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

• URL: http://arxiv.org/abs/2112.06549v1
• Date: Mon, 13 Dec 2021 10:35:37 GMT
• Title: Generating Haar-uniform Randomness using Stochastic Quantum Walks on a Photonic Chip
• Authors: Hao Tang, Leonardo Banchi, Tian-Yu Wang, Xiao-Wen Shang, Xi Tan, Wen-Hao Zhou, Zhen Feng, Anurag Pal, Hang Li, Cheng-Qiu Hu, M.S. Kim and Xian-Min Jin
• Abstract summary: 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 quantum walks to generate Haar-uniform random operations. Here, we implement a two-dimensional 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-padar-uniform randomness.
• Score: 14.111146438141967
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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