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Temporal noise correlations are ubiquitous in quantum systems, yet oftenneglected in the analysis of quantum circuits due to the complexity required toaccurately characterize and model them. Autoregressive moving average (ARMA)models are a well-known technique from time series analysis that model timecorrelations in data. By identifying the space of completely positive tracereserving (CPTP) quantum operations with a particular matrix manifold, wegeneralize ARMA models to the space of CPTP maps to parameterize and simulatetemporally correlated noise in quantum circuits. This approach, denotedSchr\"odinger Wave ARMA (SchWARMA), provides a natural path for generalizationof classic techniques from signal processing, control theory, and systemidentification for which ARMA models and linear systems are essential. Thisenables the broad theory of classical signal processing to be applied toquantum system simulation, characterization, and noise mitigation.

SchWARMA: A model-based approach for time-correlated noise in quantum circuits