Quantum algorithm and circuit design solving the Poisson equation
Date of this Version
1-11-2013Citation
Yudong Cao, Anargyros Papageorgiou, Iasonas Petras, Joseph Traub and Sabre Kais Published 11 January 2013 • IOP Publishing and Deutsche Physikalische Gesellschaft New Journal of Physics, Volume 15, January 2013
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 epsilon. 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 epsilon(-1). We present quantum circuit modules together with performance guarantees which can also be used for other problems.
Discipline(s)
Nanoscience and Nanotechnology
Download
Comments
Copyright (2013) Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Institute of Physics. The following article appeared in New Journal of Physics, Volume 15, January 2013 and may be found at http://dx.doi.org/10.1088/1367-2630/15/1/013021. The following article has been submitted to/accepted by New Journal of Physics. Copyright (2013) Yudong Cao, Anargyros Papageorgiou, Iasonas Petras, Joseph Traub and Sabre Kais. This article is distributed under a Creative Commons Attribution 3.0 Unported License.