### Abstract

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 ε. We assume we are given a superposition 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 ε^{-1}. We present quantum circuit modules together with performance guarantees which can also be used for other problems.

Original language | English |
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Article number | 013021 |

Journal | New Journal of Physics |

Volume | 15 |

DOIs | |

Publication status | Published - 1 Jan 2013 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*New Journal of Physics*,

*15*, [013021]. https://doi.org/10.1088/1367-2630/15/1/013021