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 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：量子计算机验证的核心挑战在于整体性能基准测试与计算能力展示。本工作发现了一种可同时实现上述目标的量子计算模型——贝尔采样，为迈向容错量子计算提供了理想跳板。在贝尔采样中，我们对量子电路制备的量子态的两个副本进行横向贝尔基测量。研究表明，贝尔样本在经典计算上难以生成，同时构成了我们所谓的"电路阴影"：从贝尔样本中既能高效提取制备量子态电路的拓扑信息，又能诊断电路错误。除了已知可从贝尔样本中高效提取的特性外，我们提出两种新型高效协议：电路深度测试算法与电路T门数下界估计算法。通过附加测量，该算法可完整描述低T门数电路制备的量子态。