Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently the first large-scale implementations of quantum random sampling have arguably surpassed the boundary of what can be simulated on existing classical hardware. Here the theoretical underpinning of quantum random sampling is comprehensively reviewed in terms of computational complexity and verifiability, as are the practical aspects of its experimental implementation using superconducting and photonic devices and its classical simulation. Open questions in the field are discussed, and perspectives for the road ahead, including potential applications of quantum random sampling, are provided.

中文翻译：

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量子随机采样的计算优势

量子随机采样是证明量子计算机相对于经典计算机的计算优势的主要提议。最近，量子随机采样的首次大规模实现可以说已经超越了现有经典硬件上可以模拟的边界。这里从计算复杂性和可验证性方面全面回顾了量子随机采样的理论基础，以及使用超导和光子器件及其经典模拟进行实验实现的实际方面。讨论了该领域的开放性问题，并提供了未来的前景，包括量子随机采样的潜在应用。