Quantum algorithm and circuit design solving the Poisson equation

Yudong Cao, Anargyros Papageorgiou, Iasonas Petras, Joseph Traub, Sabre Kais

Research output: Contribution to journalArticlepeer-review

114 Scopus citations


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 languageEnglish (US)
Article number013021
JournalNew Journal of Physics
StatePublished - Jan 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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