Yudong Cao, Anargyros Papageorgiou, Iasonas Petras, Joseph Traub, Sabre Kais
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 with error {\epsilon}. The cost is almost linear in d and polylog in {\epsilon}^-1, showing an exponential speedup. The circuit uses a number of qubits which is also almost linear in d and polylog in {\epsilon}^-1 . We present quantum circuit modules together with performance guarantees which can be also used for other problems.
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http://arxiv.org/abs/1207.2485
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