一种用于计算低能本征态的递归模块耦合算法
A Recursive Module-Coupling Algorithm for Computing Low-Energy Eigenstates
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中文总结 AI 辅助
针对多体哈密顿量本征态求解难题，提出递归模块耦合算法，构建物理适配变分基获取多低能态，可衍生递归量子变分算法，经经典模拟与IBM量子处理器实验验证有效
中文摘要 AI 辅助
求解多体哈密顿量的本征态是物理学与计算科学中的基础挑战。由于搜索空间随系统规模呈指数增长，人们已开发出大量经典与量子算法来应对这一问题。一种实用策略是识别受物理启发的低维子空间，该子空间可有效容纳低能本征态，从而降低计算复杂度。本文提出一种递归模块耦合算法，该算法将系统迭代处理为局部耦合的较小模块的组合，低能子空间则根据同一递归结构依次估计。与密度矩阵重整化群（DMRG）方法不同，DMRG通过重复的局部扫描优化全局矩阵乘积态并依次获取激发态，我们的算法从模块本征态构建符合物理特性的变分基，并平等地获取多个低能态，若目标为中等精度则可大幅提速。本文提出的方法还自然衍生出一种递归量子变分算法，提供了与当代基于门的量子架构兼容的系统且模块化的电路构建框架。在每个递归层级，训练块编码器以将逻辑基态映射到保留的物理子空间，随后在该子空间内构建变分电路。量子电路实现不仅提供了量子多本征态求解器，还提供了分层构建量子态制备电路的系统方案。经典模拟验证了该方法的准确性与效率，而在IBM量子处理器上的实验表明，即便在当前的含噪声中等规模量子（NISQ）时代，也可实现具有合理保真度的本征态制备。
英文摘要
Finding the eigenstates of a many-body Hamiltonian is a fundamental challenge in physics and computational science. Since the search space grows exponentially with system size, numerous classical and quantum algorithms have been developed to address this problem. A practical strategy is to identify a physics-informed low-dimensional subspace that effectively accommodates the low-lying eigenstates, thereby reducing the computational complexity. In this paper, we propose a recursive module-coupling algorithm, which iteratively treats a system as a composition of locally-coupled smaller modules, with low-energy subspace estimated successively according to the same recursive structure. Unlike the density matrix renormalization group (DMRG) approach that optimizes a global matrix product state through repeated local sweeps and obtains excited states sequentially, our algorithm constructs a physically tailored variational basis from module eigenstates and obtains several low-energy states on an equal footing, leading to substantial speedups if targeting moderate accuracy. Our proposed method further leads naturally to a recursive quantum variational algorithm, providing a systematic and modular circuit-construction framework compatible with contemporary gate-based quantum architectures. At each recursive level, block encoders are trained to map logical basis states onto the retained physical subspace, within which a variational circuit is subsequently optimized. Such a quantum-circuit implementation provides not only a quantum multistate eigensolver, but also a systematic prescription for hierarchically constructing quantum state-preparation circuits. Classical simulations demonstrate the accuracy and efficiency of the proposed method, whereas experiments on IBM quantum processors show that eigenstate preparation with reasonable fidelities is achievable even in the current NISQ era.
发表机构
- National University of Singapore（新加坡国立大学）
- Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）
- Institute of Advanced Intelligence and Computing (IAIC), Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局高级智能与计算研究所）
- Bioinformatics Institute, Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局生物信息学研究所）
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