Quantum Fast Hitting on Glued Trees Mapped on a Photonic chip

TL;DR

This paper demonstrates the physical implementation of quantum walks on complex glued trees using photonic chips, showing exponential speedup over classical methods and exploring effects of increased branching rates.

Contribution

First experimental realization of quantum fast hitting on large glued trees with up to 16 layers using photonic waveguides and photons.

Findings

Quantum walks outperform classical walks in hitting efficiency.

Increasing branching rate enhances quantum advantage.

Successful simulation of large-depth trees with photonic chips.

Abstract

Hitting the exit node from the entrance node faster on a graph is one of the properties that quantum walk algorithms can take advantage of to outperform classical random walk algorithms. Especially, continuous-time quantum walks on central-random glued binary trees have been investigated in theories extensively for their exponentially faster hitting speed over classical random walks. Here, using heralded single photons to represent quantum walkers and waveguide arrays written by femtosecond laser to simulate the theoretical graph, we are able to demonstrate the hitting efficiency of quantum walks with tree depth as high as 16 layers for the first time. Furthermore, we expand the graph's branching rate from 2 to 5, revealing that quantum walks exhibit more superiority over classical random walks as branching rate increases. Our results may shed light on the physical implementation of quantum walk algorithms as well as quantum computation and quantum simulation.