Generating Haar-uniform Randomness using Stochastic Quantum Walks on a Photonic Chip

TL;DR

This paper demonstrates a scalable method to generate Haar-uniform randomness in quantum operations using stochastic quantum walks on a photonic chip, with faster convergence in two dimensions.

Contribution

It experimentally implements a two-dimensional stochastic quantum walk on a photonic chip, showing improved convergence to Haar randomness over one-dimensional setups.

Findings

Average distribution converges to uniform with increased evolution length.

Two-dimensional array outperforms one-dimensional array in convergence speed.

Method provides a scalable way to generate Haar-uniform quantum randomness.

Abstract

As random operations for quantum systems are intensively used in various quantum information tasks, a trustworthy measure of the randomness in quantum operations is highly demanded. The Haar measure of randomness is a useful tool with wide applications such as boson sampling. Recently, a theoretical protocol was proposed to combine quantum control theory and driven stochastic quantum walks to generate Haar-uniform random operations. This opens up a promising route to converting classical randomness to quantum randomness. Here, we implement a two-dimensional stochastic quantum walk on the integrated photonic chip and demonstrate that the average of all distribution profiles converges to the even distribution when the evolution length increases, suggesting the 1-pad Haar-uniform randomness. We further show that our two-dimensional array outperforms the one-dimensional array of the same number of waveguide for the speed of convergence. Our work demonstrates a scalable and robust way to generate Haar-uniform randomness that can provide useful building blocks to boost future quantum information techniques.