1 research outputs found
Quantum algorithm and circuit design solving the Poisson equation
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.Comment: 30 pages, 9 figures. This is the revised version for publication in
New Journal of Physic