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arXiv:2507.00074

Studying few cluster resonances with quantum neural network driven iterative Harrow-Hassidim-Lloyd algorithm

Hantao Zhang, Bai, Dong, Zhongzhou Ren

Published Jun 29, 2025• 0 citations
arXivHTMLPDF

Abstract

By using the quantum computing the properties of hypernuclei ${}^5_Λ$He, ${}^{\ 6}_{ΛΛ}$He and ${}^9_Λ$Be can be investigated within microscopic cluster model. Our approach combines quantum neural network (QNN) with iterative Harrow-Hassidim-Lloyd (IHHL) algorithm (abbreviated as QNN-IHHL) to solve the quantum many-body problem. To efficiently describe resonance phenomena, we employ complex scaling and eigenvector continuation techniques, providing a robust framework for identifying few-cluster resonance parameters within quantum computing. To validate our quantum algorithm, the resonant $4^{+}$ state of ${}^9_Λ$Be is chosen as a core example. With QNN-IHHL algorithm we realize a fully quantum workflow, which provides a novel framework and some ground work for exploring resonance properties in complex nuclear many-body systems.

DOI
10.48550/arxiv.2507.00074

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By using the quantum computing the properties of hypernuclei Λ5{}^5_ΛΛ5​He, ΛΛ 6{}^{\ 6}_{ΛΛ}ΛΛ 6​He and Λ9{}^9_ΛΛ9​Be can be investigated within microscopic cluster model. Our approach combines quantum neural network (QNN) with iterative Harrow-Hassidim-Lloyd (IHHL) algorithm (abbreviated as QNN-IHHL) to solve the quantum many-body problem. To efficiently describe resonance phenomena, we employ complex scaling and eigenvector continuation techniques, providing a robust framework for identifying few-cluster resonance parameters within quantum computing. To validate our quantum algorithm, the resonant 4+4^{+}4+ state of Λ9{}^9_ΛΛ9​Be is chosen as a core example. With QNN-IHHL algorithm we realize a fully quantum workflow, which provides a novel framework and some ground work for exploring resonance properties in complex nuclear many-body systems.
We propose a novel quantum algorithm for solving nuclear resonances, which is based on the iterative Harrow-Hassidim-Lloyd algorithm and eigenvector continuation with complex scaling. To validate this approach, we compute the resonant states of α − α system and achieve results in good agreement with traditional methods. Our study offers a new perspective on calculating eigenvalues of non-Hermitian operators and lays some groundwork for further exploration of nuclear resonances using quantum computing.
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Rapid progress in developing near- and long-term quantum algorithms for quantum chemistry has provided us with an impetus to move beyond traditional approaches and explore new ways to apply quantum computing to electronic structure calculations. In this work, we identify the connection between quantum many-body theory and a quantum linear solver, and implement the Harrow-Hassidim-Lloyd (HHL) algorithm to make precise predictions of correlation energies for light molecular systems via the (non-unitary) linearised coupled cluster theory. We alter the HHL algorithm to integrate two novel aspects- (a) we prescribe a novel scaling approach that allows one to scale any arbitrary symmetric positive definite matrix A, to solve for Ax = b and achieve x with reasonable precision, all the while without having to compute the eigenvalues of A, and (b) we devise techniques that reduce the depth of the overall circuit. In this context, we introduce the following variants of HHL for different eras of quantum computing- AdaptHHLite in its appropriate forms for noisy intermediate scale quantum (NISQ), late-NISQ, and the early fault-tolerant eras, as well as AdaptHHL for the fault-tolerant quantum computing era. We demonstrate the ability of the NISQ variant of AdaptHHLite to capture correlation energy precisely, while simultaneously being resource-lean, using simulation as well as the 11-qubit IonQ quantum hardware.
Binary Neural Networks are a promising technique for implementing efficient deep models with reduced storage and computational requirements. The training of these is however, still a compute-intensive problem that grows drastically with the layer size and data input. At the core of this calculation is the linear regression problem. The Harrow-Hassidim-Lloyd (HHL) quantum algorithm has gained relevance thanks to its promise of providing a quantum state containing the solution of a linear system of equations. The solution is encoded in superposition at the output of a quantum circuit. Although this seems to provide the answer to the linear regression problem for the training neural networks, it also comes with multiple, difficult-to-avoid hurdles. This paper shows, however, that useful information can be extracted from the quantum-mechanical implementation of HHL, and used to reduce the complexity of finding the solution on the classical side.
Quantum many-body computation is a central challenge across multiple domains of scientific research, and Monte Carlo method has emerged as one of the most effective numerical techniques for investigating large-scale many-body systems. In recent years, the integration of Monte Carlo methods with machine learning has led to the development of neural quantum state approach. Quantum neural networks (QNNs) offer superior expressiveness compared to classical neural networks. In this paper, we propose a novel Quantum Neural Network Quantum State (QNNQS) method, based on the variational Monte Carlo framework. This approach leverages a quantum neural network to represent the many-body quantum state, and optimizes it iteratively through gradient descent to determine the ground-state energy. To assess the performance of this method, we conduct simulations of the one-dimensional transverse-field Ising model, investigating the influence of quantum circuit architecture on circuit expressibility, entangling capability, and computational accuracy. The results demonstrate that the QNNQS method achieves comparable simulation accuracy while utilizing significantly fewer parameters and requiring less training resources than classical network quantum state methods.
A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the nuclear quantum many-body problem with high accuracy across a wide range of length scales and density regimes. In this review, we discuss how artificial neural network representations of the nuclear many-body wave function have significantly extended the capabilities of continuum quantum Monte Carlo methods. In particular, neural network quantum states enable calculations of larger systems than were previously accessible and provide a flexible framework for capturing phenomena that challenge conventional approaches, including the emergence of nuclear clusters and superfluid phases in dense matter. We highlight recent applications to finite nuclei, infinite nuclear and neutron matter, and dynamical processes relevant to lepton-nucleus and nucleus-nucleus scattering. We also discuss conceptual and methodological connections with condensed matter physics, emphasizing developments in neural network quantum states that bridge strongly correlated systems across disciplines. Together, these developments demonstrate how neural-network methods open new avenues toward unified and accurate descriptions of nuclear structure, matter, and reactions.