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，整体性能基准测试与计算能力演示是关键任务。本工作发现了一种通用量子计算模型——贝尔采样，可同时满足上述两种需求，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，我们以横向贝尔基测量量子电路制备态的两个副本。研究表明，贝尔样本在经典计算上难以生成，同时构成了所谓的电路阴影：从贝尔样本中，我们既能高效提取关于制备该态量子电路的信息，也能诊断电路错误。除已知可从贝尔样本高效提取的特性外，我们还提出两种新型高效协议：电路深度测试方案与T门数量下界估计算法。通过额外测量，该算法可完整学习由低T计数电路制备的量子态描述。