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Physica Scripta

Calculating the binding energies of the first 29 light nuclei with VQE on quantum computing

Taylan Baskan, Ahmet Hakan Yılmaz

Published Mar 4, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ae4dc7

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Accurate calculations of nuclear binding energies in theory is a long-standing problem in nuclear physics, as it provides critical insights the effective interactions and structures of atomic nuclei. Currently, there are severe limitations in theory due to the exponential growth of the Hilbert space with increasing nucleon number, i.e., curse of the dimension. There are some effort to mitigate this problem by using the state-of-art methods, such as the machine learning and quantum computing. Recent advances in quantum computing have opened new avenues for addressing these challenges, enabling the direct simulation of nuclear many-body systems on quantum hardware. In this work, a detailed study on the calculation of nuclear binding energies using the full quantum eigensolver (FQE) algorithm, implemented on a real quantum processor, i.e. Quafu, was presented. Two nuclear systems (2H and 6He) were investigated. The deuteron, as the simplest bound nucleus with just one proton and one neutron, serves as an ideal benchmark for testing quantum algorithms, FQE. 6He, a light, two-valence neutron nucleus, was used for estimating the ability of the Quafu quantum cloud platform and its “Baihua” quantum chip. Our results demonstrate that for the deuteron, the FQE algorithm on the “Baihua” quantum processor achieves a higher level of accuracy compared to previously reported results obtained using the variational quantum eigensolver (VQE) on the IBM_QX5 and IBM_19Q platforms, as discussed in Dumitrescu’s article. For 6He, the FQE-calculated binding energy shows accuracy comparable to recent VQE-based calculations reported in Yoshida’s article. These findings highlight the feasibility of performing precise nuclear structure calculations on near-term quantum devices and underscore the potential of the FQE approach for future applications in nuclear physics. Overall, this study extends the scope of quantum computing in nuclear physics by demonstrating that the FQE algorithm can serve as a practical and accurate tool for computing binding energies on real quantum hardware. The results provide a benchmark for future developments in quantum simulations of nuclei and suggest promising directions for scaling these methods to larger nuclear systems, ultimately contributing to a deeper understanding of nuclear structure and dynamics.
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 In this work, we introduce a new qubit mapping strategy for the Variational Quantum Eigensolver (VQE) applied to nuclear shell model calculations, where each Slater Determinant (SD) is mapped to a qubit, rather than assigning qubits to individual single-particle states. While this approach may increase the total number of qubits required in some cases, it enables the construction of simpler quantum circuits that are more compatible with current noisy intermediate-scale quantum (NISQ) devices. We apply this method to seven nuclei: Four lithium isotopes 6−9{}^{6-9}6−9 Li from the p -shell, 18{}^{18}18 F from the sd -shell, and two heavier nuclei ( 210{}^{210}210 Po, and 210{}^{210}210 Pb). We run circuits representing their ground states on a noisy simulator (IBM’s FakeFez backend) and quantum hardware ( ibm_pittsburghibm\_pittsburghibm_pittsburgh ). For heavier nuclei, we demonstrate the feasibility of simulating 210{}^{210}210 Po and 210{}^{210}210 Pb as 22- and 29-qubit systems, respectively. Additionally, we employ Zero-Noise Extrapolation (ZNE) via two-qubit gate folding to mitigate errors in both simulated and hardware-executed results. Post-mitigation, the best results show less than 4 % deviation from shell model binding energy predictions across all nuclei studied. This SD-based qubit mapping proves particularly effective for lighter nuclei and two-nucleon systems, offering a promising route for near-term quantum simulations in nuclear physics.
Abstract In this work, we introduce a new qubit mapping strategy for the Variational Quantum Eigensolver (VQE) applied to nuclear shell model calculations, where each Slater determinant (SD) is mapped to a qubit, rather than assigning qubits to individual single-particle states. While this approach may increase the total number of qubits required in some cases, it enables the construction of simpler quantum circuits that are more compatible with current noisy intermediate-scale quantum (NISQ) devices. We apply this method to seven nuclei: Four lithium isotopes 6−9^{6-9}6−9Li from the \textit{p}-shell, 18^{18}18F from the \textit{sd}-shell, and two heavier nuclei (210^{210}210Po, and 210^{210}210Pb). We run circuits representing their ground states on a noisy simulator (IBM's \textit{FakeFez} backend) and quantum hardware (ibm_pittsburghibm\_pittsburghibm_pittsburgh). For heavier nuclei, we demonstrate the feasibility of simulating 210^{210}210Po and 210^{210}210Pb as 22- and 29-qubit systems, respectively. Additionally, we employ Zero-Noise Extrapolation (ZNE) via two-qubit gate folding to mitigate errors in both simulated and hardware-executed results. Post-mitigation, the best results show less than 4 \% deviation from shell model predictions across all nuclei studied. This SD-based qubit mapping proves particularly effective for lighter nuclei and two-nucleon systems, offering a promising route for near-term quantum simulations in nuclear physics. PACS numbers: 21.60.Cs, 21.30.Fe, 21.10.Dr, 27.20.+n
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: 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.