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 \varepsilon. 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 \varepsilon^{-1}. We present quantum circuit modules together with performance guarantees which can be also used for other problems.
@article{arxiv.1207.2485,
title = {Quantum algorithm and circuit design solving the Poisson equation},
author = {Yudong Cao and Anargyros Papageorgiou and Iasonas Petras and Joseph Traub and Sabre Kais},
journal= {arXiv preprint arXiv:1207.2485},
year = {2013}
}
Comments
30 pages, 9 figures. This is the revised version for publication in New Journal of Physics