EPJ Web of Conferences

Variational Quantum Simulation of Deuteron Ground State Energy at Higher Order Expansion

Changyuan Liu

Published Jan 1, 2024• 0 citations

Abstract

Recent development of quantum computing has been extended to nuclear physics. Researchers have demonstrated that the quantum simulation of deuteron ground state energy using the variational quantum eigenvalue solver. In this existing work, only 2 and 3 qubits are used. In this work, the theory of higher order expansion of the deuteron ground state Hamiltonian has been established. On a classical quantum simulator, the convergence of the ground state energy as the number of qubits increases has been verified up to 22 qubits.

DOI: 10.1051/epjconf/202430217002

Related papers

Estimation of deuteron binding energy with renormalization group-based effective interactions using the variational quantum eigensolver

Sreelekshmi Pillai, S. Ramanan, V. Balakrishnan +1 more

Abstract We have obtained the energy of the deuteron on a quantum simulator using the variational quantum eigensolver. We have employed realistic two-body interactions, namely, chiral N4LO and AV 18 , thus incorporating the role of tensor forces. These interactions are subsequently evolved to low resolution scales using the similarity renormalization group approach with parameter λ . The deuteron ground state energy has been calculated in the truncated harmonic oscillator basis, using the Qiskit-Aer simulator in both noise-free and noisy cases. The noise models have been taken from the actual IBM quantum hardware, and the results obtained have been extrapolated to the zero noise limit. The number of harmonic oscillator basis states (hence qubits) needed for computing the energy to within 1 percent of the experimental value in the quantum simulator, decreases with decreasing λ . We have analysed the extent of entanglement between oscillator modes using concurrence as the entanglement quantifier. It is seen that the entanglement decreases as λ is lowered from the bare value to ∼1.0 fm −1 independent of the form of the bare interaction and the number of harmonic oscillator basis states.

arXiv:2509.08948Physica ScriptaMay 7, 20260 citations

Full Quantum Computing on Binding Energy of Light Nuclei

PENG Baining1, CUI Ying1, YAN Yuliang1, GAO Zaochun1, WEI Shijie2 , ZHANG Yingxun1, 3, 4

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.

May 1, 20260 citations

Variational quantum solver employing the PDS energy functional

Bo Peng, Karol Kowalski

Recently a new class of quantum algorithms that are based on the quantum computation of the connected moment expansion has been reported to find the ground and excited state energies. In particular, the Peeters-Devreese-Soldatov (PDS) formulation is found variational and bearing the potential for further combining with the existing variational quantum infrastructure. Here we find that the PDS formulation can be considered as a new energy functional of which the PDS energy gradient can be employed in a conventional variational quantum solver. In comparison with the usual variational quantum eigensolver (VQE) and the original static PDS approach, this new variational quantum solver offers an effective approach to navigate the dynamics to be free from getting trapped in the local minima that refer to different states, and achieve high accuracy at finding the ground state and its energy through the rotation of the trial wave function of modest quality, thus improves the accuracy and efficiency of the quantum simulation. We demonstrate the performance of the proposed variational quantum solver for toy models, H 2 molecule, and strongly correlated planar H 4 system in some challenging situations. In all the case studies, the proposed variational quantum approach outperforms the usual VQE and static PDS calculations even at the lowest order. We also discuss the limitations of the proposed approach and its preliminary execution for model Hamiltonian on the NISQ device.

arXiv:2101.08526QuantumJun 10, 202118 citations

Using VQE to determine the ground state energy of simple molecules

Timothy P. Powers

Key properties of physical systems can be described by the eigenvalues of matrices that represent the system. Computational algorithms that determine the eigenvalues of these matrices exist, but they generally suffer from a loss of performance as the matrix grows in size. This process can be expanded to quantum computation to find the eigenvalues with better performance than the classical algorithms. One application of such an eigenvalue solver is to determine energy levels of a molecule given a matrix representation of its Hamiltonian using the variational principle. Using a variational quantum eigensolver, we determine the ground state energies of different molecules. We focus on the choice of optimization strategy for a Qiskit simulator on low-end hardware. The benefits of several different optimizers were weighed in terms of accuracy in comparison to an analytic classical solution as well as code efficiency.

Jan 1, 20230 citations

Quantum computing calculations for nuclear structure and nuclear data

Isaac Hobday, P. D. Stevenson, James Benstead

Calculations of nuclear properties and nuclear models are performed using quantum computing algorithms on simulated and real quantum computers. The models are a realistic calculation of deuteron binding based on effective field theory, and a simplified two-level version of the nuclear shell model. A method of reducing the number of qubits needed for practical calculation is presented, the reduction being with respect to that used when the standard Jordan-Wigner encoding is used. Its efficacy is shown in the case of the deuteron binding and shell model. A version of the variational quantum eigensolver in which all eigenstates in a spectrum are targeted on an equal basis is shown. The method involves finding the minima of the variance of the Hamiltonian, and its ability to find the full spectrum of small version of the simplified shell model is presented.

arXiv:2205.05576SPIE Quantum TechnologiesMay 6, 20225 citations

Simulator Demonstration of Large Scale Variational Quantum Algorithm on HPC Cluster

Mikio Morita, Yoshinori Tomita, Junpei Koyama +1 more

Advances in quantum simulator technology are increasingly required because research on quantum algorithms is becoming more sophisticated and complex. State vector simulation utilizes CPU and memory resources in computing nodes exponentially with respect to the number of qubits; furthermore, in a variational quantum algorithm, the large number of repeated runs by classical optimization is also a heavy load. This problem has been addressed by preparing numerous computing nodes or simulation frameworks that operate effectively. This study aimed to accelerate quantum simulation using two newly proposed methods: to efficiently utilize limited computational resources by adjusting the ratio of the MPI and distributed processing parallelism corresponding to the target problem settings and to slim down the Hamiltonian by considering the effect of accuracy on the calculation result. Ground-state energy calculations of a fermionic model were performed using a variational quantum eigensolver (VQE) on an HPC cluster with up to 1024 FUJITSU Processor A64FX connected to each other by InfiniBand; the processor is also used on supercomputer Fugaku. We achieved 200 times higher speed over VQE simulations and demonstrated 32 qubits ground-state energy calculations in acceptable time. This result indicates that > 30 qubit state vector simulations can be realistically utilized for further research on variational quantum algorithms.

arXiv:2402.11878IEEE AccessJan 1, 20248 citations