Year: 2025
Type: preprint
Abstract: As quantum hardware rapidly advances toward the early fault-tolerant era, a key challenge is to develop quantum algorithms that are not only theoretically sound but also hardware-friendly on near-term devices. In this work, we propose a quantum algorithm for solving linear ordinary differential equations (ODEs) with a provable runtime guarantee. Our algorithm uses only a single ancilla qubit, and is locality preserving, i.e., when the coefficient matrix of the ODE is $k$-local, the algorithm only needs to implement the time evolution of $(k+1)$-local Hamiltonians. We also discuss the connection between our proposed algorithm and Lindbladian simulation. By applying our algorithm to the interacting Hatano-Nelson model, a widely studied non-Hermitian model with rich phenomenology, and numerically simulating it under realistic noise models, we demonstrate its practical feasibility on near-term quantum devices.
Source: arXiv (Cornell University)
Authors: Fang, Di, George, David Lloyd, Tong, Yu
Institution: Duke University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414877936
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