Experimental Quantum Fast Hitting on Hexagonal Graphs

TL;DR

This paper demonstrates scalable quantum fast hitting on hexagonal graphs with up to 160 nodes using photonic chips, showing potential for quantum speed-up in complex computational problems.

Contribution

It introduces a polynomially scalable graph structure and experimentally implements quantum walks on it, advancing practical quantum speed-up methods.

Findings

Successful implementation of quantum walks on 160-node graphs

Linear relationship between hitting time and network depth

Scalable photonic chip architecture for quantum simulations

Abstract

Quantum walks are powerful kernels in quantum computing protocols that possess strong capabilities in speeding up various simulation and optimisation tasks. One striking example is given by quantum walkers evolving on glued trees for their faster hitting performances than in the case of classical random walks. However, its experimental implementation is challenging as it involves highly complex arrangements of exponentially increasing number of nodes. Here we propose an alternative structure with a polynomially increasing number of nodes. We successfully map such graphs on quantum photonic chips using femtosecond laser direct writing techniques in a geometrically scalable fashion. We experimentally demonstrate quantum fast hitting by implementing two-dimensional quantum walks on these graphs with up to 160 nodes and a depth of 8 layers, achieving a linear relationship between the optimal hitting time and the network depth. Our results open up a scalable way towards quantum speed-up in complex problems classically intractable.