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arXiv:2504.11685 · Physical Review C

Quantum simulations of nuclear resonances with variational methods

Ashutosh Singh, Pooja Siwach, P. Arumugam

Published Jul 18, 2025• 7 citations
arXivHTMLPDF

Abstract

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 $D$- and $G$-wave resonance energies with a basis size of $N=16$, 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.

DOI
10.1103/x8vx-y5mh

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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 \ensuremathθ\ensuremath{\theta}\ensuremathθ-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 \ensuremathα\ensuremath-\ensuremathα\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}\ensuremathα\ensuremath-\ensuremathα 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 \ensuremathθ\ensuremath{\theta}\ensuremathθ-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.
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.
Quantum computing opens up new possibilities for the simulation of many-body nuclear systems. As the number of particles in a many-body system increases, the size of the space if the associated Hamiltonian increases exponentially. This presents a challenge when performing calculations on large systems when using classical computing methods. By using a quantum computer, one may be able to overcome this difficulty thanks to the exponential way the Hilbert space of a quantum computer grows with the number of quantum bits (qubits). Our aim is to develop quantum computing algorithms which can reproduce and predict nuclear structure such as level schemes and level densities. As a sample Hamiltonian, we use the Lipkin-Meshkov-Glick model. We use an efficient encoding of the Hamiltonian onto many-qubit systems, and have developed an algorithm allowing the full excitation spectrum of a nucleus to be determined with a variational algorithm capable of implementation on today's quantum computers with a limited number of qubits. Our algorithm uses the variance of the Hamiltonian, ⟨H2⟩−⟨H⟩2\langle H^2\rangle - \langle H\rangle ^2⟨H2⟩−⟨H⟩2, as a cost function for the widely-used variational quantum eigensolver (VQE). In this work we present a variance based method of finding the excited state spectrum of a small nuclear system using a quantum computer, using a reduced-qubit encoding method.
Background: Quantum simulations offer the potential to predict the structure and dynamics of nuclear many-body systems that are beyond the capabilities of classical computing. Generally, preparing the ground state of strongly interacting many-body systems relevant to nuclear physics is, however, inefficient, even using ideal quantum computers. In addition, currently available noisy intermediate-scale quantum (NISQ) era quantum devices possess modest numbers of qubits, limiting the size of quantum many-body systems that can be simulated. In this context, a reformulation of the quantum many-body problems using truncated model spaces and Hamiltonians is desirable to make them more amenable to near-term quantum computers. The importance of symmetries in low-energy theories, including effective field theories (EFTs), lattice quantum chromodynamics (QCD), and effective model spaces for nuclear systems, in particular their interplay with the reduction of active Hilbert spaces, is well known. Lesser known is the fact that the noncommutivity of some symmetries and truncations of the model space can be profitably combined with variational calculations to rearrange the entanglement into localized structures and enable more efficient simulations.Purpose: The goal of the present study is to explore and utilize the noncommutivity of symmetries and model-space truncations of quantum many-body systems important to nuclear physics, particularly in combination with variational algorithms for quantum simulations and effective Hamiltonian learning.Method: We introduce an iterative hybrid classical-quantum algorithm, the Hamiltonian learning variational quantum eigensolver (HL-VQE), that simultaneously optimizes an effective Hamiltonian, thereby rearranging entanglement into the effective model space, and the associated ground-state wave function. Quantum simulations, using classical computers and IBM's superconducting-qubit quantum computers, are performed to demonstrate the HL-VQE algorithm, in the context of the Lipkin-Meshkov-Glick (LMG) model of interacting fermions, where the Hamiltonian transformation corresponds to an orbital rotation. We use a mapping where the number of qubits scales with the logarithm\mathrm{logarithm}logarithm of the size of the effective model space, rather than the particle number.Results: HL-VQE is found to provide an exponential improvement in LMG-model calculations of the ground-state energy and wave function, compared to naive truncations without Hamiltonian learning, throughout a significant fraction of the Hilbert space. In the context of EFT, this corresponds to counterterms scaling exponentially with the cutoff as opposed to power law. Implementations on IBM's QExperience quantum computers and simulators for one- and two-qubit effective model spaces are shown to provide accurate and precise results, reproducing classical predictions.Conclusions: For a range of parameters defining the LMG model, the HL-VQE algorithm is found to have better scaling of quantum resources requirements than previously explored algorithms. In particular, the HL-VQE scales efficiently over a large fraction of the model space, in contrast to VQE alone. This work constitutes a step in the development of entanglement-driven quantum algorithms for descriptions of nuclear many-body systems. This, in part, leverages the potential of noisy intermediate-scale quantum (NISQ) devices. The exponential scaling of counterterms observed in this study suggests the possibility of more general applicability to other nonperturbative EFTs.
Classical simulations of real-space quantum dynamics are challenging due to the exponential scaling of computational cost with system dimensions. Quantum computers offer the potential to simulate quantum dynamics with polynomial complexity; however, existing quantum algorithms based on the split-operator techniques require large-scale fault-tolerant quantum computers that remain elusive in the near future. Here, we present variational simulations of real-space quantum dynamics suitable for implementation in noisy intermediate-scale quantum (NISQ) devices. The Hamiltonian is first encoded onto qubits using a discrete variable representation and binary encoding scheme. We show that direct application of a real-time variational quantum algorithm based on the McLachlan's principle is inefficient as the measurement cost grows exponentially with the qubit number for general potential energy, and an extremely small time-step size is required to achieve accurate results. Motivated by the insights that many chemical dynamics occur in the low-energy subspace, we propose a subspace expansion method by projecting the total Hamiltonian, including the time-dependent driving field, onto the system low-energy eigenstate subspace using quantum computers, and the exact quantum dynamics within the subspace can then be solved classically. We show that the measurement cost of the subspace approach grows polynomially with dimensionality for general potential energy. Our numerical examples demonstrate the capability of our approach, even under intense laser fields. Our work opens the possibility of simulating chemical dynamics with NISQ hardware.
Nuclear lattice effective field theory has become an important framework for quantum many-body calculations in nuclear physics, yet its classical implementation remains increasingly challenging for more general interactions and larger systems. In this work, we develop a quantum-computing framework for a three-dimensional nuclear lattice model. We construct a variational quantum eigensolver framework and systematically compare the Jordan-Wigner and Gray code encodings. Our analysis shows that for the few-body systems considered here, Gray code combined with symmetry reduction yields a substantially more compact qubit representation. Based on this framework, we perform numerical studies for 2H^{2}\mathrm{H}2H, 3H^{3}\mathrm{H}3H, and 4He^{4}\mathrm{He}4He on finite lattices. The calculated ground-state energies exhibit a clear approach toward the corresponding experimental binding energies as the lattice size increases. These results provide a proof-of-principle foundation for future quantum simulations of nuclear many-body problems.
Abstract The nuclear binding energy problem is one of the fundamental challenges of the nuclear many-body problem, as calculating the corresponding binding energies by various approximate methods remains computationally challenging for a wide range of nuclei. In this work, a binding energy model derived from quantum computational approaches to nuclear physics is proposed and implemented in a quantum computer simulator to address the nuclear binding energy problem. The goal is to develop a framework capable of calculating the binding energies of multiple nuclei within a unified scheme. To this end, appropriate potential expressions are selected and tuned to accommodate varying nuclear properties. The defined Hamiltonian is parameterized and transformed into a form suitable for implementation on a quantum computer. Depending on the number of nucleons, the program is run on 2 to 12 qubits to obtain the minimum eigenvalue of the Hamiltonian corresponding to the ground state energy (binding energy of the nucleus) according to the variational principle of quantum mechanics. This framework provides, the binding energies of the first 29 nuclei with a total deviation of 16.86% ( 2 H, 3 H, 3 He, 4 He, 6 He, 8 He, 6 Li, 7 Li, 8 Li, 9 Li, 11 Li, 7 Be, 8 Be, 9 Be, 10 Be, 11 Be, 12 Be, 8 B, 9 B, 10 B, 11 B, 12 B, 9 C, 10 C, 11 C, 12 C, 11 N, 12 N, 12 O) obtained by quantum computation following the steps of Variational Quantum Eigensolver (VQE). These results support the feasibility of the proposed approach for nuclear binding energy calculations. In this sense, this work contributes to quantum computing and nuclear physics by providing a model able to calculate the binding energies for the first 29 nuclei using quantum computer simulator and offers a promising route for future large-scale applications.