Error recovery protocols within metastable Decoherence-Free Subspaces

TL;DR

This paper investigates how metastable decoherence-free subspaces in open quantum systems can serve as passive error correction codes, analyzing their effectiveness and limitations through two models.

Contribution

It introduces a protocol for error recovery within metastable DFS and characterizes the types of errors that can be autonomously reversed.

Findings

Bit-flip and spontaneous emission errors can be partially recovered in the qubit model.

Dephasing errors on cat states can be partially corrected, with a fidelity-recovery time trade-off.

Metastable DFS offer transient error correction capabilities with specific limitations.

Abstract

Open quantum systems governed by quantum master equations can exhibit quantum metastability, where decoherence-free subspaces (DFS) remain approximately invariant for long transient times before relaxing to a unique steady state. In this work, we explore the use of such metastable DFS as code spaces for passive quantum error correction. We focus on two representative models: a two-qubit system under collective dissipation, and a nonlinear driven-dissipative Kerr resonator. After characterizing the parameter regimes that support metastability, we introduce and analyze a protocol for error recovery during the metastable dynamics. Using spectral properties of the Liouvillian, we characterize which types of errors can be possibly autonomously reversed. In particular, we show that in the qubit model, the state affected by either bit-flip error or spontaneous emission can be recovered up to a certain measure. Instead, phase-flip errors would require further strategies. For the bosonic system, we show that dephasing-induced errors on cat states can be partially recovered, with a trade-off between fidelity and recovery time. These findings highlight the limitations and capabilities of metastable DFS as a transient resource for error correction.