A Theory of Quantum Differential Equation Solver: From Lower Bounds to Fast-Forwarding

Quantum computers are naturally good at simulating unitary quantum systems, yet their potential to solve a broader class of non-quantum dynamical problems involving dissipation or driving remains an open question. We try to answer a core question: w without imposing extra structural assumptions, what are the fundamental boundaries of quantum speed-up?

This talk will first examine the general limitations of quantum ODE solvers, revealing that the “non-quantum” nature of a system—specifically the real-part gap and non-normality—are important sources of computational overhead. Secondly, “fast-forwarding” techniques will also be presented: when the coefficient matrix satisfies certain conditions (e.g., being negative-definite or having a known eigensystem), it is possible to bypass those limitations and achieve quadratic or even exponential speed-ups. Recent progress over the past few years will also be briefly discussed. This talk is based on arxiv:2211.05246.

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Organizer

组织者

Jin-Peng Liu 刘锦鹏

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Speaker

报告人

Junkai Wang

Junkai Wang is a visiting Student at YMSC, Tsinghua.

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Time

时间

Tues., 16:00-17:00, May 27, 2025

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Venue

参与方式

Offline：Ningzhai 104

Online Tencent: 603-0692-7681