Stabilizing Non-Abelian Topological Order against Heralded Noise via Local Lindbladian Dynamics

• URL: http://arxiv.org/abs/2410.21402v1
• Date: Mon, 28 Oct 2024 18:07:23 GMT
• Title: Stabilizing Non-Abelian Topological Order against Heralded Noise via Local Lindbladian Dynamics
• Authors: Sanket Chirame, Abhinav Prem, Sarang Gopalakrishnan, Fiona J. Burnell,
• Abstract summary: We show how robust steady-state phases with both Abelian and non-Abelian mixed-state topological order can be stabilized against generic heralded" noise. These topologically ordered steady states are two-way connected to pure topologically ordered ground states using local quantum channels.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: An important open question for the current generation of highly controllable quantum devices is understanding which phases can be realized as stable steady-states under local quantum dynamics. In this work, we show how robust steady-state phases with both Abelian and non-Abelian mixed-state topological order can be stabilized against generic ``heralded" noise using active dynamics that incorporate measurement and feedback, modeled as a $\textit{fully local}$ Lindblad master equation. These topologically ordered steady states are two-way connected to pure topologically ordered ground states using local quantum channels, and preserve quantum information for a time that is exponentially large in the system size. Specifically, we present explicit constructions of families of local Lindbladians for both Abelian ($\mathbb{Z}_2$) and non-Abelian ($D_4$) topological order whose steady-states host mixed-state topological order when the noise is below a threshold strength. As the noise strength is increased, these models exhibit first-order transitions to intermediate mixed state phases where they encode robust classical memories, followed by (first-order) transitions to a trivial steady state at high noise rates. When the noise is imperfectly heralded, steady-state order disappears but our active dynamics significantly enhances the lifetime of the encoded logical information. To carry out the numerical simulations for the non-Abelian $D_4$ case, we introduce a generalized stabilizer tableau formalism that permits efficient simulation of the non-Abelian Lindbladian dynamics.

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