2025/07/22 by Di Fang, Fang, Di, David L. George +3 · 4 citations
Computer Science · #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2507.16995
openalex publication_date 2025/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 as well as its application to the interacting Hatano-Nelson model, a widely studied non-Hermitian model with rich phenomenology.