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 several new and efficient protocols: an estimator of state fidelity, 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：量子计算机验证的一个核心挑战在于对其整体性能进行基准测试并展示其计算能力。在本研究中，我们发现了一种通用量子计算模型——贝尔采样，该模型可同时用于上述两项任务，从而为实现容错量子计算提供了理想的过渡路径。在贝尔采样中，我们对量子电路制备态的两个副本进行横向贝尔基测量。我们证明贝尔样本在经典计算层面难以生成，同时其构成了我们称为"电路阴影"的载体：通过贝尔样本，我们能够高效提取关于制备该态的量子电路信息，并诊断电路错误。除了已知可从贝尔样本高效提取的特性外，我们提出了若干新型高效协议：态保真度估计器、电路深度测试算法以及电路T门数量下界估计算法。通过附加测量，我们的算法能够完整学习低T门数量电路所制备态的完整描述。