Classical Simulation and Complexity of Quantum Computations

Abstract

AbstractQuantum computing is widely regarded as being able to offer computational complexity benefits beyond the possibilities of classical computing. Yet the relationship of quantum to classical computational complexity is little understood. A fundamental approach to exploring this issue is to study the extent to which quantum computations (especially with restricted sub-universal ingredients) can be classically efficiently simulated. We will discuss a series of results relating to the classical simulation of some interesting classes of quantum computations, particularly Clifford circuits, matchgate circuits and a simple class of quantum circuits (so-called IQP circuits) comprising commuting gates. We will outline an argument that a suitably efficient classical simulation of the latter class would imply a collapse of the polynomial hierarchy.KeywordsQuantum computationquantum complexityclassical simulationmatchgates