Quantum error mitigation in the presence of time-correlated noise

Zero-noise extrapolation (ZNE) is a quantum error mitigation technique that can be applied in the presence of different noise models, although the usual assumption is that the noise is time-independent. However, time-correlated noise can have a strong influence on quantum circuits and has been widely observed in real physical devices. Schrödinger Wave Auto-Regressive Moving Average (SchWARMA) [1] models allow one to study such time-correlated noise models in quantum circuits, by leveraging the established theory of classical signal processing. We integrate SchWARMA with Mitiq [2] to investigate the performance of zero-noise extrapolation in the presence of temporally correlated noise. We show that the standard ZNE approach breaks down in the presence of time-correlated noise, and we propose how one could overcome these limitations with alternative extrapolation methods.

[1] Kevin Schultz, Gregory Quiroz, Paraj Titum, B. D. Clader, “SchWARMA: A model-based approach for time-correlated noise in quantum circuits”, ArXiv:2010.04580, 2020.
[2] Ryan LaRose, Andrea Mari, Peter J. Karalekas, Nathan Shammah, William J. Zeng, “Mitiq: A software package for error mitigation on noisy quantum computers”, ArXiv:2009.04417, 2020.