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Frontiers of Physics

Toward nuclear physics on a spin quantum simulator by detecting quantum phase transitions in the Agassi model

Yufang Feng, Xinyue Long, Hongfeng Liu, Xiangyu Wang, Keyi Huang, Yu-ang Fan, Yuxuan Zheng, Jack Tsz Fai Ng, Xinfang Nie, Dawei Lu

Published Jan 1, 2025• 1 citation
Publisher

Abstract

A central challenge in nuclear physics is understanding quantum many-body systems governed by the strong nuclear force. The inherent complexity of these systems, combined with the limitations of classical computational methods, underscores the need for new approaches to study nuclear structure and dynamics. Here, we demonstrate that a spin-based digital quantum simulator using nuclear magnetic resonance, where nuclear spins simulate interacting fermions, offers a powerful tool to address this challenge. As a first step, we experimentally simulate the Agassi model, which encapsulates the interplay between collective and single-particle behaviors in finite nuclei. By representing nucleons as both bosons (nucleon pairs) and fermions (individual unpaired nucleons), the Agassi model captures highly non-linear interactions and is particularly suited for studying nuclear phase transitions, such as those between spherical and deformed shapes. We experimentally measure the correlation function as an order parameter during the evolution of the many-body system, successfully detecting a quantum phase transition. Specifically, we observe a sharp transition between the symmetric phase and the broken symmetry phase. This work underscores the potential of quantum simulation as a transformative tool in nuclear physics, particularly for exploring complex quantum many-body systems with applications in nuclear structure and reaction dynamics.

DOI
10.15302/frontphys.2025.053201

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A central challenge in nuclear physics is understanding quantum many-body systems governed by the strong nuclear force. The inherent complexity of these systems, combined with the limitations of classical computational methods, underscores the need for new approaches to study nuclear structure and dynamics. Here, we demonstrate that a spin-based digital quantum simulator using nuclear magnetic resonance, where nuclear spins simulate interacting fermions, offers a powerful tool to address this challenge. As a first step, we experimentally simulate the Agassi model, which encapsulates the interplay between collective and single-particle behaviors in finite nuclei. By representing nucleons as both bosons (nucleon pairs) and fermions (individual unpaired nucleons), the Agassi model captures highly non-linear interactions and is particularly suited for studying nuclear phase transitions, such as those between spherical and deformed shapes. We experimentally measure the correlation function as an order parameter during the evolution of the many-body system, successfully detecting a quantum phase transition. Specifically, we observe a sharp transition between the symmetric phase and the broken symmetry phase. This work underscores the potential of quantum simulation as a transformative tool in nuclear physics, particularly for exploring complex quantum many-body systems with applications in nuclear structure and reaction dynamics.
A digital quantum simulation for the extended Agassi model is proposed using a quantum platform with eight trapped ions. The extended Agassi model is an analytically solvable model including both short range pairing and long range monopole-monopole interactions with applications in nuclear physics and in other many-body systems. In addition, it owns a rich phase diagram with different phases and the corresponding phase transition surfaces. The aim of this work is twofold: on one hand, to propose a quantum simulation of the model at the present limits of the trapped ions facilities and, on the other hand, to show how to use a machine learning algorithm on top of the quantum simulation to accurately determine the phase of the system. Concerning the quantum simulation, this proposal is scalable with polynomial resources to larger Agassi systems. Digital quantum simulations of nuclear physics models assisted by machine learning may enable one to outperform the fastest classical computers in determining fundamental aspects of nuclear matter.
A digital quantum simulation of the Agassi model from nuclear physics is proposed and analyzed. The proposal is worked out for the case with four different sites. Numerical simulations and analytical estimations are presented to illustrate the feasibility of this proposal with current technology. The proposed approach is fully scalable to a larger number of sites. The use of a quantum correlation function as a probe to explore the quantum phases by quantum simulating the time dynamics, with no need of computing the ground state, is also studied. Evidence is given showing that the amplitude of the time dynamics of a correlation function in this quantum simulation is linked to the different quantum phases of the system. This approach establishes an avenue for the digital quantum simulation of useful models in nuclear physics.
Background: The many-body nature of nuclear physics problems poses significant computational challenges. These challenges become even more pronounced when studying the resonance states of nuclear systems, which are governed by the non-Hermitian Hamiltonian. Quantum computing, particularly for quantum many-body systems, offers a promising alternative, especially within the constraints of current noisy intermediate-scale quantum (NISQ) devices.Purpose: This work aims to simulate nuclear resonances using quantum algorithms by developing a variational framework compatible with non-Hermitian Hamiltonians and implementing it fully on a quantum simulator.Methods: We employ the complex scaling technique to extract resonance positions classically and adapt it for quantum simulations using a two-step algorithm. First, we transform the non-Hermitian Hamiltonian into a Hermitian form by using the energy variance as a cost function within a variational framework. Second, we perform $\ensuremath{\theta}$-trajectory calculations to determine optimal resonance positions in the complex energy plane. To address resource constraints on NISQ devices, we utilize Gray code (GC) encoding to reduce qubit requirements.Results: We first validate our approach using a schematic potential model that mimics a nuclear potential, successfully reproducing known resonance energies with high fidelity. We then extend the method to a more realistic $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}$ nuclear potential and compute the DDD- and GGG-wave resonance energies with a basis size of N=16N=16N=16, using only four qubits. The quantum simulation results closely match the classical values, demonstrating the feasibility of our approach.Conclusions: This study demonstrates, for the first time, that the complete $\ensuremath{\theta}$-trajectory method can be implemented on a quantum computer without relying on any classical input beyond the Hamiltonian. The results establish a scalable and efficient quantum framework for simulating resonance phenomena in nuclear systems. This work represents a significant step toward quantum simulations of open quantum systems and lays the foundation for future investigations into resonance structures in nuclear, atomic, and molecular physics.
Abstract Quantum computers have proven to be effective in simulating many quantum systems. Simulating nuclear processes and state preparation poses significant challenges, even for traditional supercomputers. This study demonstrates the feasibility of a complete simulation of a nuclear transition, including the preparation of both ground and first excited states. To tackle the complexity of strong interactions between two and three nucleons, the states are modeled on the tritium nucleus. Both the initial and final states are represented using quantum circuits with variational quantum algorithms and inductive biases. Describing the spin‐isospin states requires four qubits, and a parameterized quantum circuit that exploits a total of 16 parameters is initialized. The estimated energy has a relative error of 2% for the ground state and 10% for the first excited state of the system. The simulation estimates the transition probability between the two states as a function of the dipole polarization angle. This work marks a first step toward leveraging digital quantum computers to simulate nuclear physics.
Quantum computers promise advantages for simulating strongly correlated quantum many-body systems, like atomic nuclei, that are beyond the reach of classical computers. Realizing this potential requires understanding the quantum complexity structure of the target problem. We investigate the time-evolution of two key indicators of quantum complexity, bipartite entanglement entropy and non-local magic (non-stabilizerness), in nuclear reaction dynamics. We analyze two representative dynamical processes: scattering in a one-dimensional model of strongly interacting fermions governed by the Negele potential, and a realistic simulation of 240^{240}240Pu fission within time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. In the former case, we find that interactions dynamically generate both entanglement and non-local magic, leaving persistent signatures of quantum complexity in the outgoing states. In the latter, we observe that substantial quantum complexity survives in the spatial bipartition of daughter fragments well beyond scission. The presence of significant non-local magic and entanglement in both cases strongly indicate that quantum computers would provide substantial advantages for accurately simulating nuclear reaction dynamics.
We demonstrate quantum simulations of strongly correlated nuclear many-body systems on the RIKEN-Quantinuum Reimei trapped-ion quantum computer, targeting ground states of oxygen, calcium, and nickel isotopes. By combining a hard-core-boson representation of the nuclear shell model with a pair-unitary coupled-cluster doubles ansatz, we achieve subpercent relative error in the ground-state energies compared to noise-free state vector simulations. Our approach leverages symmetry-aware state preparation and particle-number postselection to efficiently capture pairing correlations characteristic of systems with same-species nucleons. These findings highlight the viability of high-fidelity trapped-ion platforms for nuclear physics applications and provide a foundation for scaling to more complex nuclear systems.