Quantum Random Walks Hit Exponentially Faster

TL;DR

This paper demonstrates that quantum random walks on hypercubes can reach opposite corners exponentially faster than classical walks, revealing a significant quantum advantage in hitting times.

Contribution

It introduces the first exponential quantum-classical gap in hitting times for discrete quantum walks and establishes a framework for quantum hitting time on general graphs.

Findings

Quantum walks on hypercubes have polynomial hitting time.

First exponential quantum-classical gap in hitting times.

Framework for quantum hitting time on general graphs.

Abstract

We show that the hitting time of the discrete time quantum random walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum random walks. We provide the framework for quantum hitting time and give two alternative definitions to set the ground for its study on general graphs. We then give an application to random routing.