Quantum Linear Multistep Method for Using a Quantum Oracle with Differential Equations Article Swipe

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Kyoung Keun Park , Kwangyeul Choi , Minwoo Kim , Gi‐Won Song , Tae Hyun Kim ·

YOU? · · 2025 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2501.03781

Differential equations are a crucial mathematical tool used in a wide range of applications. If the solution to an initial value problem (IVP) can be transformed into an oracle, it can be utilized in various fields such as search and optimization, achieving quadratic speedup with respect to the number of candidates compared to its classical counterpart. In the past, attempts have been made to implement such an oracle using the Euler method. In this study, we propose a quantum linear multistep method (QLMM) that applies the linear multistep method, commonly used to numerically solve IVPs on classical computers, to generate a numerical solution of the IVP for use in a quantum oracle. We also propose a method to find the optimal form of QLMM for a given IVP. Finally, through computer simulations, we derive the QLMM formulation for an example IVP and show that the solution from the optimized QLMM can be used in an optimization problem.

Related Topics

Quantum

Oracle

Mathematics

Differential Equation

Physics

Mathematical Analysis

Computer Science

Quantum Mechanics

Software Engineering

Concepts

Quantum Linear multistep method Oracle Mathematics Differential equation Applied mathematics Physics Mathematical analysis Computer science Quantum mechanics Differential algebraic equation Ordinary differential equation Software engineering

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2501.03781
PDF: https://arxiv.org/pdf/2501.03781
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Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.2501.03781

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Title: Quantum Linear Multistep Method for Using a Quantum Oracle with Differential Equations

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Language: en

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Publication year: 2025

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Publication date: 2025-01-07

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Authors: Kyoung Keun Park, Kwangyeul Choi, Minwoo Kim, Gi‐Won Song, Tae Hyun Kim

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Landing page: https://arxiv.org/abs/2501.03781

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Concepts: Quantum, Linear multistep method, Oracle, Mathematics, Differential equation, Applied mathematics, Physics, Mathematical analysis, Computer science, Quantum mechanics, Differential algebraic equation, Ordinary differential equation, Software engineering

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