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With the advent of quantum processors exceeding $100$ qubits and the highengineering complexities involved, there is a need for holisticallybenchmarking the processor to have quality assurance. Linear cross-entropybenchmarking (XEB) has been used extensively for systems with $50$ or morequbits but is fundamentally limited in scale due to the exponentially largecomputational resources required for classical simulation. In this work wepropose conducting linear XEB with Clifford circuits, a scheme we call CliffordXEB. Since Clifford circuits can be simulated in polynomial time, Clifford XEBcan be scaled to much larger systems. To validate this claim, we run numericalsimulations for particular classes of Clifford circuits with noise and observeexponential decays. When noise levels are low, the decay rates arewell-correlated with the noise of each cycle assuming a digital error model. Weperform simulations of systems up to 1,225 qubits, where the classicalprocessing task can be easily dealt with by a workstation. Furthermore, usingthe theoretical guarantees in Chen et al. (arXiv:2203.12703), we prove thatClifford XEB with our proposed Clifford circuits must yield exponential decaysunder a general error model for sufficiently low errors. Our theoreticalresults explain some of the phenomena observed in the simulations and shedlight on the behavior of general linear XEB experiments.

Linear Cross Entropy Benchmarking with Clifford Circuits