A central challenge in the verification of quantum computers is benchmarking their performance as a whole and demonstrating their computational capabilities. We provide a survey of the status of and challenges with global assessments of quantum computer performance based on quantum random circuit sampling. We then present a comprehensive approach to efficiently verifiable benchmarks using a universal model of computation based on Bell sampling. Finally, we discuss a related proposal, and recent experimental demonstration in neutral atom arrays, of computational benchmarks for encoded fault-tolerant quantum computation. Overall, these results establish a practical, scalable path towards demonstrations of quantum computational advantage in noisy quantum processors.
Based in part on arXiv:2305.04954 and arXiv:2306.00083
