A Noisy Approach to Intrinsically Mixed-State Topological Order

Abstract

We propose a general framework for studying two-dimensional (2D) topologically ordered states subject to local correlated errors and show that the resulting mixed-state can display intrinsically mixed-state topological order (imTO) -- topological order which is not expected to occur in the ground state of 2D local gapped Hamiltonians. Specifically, we show that decoherence, previously interpreted as anyon condensation in a doubled Hilbert space, is more naturally phrased as, and provides a physical mechanism for, ``gauging out" anyons in the original Hilbert space. We find that gauging out anyons generically results in imTO, with the decohered mixed-state strongly symmetric under certain anomalous 1-form symmetries. This framework lays bare a striking connection between the decohered density matrix and topological subsystem codes, which can appear as anomalous surface states of 3D topological orders. Through a series of examples, we show that the decohered state can display a classical memory, encode logical qubits (i.e., exhibit a quantum memory), and even host chiral or non-modular topological order. We argue that a partial classification of imTO is given in terms of non-modular braided fusion categories.

arXiv comment17 pages, 2 figures. Both authors contributed equally to this work. v2: typos fixed and references updated. v3: clarified definition of imTO in terms of strong 1-form symmetries, added a section on locally detectable anyon types, and added a discussion regarding mixed-state phases

References in corpus (73)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Separability Criterion for Density Matrices
• A computable measure of entanglement
• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Decoherence Free Subspaces for Quantum Computation
• Topological quantum memory
• Generalized Global Symmetries
• The logarithmic negativity: A full entanglement monotone that is not convex
• String-net condensation: A physical mechanism for topological phases
• On the volume of the set of mixed entangled states
• Noiseless Quantum Codes
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Symmetries and conserved quantities in Lindblad master equations
• Topological quantum order: stability under local perturbations
• A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains
• Generalized Symmetries in Condensed Matter
• A comparison of entanglement measures
• Topological boundary conditions in abelian Chern-Simons theory
• Quantum memories at finite temperature
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Fracton topological order via coupled layers
• A short proof of stability of topological order under local perturbations
• Stability of Frustration-Free Hamiltonians
• Anyon condensation and its applications
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Topological Order at Non-zero Temperature
• Quantum criticality under decoherence or weak measurement
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Entanglement negativity and topological order
• Negativity and topological order in the toric code
• Dissipation and Decoherence in a Quantum Register
• Average Symmetry-Protected Topological Phases
• Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories
• Condensation of achiral simple currents in topological lattice models: a Hamiltonian study of topological symmetry breaking
• Diagnostics of mixed-state topological order and breakdown of quantum memory
• Universal topological phase of 2D stabilizer codes
• Detecting Topological Order at Finite Temperature Using Entanglement Negativity
• Phase transitions in topological lattice models via topological symmetry breaking
• Cage-Net Fracton Models
• Feasibility of self-correcting quantum memory and thermal stability of topological order
• Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer
• Structure of 2D Topological Stabilizer Codes
• Topological Protection and Quantum Noiseless Subsystems
• Topological entanglement negativity in Chern-Simons theories
• Chiral central charge from a single bulk wave function
• Intrinsic Mixed-state Topological Order
• Pauli stabilizer models of twisted quantum doubles
• Classification of phases for mixed states via fast dissipative evolution
• Topological order and topological entropy in classical systems
• Quantum Cellular Automata, Tensor Networks, and Area Laws
• Towards a classification of mixed-state topological orders in two dimensions
• Entanglement negativity and sudden death in the toric code at finite temperature
• Separability transitions in topological states induced by local decoherence
• Modular commutator in gapped quantum many-body systems
• Pauli topological subsystem codes from Abelian anyon theories
• Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
• Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies
• Interacting Anyonic Fermions in a Two-Body Color Code Model
• Symmetry-enforced many-body separability transitions
• Multipartitioning topological phases by vertex states and quantum entanglement
• From entanglement generated dynamics to the gravitational anomaly and chiral central charge
• A universal tripartite entanglement signature of ungappable edge states
• Modular Commutators in Conformal Field Theory
• Gravitational anomaly of 3+1 dimensional Z_2 toric code with fermionic charges and fermionic loop self-statistics
• Robust teleportation of a surface code and cascade of topological quantum phase transitions
• Theory of oblique topological insulators
• Entanglement in tripartitions of topological orders: a diagrammatic approach
• Renyi entropies for classical stringnet models
• Multipartite entanglement in two-dimensional chiral topological liquids
• Self-correction in Wegner's 3D Ising lattice gauge theory

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• Intrinsic Mixed-state Topological Order
• Towards a classification of mixed-state topological orders in two dimensions
• Stability of mixed-state quantum phases via finite Markov length
• Mixed-state topological order and the errorfield double formulation of decoherence-induced transitions
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order
• Efficient Detection of Strong-To-Weak Spontaneous Symmetry Breaking via the Rényi-1 Correlator
• Strong and weak symmetries and their spontaneous symmetry breaking in mixed states emerging from the quantum Ising model under multiple decoherence
• Stability and Loop Models from Decohering Non-Abelian Topological Order
• Average-exact mixed anomalies and compatible phases
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak
• Decoherence and wavefunction deformation of $D_4$ non-Abelian topological order
• Intrinsic mixed state topological order in a stabilizer system under stochastic decoherence: Strong-to-weak spontaneous symmetry breaking from percolation point of view
• Mixed-state phase transitions in spin-Holstein models
• Finite-temperature quantum topological order in three dimensions
• Gauge theory and mixed state criticality
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Hardness of observing strong-to-weak symmetry breaking
• Mixed-State Topological Order under Coherent Noise
• Stabilizing Non-Abelian Topological Order against Heralded Noise via Local Lindbladian Dynamics
• Many-body quantum catalysts for transforming between phases of matter
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Anyon condensation in mixed-state topological order
• Quantum circuit complexity and unsupervised machine learning of topological order
• Simulation of bilayer Hamiltonians based on monitored quantum trajectories
• Revisiting Nishimori multicriticality through the lens of information measures
• The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems
• Symmetry Properties of Quantum Dynamical Entropy
• Simulating Topological Order on Quantum Processors
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Attention to Quantum Complexity
• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity
• Phases of Floquet code under local decoherence
• Spacetime Markov length: a diagnostic for fault tolerance via mixed-state phases
• Universal Decay of Mutual Information and Conditional Mutual Information in Gapped Pure- and Mixed-State Quantum Matter
• Holographic duality between bulk topological order and boundary mixed-state order