Modeling and Characterizing Noise in Quantum Annealers via ARMA Models

Accurate characterization of noise processes in quantum hardware is key to understanding device dynamics and building precise noise models. Thus far, noise modeling efforts for quantum annealing hardware haven been solely limited to the adiabatic Markovian master equation. Here, we examine an alternative approach for building noise models of quantum annealers based on autoregressive moving average (ARMA) models, a classic technique from time series analysis that models time correlations in data. This approach, known as Schroedinger Wave ARMA (SchWARMA), adapts ARMA modeling to the tanget space of a matrix manifold on which a family of probability distributions on the space of completely positive trace preserving (CPTP) maps yields the average CPTP maps as a sufficient statistic. We investigate the applicability and extension of SchWARMA to modeling and characterizing noise in quantum annealers using measurements of the average energy of the system as a function of (1) discrete times throughout the quantum annealing evolution and (2) the total annealing time. Considering a range of ARMA models, we discuss the viability of SchWARMA for experimental characterization of quantum annealers and potential pitfalls.