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

TL;DR

SchWARMA introduces a novel model-based method that adapts classical ARMA time series models to quantum circuits, enabling accurate simulation and analysis of time-correlated noise in quantum systems.

Contribution

This work generalizes ARMA models to the space of CPTP quantum operations, bridging classical signal processing techniques with quantum noise modeling.

Findings

Enables simulation of temporally correlated quantum noise.

Provides a framework for quantum noise characterization.

Facilitates noise mitigation strategies in quantum computing.

Abstract

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.