Quantum algorithm and circuit design solving the Poisson equation

Y. Cao, A. Papageorgiou, I. Petras, J. Traub, S. Kais · 2013 · New J. Phys. 15, 013021

| 编号 QC014 | 主题 量子算法工具箱 | 链接 arXiv:1207.2485 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

The Poisson equation occurs in many areas of science and engineering. Here we focus on its numerical solution for an equation in $d$ dimensions. In particular we present a quantum algorithm and a scalable quantum circuit design which approximates the solution of the Poisson equation on a grid with error $\epsilon$ . We assume we are given a supersposition of function evaluations of the right hand side of the Poisson equation. The algorithm produces a quantum state encoding the solution. The number of quantum operations and the number of qubits used by the circuit is almost linear in $d$ and polylog in ${\epsilon }^{-1}$ . We present quantum circuit modules together with performance guarantees which can be also used for other problems.

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