Stable Symmetry-Protected Topological Phases in Systems with Heralded Noise

Stable Symmetry-Protected Topological Phases in Systems with Heralded Noise

May 8, 2024 | Sanket Chirame, Fiona J. Burnell, Sarang Gopalakrishnan, and Abhinav Prem
This paper presents a family of local quantum channels whose steady-states exhibit stable mixed-state symmetry-protected topological (SPT) order. The study is motivated by recent experimental progress in "erasure conversion" techniques, which allow identification of heralded decoherence processes. The authors consider open systems with biased erasure noise, leading to strongly symmetric heralded errors. They utilize heralding to construct a local correction protocol that confines errors into short-ranged pairs in the steady-state. Numerical simulations and mean-field analysis show that the protocol stabilizes SPT order against a sufficiently low rate of decoherence. As the rate of heralded noise increases, SPT order is eventually lost through a directed percolation transition. The correction protocol ensures local SPT order persists with a correlation length that diverges as ξ ~ (1 - f_e)^{-1/2}, where f_e is the fraction of heralded errors. The paper discusses the stability of SPT order in open quantum systems, where only "strong" symmetries correspond to the conservation of symmetry charges. While pure SPT states are stable to strongly symmetric finite-depth local channels, the authors demonstrate that mixed SPT phases can arise as stable steady-states under local Lindbladian evolution. The approach is motivated by the recent experimental technique of erasure conversion, which can increase error correction thresholds. The authors focus on biased erasure noise, which naturally preserves the strong symmetry and ensures that the noise pair-creates defects. They exploit this information to construct a fully local error correction procedure that stabilizes steady-state string-order up to a finite noise threshold. The paper also discusses the nature of the phase transition, showing that the proliferation of erasures is an absorbing state transition of the type discussed in previous studies and can be mapped to directed percolation. The authors find that the critical exponents match those of directed percolation, with δ_Ω = 2δ_d. The study shows that the correction protocol significantly enhances the lifetime of string-order in the presence of unheralded errors. The results suggest that the protocol can stabilize SPT order in open quantum systems with biased erasure noise, even at finite temperatures. The paper concludes that the protocol is effective in stabilizing SPT order in open quantum systems with biased erasure noise, even at finite temperatures.This paper presents a family of local quantum channels whose steady-states exhibit stable mixed-state symmetry-protected topological (SPT) order. The study is motivated by recent experimental progress in "erasure conversion" techniques, which allow identification of heralded decoherence processes. The authors consider open systems with biased erasure noise, leading to strongly symmetric heralded errors. They utilize heralding to construct a local correction protocol that confines errors into short-ranged pairs in the steady-state. Numerical simulations and mean-field analysis show that the protocol stabilizes SPT order against a sufficiently low rate of decoherence. As the rate of heralded noise increases, SPT order is eventually lost through a directed percolation transition. The correction protocol ensures local SPT order persists with a correlation length that diverges as ξ ~ (1 - f_e)^{-1/2}, where f_e is the fraction of heralded errors. The paper discusses the stability of SPT order in open quantum systems, where only "strong" symmetries correspond to the conservation of symmetry charges. While pure SPT states are stable to strongly symmetric finite-depth local channels, the authors demonstrate that mixed SPT phases can arise as stable steady-states under local Lindbladian evolution. The approach is motivated by the recent experimental technique of erasure conversion, which can increase error correction thresholds. The authors focus on biased erasure noise, which naturally preserves the strong symmetry and ensures that the noise pair-creates defects. They exploit this information to construct a fully local error correction procedure that stabilizes steady-state string-order up to a finite noise threshold. The paper also discusses the nature of the phase transition, showing that the proliferation of erasures is an absorbing state transition of the type discussed in previous studies and can be mapped to directed percolation. The authors find that the critical exponents match those of directed percolation, with δ_Ω = 2δ_d. The study shows that the correction protocol significantly enhances the lifetime of string-order in the presence of unheralded errors. The results suggest that the protocol can stabilize SPT order in open quantum systems with biased erasure noise, even at finite temperatures. The paper concludes that the protocol is effective in stabilizing SPT order in open quantum systems with biased erasure noise, even at finite temperatures.
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