Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the boundary of what can be simulated on existing classical hardware. In this article, we comprehensively review the theoretical underpinning of quantum random sampling in terms of computational complexity and verifiability, as well as the practical aspects of its experimental implementation using superconducting and photonic devices and its classical simulation. We discuss in detail open questions in the field and provide perspectives for the road ahead, including potential applications of quantum random sampling.

翻译：量子随机抽样是展示量子计算机相对于经典计算机计算优势的主要方案。近期，首次大规模量子随机抽样的实现据称已超越了现有经典硬件可模拟的边界。本文从计算复杂性与可验证性角度全面综述了量子随机抽样的理论基础，以及利用超导与光子器件进行实验实现的实际方面及其经典模拟方法。我们详细讨论了该领域的未解决问题，并展望了未来发展路径，包括量子随机抽样的潜在应用。