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

Sanket Chirame1,*, Abhinav Prem2,3, Sarang Gopalakrishnan4, and Fiona J. Burnell1

  • 1School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 2School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA
  • 3Physics Program, Bard College, 30 Campus Road, Annandale-on-Hudson, New York 12504, USA
  • 4Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA

  • *Contact author: chira012@umn.edu
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PRX Quantum 6, 030363 – Published 25 September, 2025

DOI: https://doi.org/10.1103/zf7y-hxtq

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, in two spatial dimensions, against generic “heralded” noise using active dynamics that incorporate measurement and feedback, modeled as a 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 (Z2) and non-Abelian (D4) 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 D4 case, we introduce a generalized stabilizer tableau formalism that permits efficient simulation of the non-Abelian Lindbladian dynamics.

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Popular Summary

Quantum information is fragile and typically requires active error correction to preserve it. Topologically ordered states can protect information against local noise, but in low dimensions they require nonlocal decoding to correct errors and do not form self-correcting memories. In practice, every qubit error must be found by global syndrome processing, which limits scalability. Erasure qubits offer a different route: errors take the qubit out of the computational space and are heralded (flagged). Recent experiments have shown that, in an erasure qubit, the most likely error is the loss of the qubit state, detectable in real time. This equips each error with a local flag, providing classical information about its location.

We exploit these heralded errors to achieve two-dimensional topological memories that self-correct using only local measurements and feedback (modeled by a fully local Lindbladian). When an erasure is flagged, its location is used to move the resulting defects locally so that error strings annihilate in short-range pairs, effectively confining errors. This yields a steady state with the same mixed-state topological order as the error-free pure state, and the encoded quantum information survives for a time that grows exponentially with system size: the hallmark of a self-correcting memory.

We present explicit constructions of such local dynamics for both Abelian (Z2) and non-Abelian (D4) topological states, providing an example of passive, self-correcting topological memories in two dimensions, achievable on current erasure-qubit platforms. This work opens a practical pathway to preserving complex entangled states against decoherence using purely local error-confinement dynamics.

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PRX Quantum 6, 030363– Published 25 September, 2025
  • Received 30 November 2024
  • Accepted 12 August 2025
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