Stable Symmetry-Protected Topological Phases in Systems with Heralded Noise

Abstract

We present a family of local quantum channels whose steady-states exhibit stable mixed-state symmetry-protected topological (SPT) order. Motivated by recent experimental progress on "erasure conversion" techniques that allow one to identify ($\text{herald}$) decoherence processes, we consider open systems with biased erasure noise, which leads to strongly symmetric heralded errors. We utilize this heralding to construct a local correction protocol that effectively confines errors into short-ranged pairs in the steady-state. Using a combination of numerical simulations and mean-field analysis, we show that our 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. We further find that while introducing unheralded errors destroys SPT order in the limit of long length- and time-scales, the correction protocol is sufficient for ensuring that local SPT order persists, with a correlation length that diverges as $\xi \sim (1-f_e{)}^{-1/2}$, where $f_e$ is the fraction of errors that are heralded.

8+21 pages. v2: fixed typos, updated reference, v3: published version

References in corpus (22)

• High-fidelity gates with mid-circuit erasure conversion in a metastable neutral atom qubit
• Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays
• Quantum memories based on engineered dissipation
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Average Symmetry-Protected Topological Phases
• Quantum Error Correction with Metastable States of Trapped Ions Using Erasure Conversion
• Erasure qubits: Overcoming the $T_1$ limit in superconducting circuits
• High threshold codes for neutral atom qubits with biased erasure errors
• Controlling entanglement at absorbing state phase transitions in random circuits
• Mixed-state long-range order and criticality from measurement and feedback
• Entanglement Steering in Adaptive Circuits with Feedback
• Entanglement and Absorbing-State Transitions in Interactive Quantum Dynamics
• Lieb-Schultz-Mattis Theorem in Open Quantum Systems
• Characterizing Long-Range Entanglement in a Mixed State Through an Emergent Order on the Entangling Surface
• Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power
• A Monte Carlo investigation of the critical behavior of Stavskaya's probabilistic cellular automaton
• Can long-range interactions stabilize quantum memory at nonzero temperature?
• Matrix Product Operator Algebras II: Phases of Matter for 1D Mixed States
• Engineering unsteerable quantum states with active feedback
• Edge modes and symmetry-protected topological states in open quantum systems
• Characterizing measurement-based quantum gates in quantum many-body systems using correlation functions
• Quantum teleportation implies symmetry-protected topological order

Cited by in corpus (9)

• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Observation of average topological phase in disordered Rydberg atom array
• Population Dynamics of Schrödinger Cats
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Stabilizing Non-Abelian Topological Order against Heralded Noise via Local Lindbladian Dynamics
• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Frustration-Free Control and Absorbing-State Transport in Entangled State Preparation
• Holographic duality between bulk topological order and boundary mixed-state order