Non-Markovian Noise Suppression Simplified through Channel Representation

TL;DR

This paper introduces the Choi channel representation for non-Markovian quantum noise, enabling the adaptation of existing error suppression protocols to handle complex memory effects in quantum systems.

Contribution

The paper presents a novel Choi channel framework that simplifies non-Markovian noise modeling and facilitates the application of Markovian error correction techniques to non-Markovian environments.

Findings

Pauli twirling transforms non-Markovian noise into classically correlated noise.

The framework enables direct translation of error suppression protocols from Markovian to non-Markovian settings.

Potential for developing new non-Markovian noise mitigation strategies.

Abstract

Non-Markovian noise, arising from the memory effect in the environment, poses substantial challenges to conventional quantum noise suppression protocols, including quantum error correction and mitigation. We introduce a channel representation for arbitrary non-Markovian quantum dynamics, termed the Choi channel, as it operates on the Choi states of the ideal gate layers. This representation translates the complex dynamics of non-Markovian noise into the familiar picture of noise channels acting on ideal states, allowing us to directly apply many existing error suppression protocols originally designed for Markovian noise. These protocols can then be translated from the Choi channel picture back to the circuit picture, yielding non-Markovian noise suppression protocols. With this framework, we have devised new protocols using Pauli twirling, probabilistic error cancellation and virtual channel purification. In particular, Pauli twirling can transform any non-Markovian noise into noise that exhibits only classical temporal correlations, thereby extending the proven noise resilience of single-shot quantum error correction to arbitrary non-Markovian noise. Through these examples, the Choi channel demonstrates significant potential as a foundational bridge for connecting existing techniques and inspiring the development of novel non-Markovian noise suppression protocols.