  With the advent of quantum processors exceeding $100$ qubits and the high
engineering complexities involved, there is a need for holistically
benchmarking the processor to have quality assurance. Linear cross-entropy
benchmarking (XEB) has been used extensively for systems with $50$ or more
qubits but is fundamentally limited in scale due to the exponentially large
computational resources required for classical simulation. In this work we
propose conducting linear XEB with Clifford circuits, a scheme we call Clifford
XEB. Since Clifford circuits can be simulated in polynomial time, Clifford XEB
can be scaled to much larger systems. To validate this claim, we run numerical
simulations for particular classes of Clifford circuits with noise and observe
exponential decays. When noise levels are low, the decay rates are
well-correlated with the noise of each cycle assuming a digital error model. We
perform simulations of systems up to 1,225 qubits, where the classical
processing task can be easily dealt with by a workstation. Furthermore, using
the theoretical guarantees in Chen et al. (arXiv:2203.12703), we prove that
Clifford XEB with our proposed Clifford circuits must yield exponential decays
under a general error model for sufficiently low errors. Our theoretical
results explain some of the phenomena observed in the simulations and shed
light on the behavior of general linear XEB experiments.
