Edge modes and symmetry-protected topological states in open quantum systems

Abstract

Topological order offers possibilities for processing quantum information which can be immune to imperfections. However, the question of its stability out of equilibrium is relevant for experiments, where coupling to an environment is unavoidable. In this work we demonstrate the robustness of certain aspects of $Z_2\times Z_2$ symmetry-protected topological (SPT) order against a wide class of dissipation channels in the Lindblad and quantum trajectory formalisms of an open quantum system. This is illustrated using the one-dimensional $ZXZ$ cluster Hamiltonian along with Pauli-string jump operators. We show that certain choices of dissipation retaining strong symmetries support a steady-state manifold consisting of two non-local logical qubits, and for Hamiltonian perturbations preserving the global symmetry, states in this manifold remain metastable. In contrast, this metastability is destroyed upon breaking the above-mentioned symmetry. While the localized edge qubits of the cluster Hamiltonian are not conserved by the Lindbladian evolution, they do correspond to weak symmetries and thus retain a memory of their initial state at all times in the quantum trajectories. We utilize this feature to construct protocols to retrieve the quantum information either by monitoring jumps or error mitigation. Our work thus proposes a novel framework to study the dynamics of dissipative SPT phases and opens the possibility of engineering entangled states relevant to quantum information processing.

21 pages, 10 figures

References in corpus (44)

• Non-Abelian Anyons and Topological Quantum Computation
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Quantum trajectories and open many-body quantum systems
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect
• Quantum back-action of variable-strength measurement
• Engineered Dissipation for Quantum Information Science
• Measurement-induced topological entanglement transitions in symmetric random quantum circuits
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Tenfold Way for Quadratic Lindbladians
• Experimental multiparticle entanglement dynamics induced by decoherence
• Observation of a Majorana zero mode in a topologically protected edge channel
• Realising the Symmetry-Protected Haldane Phase in Fermi-Hubbard Ladders
• Quantum computation on the edge of a symmetry-protected topological order
• Identifying phases of quantum many-body systems that are universal for quantum computation
• Topology of density matrices
• Observation of a symmetry-protected topological time crystal with superconducting qubits
• Identification of symmetry-protected topological states on noisy quantum computers
• High-fidelity three-qubit iToffoli gate for fixed-frequency superconducting qubits
• Stable Quantum-Correlated Many Body States through Engineered Dissipation
• Noise-resilient Edge Modes on a Chain of Superconducting Qubits
• Hierarchy of relaxation timescales in local random Liouvillians
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Symmetry-resolved entanglement in symmetry-protected topological phases
• Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
• Integrability of $1D$ Lindbladians from operator-space fragmentation
• Symmetry Classification of Many-Body Lindbladians: Tenfold Way and Beyond
• Yang-Baxter integrable Lindblad equations
• Metastability in an open quantum Ising model
• The upside of noise: engineered dissipation as a resource in superconducting circuits
• Theory of classical metastability in open quantum systems
• Fragility of Time-Reversal Symmetry Protected Topological Phases
• Extensive characterization of a family of efficient three-qubit gates at the coherence limit
• Unraveling the topology of dissipative quantum systems
• Symmetry enhanced boundary qubits at infinite temperature
• Quantum scars and bulk coherence in a symmetry-protected topological phase
• Detecting and stabilizing measurement-induced symmetry-protected topological phases in generalized cluster models
• Topological phase transitions at finite temperature
• Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power
• Dissipative Boundary State Preparation
• Quantum jump Monte Carlo simplified: Abelian symmetries
• Dissipative Symmetry-Protected Topological Order
• Protection of quantum information in a chain of Josephson junctions

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• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
• Characterizing dynamical behaviors in topological open systems with boundary dissipations
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity
• Entanglement transition in a cluster spin chain coupled with free spins