Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases

Abstract

We establish a correspondence between the fault-tolerance of local stabilizer codes experiencing measurement and physical errors and the mixed-state phases of decohered resource states in one higher dimension. Drawing from recent developments in mixed-state phases of matter, this motivates a diagnostic of fault-tolerance, which we refer to as the spacetime Markov length. This is a length scale determined by the decay of the (classical) conditional mutual information of repeated syndrome measurement outcomes in spacetime. The diagnostic is independent of the decoder, and its divergence signals the intrinsic breakdown of fault tolerance. As a byproduct, we find that decoherence may be useful for exposing transitions from higher-form symmetry-protected topological phases driven by both incoherent and coherent perturbations.

References in corpus (40)

• Fault-tolerant quantum computation by anyons
• Topological quantum memory
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Quantum error correction below the surface code threshold
• Topological quantum order: stability under local perturbations
• Resilient Quantum Computation: Error Models and Thresholds
• Long-range quantum entanglement in noisy cluster states
• Stability of Frustration-Free Hamiltonians
• Dynamically Generated Logical Qubits
• Topological Order at Non-zero Temperature
• Quantum criticality under decoherence or weak measurement
• Average Symmetry-Protected Topological Phases
• Foliated Quantum Codes
• Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Statistical mechanical models for quantum codes with correlated noise
• Anyon condensation and the color code
• Intrinsic Mixed-state Topological Order
• Fracton phases via exotic higher-form symmetry-breaking
• Mixed-state long-range order and criticality from measurement and feedback
• Symmetry protected topological phases under decoherence
• Classification of phases for mixed states via fast dissipative evolution
• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Towards a classification of mixed-state topological orders in two dimensions
• Separability transitions in topological states induced by local decoherence
• High-threshold quantum computing by fusing one-dimensional cluster states
• Universal fault-tolerant measurement-based quantum computation
• Channeling quantum criticality
• Unifying flavors of fault tolerance with the ZX calculus
• Symmetry-protected self-correcting quantum memories
• 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
• Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions
• Fidelity Strange Correlators for Average Symmetry-Protected Topological Phases
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• Exact Calculations of Coherent Information for Toric Codes under Decoherence: Identifying the Fundamental Error Threshold
• Topologically Ordered Steady States in Open Quantum Systems
• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement