### 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 (US) |
---|---|

Article number | 013021 |

Journal | New Journal of Physics |

Volume | 15 |

DOIs | |

State | Published - Jan 1 2013 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

## Fingerprint Dive into the research topics of 'Quantum algorithm and circuit design solving the Poisson equation'. Together they form a unique fingerprint.

## Cite this

*New Journal of Physics*,

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