Full-Spectrum Quantum Simulation for the Nuclear Shell Model

• URL: http://arxiv.org/abs/2607.08235v1
• Date: Thu, 09 Jul 2026 08:31:31 GMT
• Title: Full-Spectrum Quantum Simulation for the Nuclear Shell Model
• Abstract summary: We introduce a single-run quantum simulation capable of obtaining multiple shell-model eigenstates simultaneously.<n>The nuclear Hamiltonian is transformed from a bit to a qubit basis using the Jordan-Wigner transformation.<n>The ADAPT-SSVQE algorithm uses a symmetry-preserving single and double-excitation operator pool.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The nuclear shell model is a general way of expressing the many-body nuclear Hamiltonian and deciphering the underlying nuclear structure. In today's era of modern and high-power computation, the primary limitation of the nuclear shell model is the enormous dimensionality of its Hilbert space, which far exceeds available storage capacity and prevents the diagonalization of the full Hamiltonian matrix in that space. Quantum computing offers a scalable solution to bypass this curse of dimensionality. In this work, we introduce a single-run quantum simulation capable of obtaining multiple shell-model eigenstates simultaneously. The nuclear Hamiltonian is transformed from a bit to a qubit basis using the Jordan-Wigner transformation, explicitly preserving fermionic anti-commutation. We employ a Subspace Search Variational Quantum Eigensolver (SSVQE) along with an Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) ansatz to construct the quantum circuit required to solve the shell-model problem. The ADAPT-SSVQE algorithm uses a symmetry-preserving single and double-excitation operator pool and optimizes a weighted energy sum to obtain the simultaneous convergence of all eigenstates within a targeted MJ subspace, eliminating the need for post-processing efforts to extract excited spectra. We benchmark this approach by solving the problem for two and three identical nucleons in a j = 9/2 orbital, successfully extracting five and ten mutually orthogonal states, respectively, within a 10-qubit active space. The algorithm achieves spectroscopic accuracy, in simulation, relative to exact diagonalization and intrinsically restores total angular momentum (\hat{J}^2) symmetry.

Related papers

• Unitary discretization of the Koopman-von Neumann equation for quantum simulation of fluid and plasma dynamics [45.88028371034407]
  KvN framework embeds the Liouville equation into a Hilbert space with norm-preserving, unitary evolution.<n>Weyl-ordered KvN generator is derived as the unique anti-Hermitian operator symmetrization for real velocity fields.
  arXiv  Detail & Related papers  (2026-05-18T23:27:02Z)
• Single-step Quantum Simulation of Two Nucleons [0.0]
  This work presents a numerical simulation of the subspace search variational quantum eigensolver (SSVQE) combined with an adaptive derivative-assembles pseudo-trotter (ADAPT) ansatz.<n>We demonstrate the accuracy of the method by benchmarking against the exact diagonalization.
  arXiv  Detail & Related papers  (2025-12-14T18:41:57Z)
• Quantum Algorithm for Low Energy Effective Hamiltonian and Quasi-Degenerate Eigenvalue Problem [7.107390133525336]
  Quasi-degenerate eigenvalue problems are central to quantum chemistry and condensed-matter physics.<n>We propose a quantum algorithm that diagonalizes such quasi-degenerate manifold by solving an effective-Hamiltonian eigenproblem in a low-dimensional subspace.<n>Our analysis provides provable bounds on eigenvalue accuracy and subspace fidelity, together with total query complexity.
  arXiv  Detail & Related papers  (2025-10-09T11:20:15Z)
• Zassenhaus Expansion in Solving the Schrödinger Equation [0.0]
  A fundamental challenge lies in approximating the unitary evolution operator ( e-imathcalHt ) where ( mathcalH ) is a large, typically non-commuting, Hermitian operator.<n>We present a refinement of the fixed-depth simulation framework introduced by E. K"okc"u et al, incorporating the second-order Zassenhaus expansion.<n>This yields a controlled, non-unitary approximation with error scaling as ( mathcalO(t
  arXiv  Detail & Related papers  (2025-05-14T14:48:47Z)
• Quantum simulations of nuclear resonances with variational methods [1.740992908651449]
  This work aims to simulate nuclear resonances using quantum algorithms by developing a variational framework compatible with non-Hermitian Hamiltonians.<n>We employ the complex scaling technique to extract resonance positions classically and adapt it for quantum simulations using a two-step algorithm.<n>The results establish a scalable and efficient quantum framework for simulating resonance phenomena in nuclear systems.
  arXiv  Detail & Related papers  (2025-04-16T01:01:56Z)
• Neutron-nucleus dynamics simulations for quantum computers [49.369935809497214]
  We develop a novel quantum algorithm for neutron-nucleus simulations with general potentials. It provides acceptable bound-state energies even in the presence of noise, through the noise-resilient training method. We introduce a new commutativity scheme called distance-grouped commutativity (DGC) and compare its performance with the well-known qubit-commutativity scheme.
  arXiv  Detail & Related papers  (2024-02-22T16:33:48Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• Variational Adiabatic Gauge Transformation on real quantum hardware for effective low-energy Hamiltonians and accurate diagonalization [68.8204255655161]
  We introduce the Variational Adiabatic Gauge Transformation (VAGT) VAGT is a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit. The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.
  arXiv  Detail & Related papers  (2021-11-16T20:50:08Z)
• Spectral density reconstruction with Chebyshev polynomials [77.34726150561087]
  We show how to perform controllable reconstructions of a finite energy resolution with rigorous error estimates. This paves the way for future applications in nuclear and condensed matter physics.
  arXiv  Detail & Related papers  (2021-10-05T15:16:13Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Variational Monte Carlo calculations of $\mathbf{A\leq 4}$ nuclei with an artificial neural-network correlator ansatz [62.997667081978825]
  We introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei. We compute the binding energies and point-nucleon densities of $Aleq 4$ nuclei as emerging from a leading-order pionless effective field theory Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-28T14:52:28Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.