Quantum circuits for partial differential equations via Schrödingerisation

J. Hu, S. Jin, N. Liu, L. Zhang · 2024 · Quantum 8, 1563

| 编号 QC029 | 主题 量子 PDE 求解 | 链接 arXiv:2403.10032 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in largescale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian simulation, which is directly applicable only to Schrödingertype equations. To address this limitation, Schrödingerisation techniques have been developed, employing the warped transformation to convert general linear PDEs into Schrödinger-type equations. However, despite the development of Schrödingerisation techniques, the explicit implementation of the corresponding quantum circuit for solving general PDEs remains to be designed. In this paper, we present a detailed implementation of a quantum algorithm for general PDEs using Schrödingerisation techniques. We provide examples of the heat equation, and the advection equation approximated by the upwind scheme, to demonstrate the effectiveness of our approach. Complexity analysis is also carried out to demonstrate the quantum advantages of these algorithms in high dimensions over their classical counterparts. Several numerical experiments demonstrate the validity of these proposed quantum circuits.

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