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arXiv · 2004.06516

Quantum vs. classical algorithms for solving the heat equation

Noah Linden·Ashley Montanaro·Changpeng Shao
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Abstract

Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equation in a rectangular region - and compare in detail the complexities of ten classical and quantum algorithms for solving it, in the sense of approximately computing the amount of heat in a given region. We find that, for spatial dimension $d \ge 2$, there is an at most quadratic quantum speedup using an approach based on applying amplitude estimation to an accelerated classical random walk. However, an alternative approach based on a quantum algorithm for linear equations is never faster than the best classical algorithms.

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Noah Linden, Ashley Montanaro, Changpeng Shao. 2020-04-14. Quantum vs. classical algorithms for solving the heat equation. https://arxiv.org/abs/2004.06516

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