Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics

TL;DR

This paper introduces a framework to analyze how non-Markovian noise affects symmetry-preserving quantum dynamics, revealing that such noise can cause specific leakage errors and impacting quantum control and error correction strategies.

Contribution

It develops an analytical framework for understanding non-Markovian noise effects on symmetries in quantum systems, extending previous Markovian-focused studies.

Findings

Symmetry-preserving noise maintains the symmetric subspace.

Nonsymmetric noise causes block-diagonal leakage errors.

Numerical studies confirm theoretical predictions.

Abstract

In quantum dynamics, symmetries are vital for identifying and assessing conserved quantities that govern the evolution of a quantum system. When promoted to the open quantum system setting, dynamical symmetries can be negatively altered by system-environment interactions, thus, complicating their analysis. Previous work on noisy symmetric quantum dynamics has focused on the Markovian setting, despite the ubiquity of non-Markovian noise in a number of widely used quantum technologies. In this Letter, we develop a framework for quantifying the impact of non-Markovian noise on symmetric quantum evolution via root space decompositions and the filter function formalism. We demonstrate analytically that symmetry-preserving noise maintains the symmetric subspace, while nonsymmetric noise leads to highly specific leakage errors that are block diagonal in the symmetry representation. We support our findings with numerical studies of a transverse-field Ising model and a quantum error detecting code subject to spatiotemporally correlated multiaxis noise. Our results are broadly applicable, providing new analytic insights into the control and characterization of open quantum system dynamics.