  Temporal noise correlations are ubiquitous in quantum systems, yet often
neglected in the analysis of quantum circuits due to the complexity required to
accurately characterize and model them. Autoregressive moving average (ARMA)
models are a well-known technique from time series analysis that model time
correlations in data. By identifying the space of completely positive trace
reserving (CPTP) quantum operations with a particular matrix manifold, we
generalize ARMA models to the space of CPTP maps to parameterize and simulate
temporally correlated noise in quantum circuits. This approach, denoted
Schr\"odinger Wave ARMA (SchWARMA), provides a natural path for generalization
of classic techniques from signal processing, control theory, and system
identification for which ARMA models and linear systems are essential. This
enables the broad theory of classical signal processing to be applied to
quantum system simulation, characterization, and noise mitigation.
