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

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 (2d), against generic ``heralded" noise using active dynamics that incorporate measurement and feedback, modeled as a \emph{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.

v2: close to the published version

References in corpus (44)

• Non-Abelian Anyons and Topological Quantum Computation
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• 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
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Quantum criticality under decoherence or weak measurement
• Erasure conversion in a high-fidelity Rydberg quantum simulator
• Measurement as a shortcut to long-range entangled quantum matter
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Digital simulation of non-Abelian anyons with 68 programmable superconducting qubits
• Average Symmetry-Protected Topological Phases
• Sparse Blossom: correcting a million errors per core second with minimum-weight matching
• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Shortest Route to Non-Abelian Topological Order on a Quantum Processor
• Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer
• 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
• Dual-rail encoding with superconducting cavities
• Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States
• Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons
• Symmetry protected topological phases under decoherence
• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Tricritical directed percolation
• Non-Abelian braiding of Fibonacci anyons with a superconducting processor
• Towards a classification of mixed-state topological orders in two dimensions
• Universal Quantum Computation with Gapped Boundaries
• Separability transitions in topological states induced by local decoherence
• Topological Phases with Average Symmetries: the Decohered, the Disordered, and the Intrinsic
• Stability of mixed-state quantum phases via finite Markov length
• Symmetry-enforced many-body separability transitions
• Mixed-state quantum anomaly and multipartite entanglement
• Matrix Product Operator Algebras II: Phases of Matter for 1D Mixed States
• Symmetry protected self correcting quantum memory in three space dimensions
• Edge modes and symmetry-protected topological states in open quantum systems
• Fault-tolerant quantum architectures based on erasure qubits
• Stable Symmetry-Protected Topological Phases in Systems with Heralded Noise
• Certified quantum gates
• Stability and Loop Models from Decohering Non-Abelian Topological Order
• Disentangling transitions in topological order induced by boundary decoherence
• Decoherence and wavefunction deformation of $D_4$ non-Abelian topological order
• Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation
• Population Dynamics of Schrödinger Cats

Cited by in corpus (2)

• Intrinsic Heralding and Optimal Decoders for Non-Abelian Topological Order
• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking