  The Poisson equation has applications across many areas of physics and
engineering, such as the dynamic process simulation of ocean current. Here we
present a quantum Fast Poisson Solver, including the algorithm and the complete
and modular circuit design. The algorithm takes the HHL algorithm as the
template. The controlled rotation is performed based on the arc cotangent
function which is evaluated by the Plouffe's binary expansion method. And the
same method is used to compute the cosine function for the eigenvalue
approximation in phase estimation. Quantum algorithms for solving square root
and reciprocal functions are developed based on the non-restoring
digit-recurrence method. These advances make the algorithm's complexity lower
and the circuit-design more modular. The number of the qubits and operations
used by the circuit are O(dlog2({\epsilon}-1)) and O(dlog3({\epsilon}-1)),
respectively. We demonstrate our circuits on a quantum virtual computing system
installed on the Sunway TaihuLight supercomputer. This is an important step
toward practical applications of quantum Fast Poisson Solver in the near-term
hybrid classical/quantum devices.
