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Towards Quantum Simulation of Rotating Nuclei using Quantum Variational Algorithms

Dhritimalya Roy, Somnath Nag

TL;DR

This study benchmarks quantum variational algorithms on CNS-inspired Hamiltonians that model rotating nuclei, using a hierarchical set of four models of increasing realism. By mapping fermionic CNS terms to qubits via Jordan-Wigner and employing model-specific ansatzes, the authors assess VQE performance against exact diagonalization across rotation frequencies. They find that simpler models deliver high energy accuracy, while the most realistic 8-spin-orbital cases expose optimization and symmetry-leakage challenges, though qualitative rotational behavior (e.g., monotonic growth of $\langle J_x\rangle$ with cranking) is captured. The work establishes a systematic baseline for NISQ nuclear-structure simulations and motivates symmetry-preserving and adaptive quantum algorithms to overcome current limitations.

Abstract

Quantum variational algorithms (QVAs) are increasingly potent tools for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. This work examines the application of the Variational Quantum Eigensolver (VQE) to four progressively complex models based on the cranked Nilsson-Strutinsky (CNS) framework. By incorporating single-particle spacings, pairing correlations, and rotational cranking terms, we evaluate VQE performance against exact diagonalization (ED) benchmarks. Our results demonstrate that while simpler models achieve high precision (errors $<0.005$), the transition to 8-spin-orbital Hamiltonians reveals significant scaling and optimization challenges. Notably, we show that Model IV, which employs a more expressive RealAmplitudes ansatz, successfully captures the qualitative physics of rotational alignment and reduces energy deviations compared to intermediate benchmarks. These results establish a systematic methodological baseline, identifying the breaking points of hardware-efficient ansatz while validating the potential of QVAs to model the complex competition between pairing and rotation in deformed nuclei.

Towards Quantum Simulation of Rotating Nuclei using Quantum Variational Algorithms

TL;DR

This study benchmarks quantum variational algorithms on CNS-inspired Hamiltonians that model rotating nuclei, using a hierarchical set of four models of increasing realism. By mapping fermionic CNS terms to qubits via Jordan-Wigner and employing model-specific ansatzes, the authors assess VQE performance against exact diagonalization across rotation frequencies. They find that simpler models deliver high energy accuracy, while the most realistic 8-spin-orbital cases expose optimization and symmetry-leakage challenges, though qualitative rotational behavior (e.g., monotonic growth of with cranking) is captured. The work establishes a systematic baseline for NISQ nuclear-structure simulations and motivates symmetry-preserving and adaptive quantum algorithms to overcome current limitations.

Abstract

Quantum variational algorithms (QVAs) are increasingly potent tools for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. This work examines the application of the Variational Quantum Eigensolver (VQE) to four progressively complex models based on the cranked Nilsson-Strutinsky (CNS) framework. By incorporating single-particle spacings, pairing correlations, and rotational cranking terms, we evaluate VQE performance against exact diagonalization (ED) benchmarks. Our results demonstrate that while simpler models achieve high precision (errors ), the transition to 8-spin-orbital Hamiltonians reveals significant scaling and optimization challenges. Notably, we show that Model IV, which employs a more expressive RealAmplitudes ansatz, successfully captures the qualitative physics of rotational alignment and reduces energy deviations compared to intermediate benchmarks. These results establish a systematic methodological baseline, identifying the breaking points of hardware-efficient ansatz while validating the potential of QVAs to model the complex competition between pairing and rotation in deformed nuclei.

Paper Structure

This paper contains 25 sections, 8 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Theoretical Models and Quantum Simulation Framework
  3. Unified CNS-Inspired Hamiltonian and Qubit Mapping
  4. General Form of the Hamiltonian
  5. Choice of Numerical Parameters in the Models
  6. Mapping to Qubit Space
  7. A Hierarchy of CNS-Inspired Quantum Hamiltonians
  8. Model I: Schematic Pauli Representation
  9. Model II: Number-Constrained Two-Fermion System
  10. Model III: Fermionic CNS Hamiltonian Without Explicit Cranking
  11. Model IV: Full Pairing + Cranking CNS Hamiltonian
  12. Quantum Methods: Ansatz Design, Optimization, and Observable Extraction
  13. Ansatz considerations for pairing and rotation
  14. Optimization and convergence behaviour
  15. Extraction of physical observables
  16. ...and 10 more sections

Figures (4)

  • Figure 1: Comparison of the exact and VQE energies for Model I.
  • Figure 2: Plots of (a) Ground state energy $E(\omega)$, (b) Angular momentum $\langle J_x \rangle (\omega)$, and (c) Entanglement entropy $S(\omega)$ as a function of cranking frequency $\omega$. The results from the VQE and Exact Diagonalization (ED) are compared for Model III.
  • Figure 3: Comparison of VQE and Exact Diagonalization: (a) Energy, (b) $\langle J_x \rangle$, (c) Entanglement entropy vs. $\omega$.
  • Figure 4: Effect of Noise on VQE Energy (Model IV).