Quantum central limit theorem and statistical hypothesis testing in discrete quantum walk

Abstract

Discrete quantum walk is one of the de facto models of quantum computation and as an efficient tool to develop quantum search algorithms. Although the theoretical model of quantum walks is straightforward, there are many complex scenarios such as coherence decay and/or decoherence in the implementations. It is hard to test experimentally if quantum walk works, or it just decays into a version of classic random walk. We propose a quantum central limit theorem (QCLT) for discrete quantum walks and conduct the statistical hypothesis testing for the standard or decayed walker probability distribution for imperfect quantum walks based on the QCLT. A reliable statistical analysis result is obtained for the imperfect distribution by the experimental quantum walk study.