Stochastic Simulation of Grover's Algorithm

TL;DR

This paper introduces a stochastic simulation method for Grover's quantum search algorithm using Hubbard-Stratonovich decomposition and Langevin equations, enabling classical simulation of quantum search processes.

Contribution

The paper presents a novel stochastic approach to simulate Grover's algorithm classically, utilizing Hubbard-Stratonovich decomposition and automated derivation of Langevin equations.

Findings

Successfully simulated Grover's algorithm for small search spaces

Demonstrated the feasibility of classical stochastic simulation of quantum algorithms

Provided numerical results validating the method

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.