Quantum vs. classical algorithms for solving the heat equation

• URL: http://arxiv.org/abs/2004.06516v2
• Date: Thu, 18 Jun 2020 10:39:45 GMT
• Title: Quantum vs. classical algorithms for solving the heat equation
• Authors: Noah Linden, Ashley Montanaro and Changpeng Shao
• Abstract summary: 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.
• Score: 0.04297070083645048
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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