  Current benchmarks for mid-circuit measurements (MCMs) are limited in
scalability or the types of error they can quantify, necessitating new
techniques for quantifying their performance. Here, we introduce a theory for
learning Pauli noise in MCMs and use it to create MCM cycle benchmarking, a
scalable method for benchmarking MCMs. MCM cycle benchmarking extracts detailed
information about the rates of errors in randomly compiled layers of MCMs and
Clifford gates, and we demonstrate how its results can be used to quantify
correlated errors during MCMs on current quantum hardware. Our method can be
integrated into existing Pauli noise learning techniques to scalably
characterize and benchmark wide classes of circuits containing MCMs.
