Quantum algorithm for partial differential equations of nonconservative systems with spatially varying parameters

作者：Yuki Sato, Hiroyuki Tezuka, Ruho Kondo, Naoki Yamamoto · 发表于：Physical Review Applied · 年份：2025 · DOI：10.1103/physrevapplied.23.014063 · 被引用次数：15 · 研究领域：Quantum Computing Algorithms and Architecture、Quantum Information and Cryptography、Quantum many-body systems

Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large computational models is essential for improving product performance and reducing development costs. However, solving large-scale PDEs, particularly for systems with spatially varying material properties, poses significant computational challenges. In this paper, we propose a quantum algorithm for solving second-order linear PDEs of nonconservative systems with spatially varying parameters, using the linear combination of the Hamiltonian simulation (LCHS) method. Our approach transforms those PDEs into ordinary differential equations represented by qubit operators, through spatial discretization using the finite-difference method. Then, we provide an algorithm that efficiently constructs the operator corresponding to the spatially varying parameters of PDEs via a logic minimization technique, which reduces the number of terms and subsequently the circuit depth. We also develop a scalable method for realizing a quantum circuit for LCHS, using a tensor-network-based technique, specifically a matrix product state (MPS). We validate our method with applications to the acoustic equation with spatially varying parameters and the dissipative heat equation. Our approach includes a detailed recipe for constructing quantum circuits for PDEs, leveraging ...