Stochastic Simulation of Grover's Algorithm

Abstract

We simulate Grover's algorithm in a classical computer by means of a stochastic method using the Hubbard-Stratonovich decomposition of n-qubit gates into one-qubit gates integrated over auxiliary fields. The problem reduces to finding the fixed points of the associated system of Langevin differential equations. The equations are obtained automatically for any number of qubits by employing a computer algebra program. We present the numerical results of the simulation for a small search space.