Quantum algorithm and circuit design solving the Poisson equation
Date of this Version1-11-2013
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
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.
Nanoscience and Nanotechnology