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

Y1 - 2013/1

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.

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

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

M3 - Article

AN - SCOPUS:84873385410

SN - 1367-2630

VL - 15

JO - New Journal of Physics

JF - New Journal of Physics

M1 - 013021

ER -