Qubit-Efficient Quantum Algorithm for Linear Differential Equations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908462026326016 |
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| author | Fang, Di George, David Lloyd Tong, Yu |
| author_facet | Fang, Di George, David Lloyd Tong, Yu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16995 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Qubit-Efficient Quantum Algorithm for Linear Differential Equations Fang, Di George, David Lloyd Tong, Yu Quantum Physics Numerical Analysis 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. |
| title | Qubit-Efficient Quantum Algorithm for Linear Differential Equations |
| topic | Quantum Physics Numerical Analysis |
| url | https://arxiv.org/abs/2507.16995 |