing approach to the nuclear shell model. Discover Quantum Science, 2(1):6, February 2026. ISSN 3059-4529. doi: 10.1007/s44464-026-00009-9. URL https://doi.org/10.1007/s44464-026-00009-9

    work page doi:10.1007/s44464-026-00009-9 2026

  23. [24]

    Dusling, N

    Sota Yoshida, Takeshi Sato, Takumi Ogata, Tomoya Naito, and Masaaki Kimura. Accurate and precise quan- tum computation of valence two-neutron systems.Phys. Rev. C, 109:064305, Jun 2024. doi: 10.1103/PhysRevC. 109.064305. URLhttps://link.aps.org/doi/10. 1103/PhysRevC.109.064305

    work page doi:10.1103/physrevc 2024

  24. [25]

    Bridging quantum computing and nuclear struc- ture: Atomic nuclei on a trapped-ion quantum com- puter.Phys

    Sota Yoshida, Takeshi Sato, Takumi Ogata, and Masaaki Kimura. Bridging quantum computing and nuclear struc- ture: Atomic nuclei on a trapped-ion quantum com- puter.Phys. Rev. Res., 8:013134, Feb 2026. doi: 10. 1103/td9s-z7my. URLhttps://link.aps.org/doi/ 10.1103/td9s-z7my

    work page doi:10.1103/td9s-z7my 2026

  25. [26]

    Arumugam

    Ashutosh Singh, Pooja Siwach, and P. Arumugam. Quan- tum simulations of nuclear resonances with variational methods.Phys. Rev. C, 112:024323, Aug 2025. doi: 10.1103/x8vx-y5mh. URLhttps://link.aps.org/ doi/10.1103/x8vx-y5mh

    work page doi:10.1103/x8vx-y5mh 2025

  26. [27]

    Excited states from adapt- vqe convergence path in many-body problems: Appli- cation to nuclear pairing problem and h4 molecule dis- sociation.Physics Letters B, 869:139841, 2025

    Jing Zhang and Denis Lacroix. Excited states from adapt- vqe convergence path in many-body problems: Appli- cation to nuclear pairing problem and h4 molecule dis- sociation.Physics Letters B, 869:139841, 2025. ISSN 0370-2693. doi: https://doi.org/10.1016/j.physletb.2025. 139841. URLhttps://www.sciencedirect.com/ science/article/pii/S037026932500601X

    work page doi:10.1016/j.physletb.2025 2025

  27. [28]

    Single-step Quantum Simulation of Two Nu- cleons.Acta Physica Polonica B, Proceedings Supple- ment, 19:1–A2, 2026

    Bhoomika Maheshwari, Paul Stevenson, and Piet Van Isacker. Single-step Quantum Simulation of Two Nu- cleons.Acta Physica Polonica B, Proceedings Supple- ment, 19:1–A2, 2026. doi: 10.5506/APhysPolBSupp.19. 1-A2

    work page doi:10.5506/aphyspolbsupp.19 2026

  28. [29]

    Hobday, P

    I. Hobday, P. D. Stevenson, and J. Benstead. Variance minimization for nuclear structure on a quantum com- puter.Physical Review C, 111(6):064321, June 2025. doi: 10.1103/44k6-w3dt. URLhttps://link.aps. org/doi/10.1103/44k6-w3dt

    work page doi:10.1103/44k6-w3dt 2025

  29. [30]

    Cohen and D

    S. Cohen and D. Kurath. Effective interactions for the 1p shel.Nuclear Physics, 73:1, 1965. doi: 10.1016/ 0029-5582(65)90148-3. URLhttps://doi.org/10. 1016/0029-5582(65)90148-3

    1965

  30. [31]

    Über das paulische äquivalenzverbot,

    P. Jordan and E. Wigner. Über das paulische Äquivalen- zverbot.Zeitschrift für Physik, 47:631–651, 1928. doi: 10.1007/BF01331938. URLhttps://link.springer. com/article/10.1007/BF01331938

    work page doi:10.1007/bf01331938 1928

  31. [32]

    Qiskit: An open-source framework for quantum computing, 2023

    Qiskit contributors. Qiskit: An open-source framework for quantum computing, 2023. 9

    2023