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：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的展示至关重要。本工作中，我们提出一种量子计算模型——贝尔采样，可同时服务于上述两个目标，从而为迈向容错量子计算提供了理想的跳板。在贝尔采样中，我们以横向贝尔基测量量子电路制备状态的两个副本。研究表明，贝尔样本在经典计算上难以生成，同时构成了我们所谓的电路阴影：从贝尔样本中可高效提取关于制备该状态的量子电路信息，并诊断电路错误。除已知的能从贝尔样本中高效提取的性质外，我们给出了两种新型高效协议：电路深度的测试算法和估算电路中T门数量下界的算法。通过额外测量，我们的算法能学习低T计数量电路制备状态的完整描述。