### 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 |
---|---|

Article number | 013021 |

Journal | New Journal of Physics |

Volume | 15 |

DOIs | |

Publication status | Published - 1 Jan 2013 |

Externally published | Yes |

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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

**Quantum algorithm and circuit design solving the Poisson equation.** / Cao, Yudong; Papageorgiou, Anargyros; Petras, Iasonas; Traub, Joseph; Kais, Sabre.

Research output: Contribution to journal › Article

*New Journal of Physics*, vol. 15, 013021. https://doi.org/10.1088/1367-2630/15/1/013021

}

TY - JOUR

T1 - Quantum algorithm and circuit design solving the Poisson equation

AU - Cao, Yudong

AU - Papageorgiou, Anargyros

AU - Petras, Iasonas

AU - Traub, Joseph

AU - Kais, Sabre

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84873385410&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873385410&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/15/1/013021

DO - 10.1088/1367-2630/15/1/013021

M3 - Article

AN - SCOPUS:84873385410

VL - 15

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

M1 - 013021

ER -