A central challenge in the verification of quantum computers is benchmarking their performance as a whole and demonstrating their computational capabilities. In this work, we find a universal model of quantum computation, Bell sampling, that can be used for both of those tasks and thus provides an ideal stepping stone towards fault-tolerance. In Bell sampling, we measure two copies of a state prepared by a quantum circuit in the transversal Bell basis. We show that the Bell samples are classically intractable to produce and at the same time constitute what we call a circuit shadow: from the Bell samples we can efficiently extract information about the quantum circuit preparing the state, as well as diagnose circuit errors. In addition to known properties that can be efficiently extracted from Bell samples, we give two new and efficient protocols, a test for the depth of the circuit and an algorithm to estimate a lower bound to the number of T gates in the circuit. With some additional measurements, our algorithm learns a full description of states prepared by circuits with low T-count.

翻译：在量子计算机验证的核心挑战中，如何整体评估其性能并展示其计算能力始终是关键问题。本研究中我们发现了一种通用的量子计算模型——贝尔采样，该模型可同时完成上述两项任务，从而为迈向容错量子计算提供了理想跳板。贝尔采样过程中，我们使用横向贝尔基对量子电路制备的状态的两个副本进行测量。研究表明，贝尔样本在经典计算上难以生成，同时构成了我们称之为电路影子（circuit shadow）的结构：通过贝尔样本我们不仅能高效提取关于制备该状态的量子电路的信息，还能诊断电路错误。除了已知可从贝尔样本中高效提取的特性外，我们提出了两种新型高效协议：电路深度测试方法，以及估算电路中T门数量下限的算法。通过额外测量，我们的算法能够完整学习低T计数电路所制备状态的完整描述。