Robustness of a state with Ising topological order against local projective measurements

Abstract

We investigate the fragility of a topologically ordered state, namely, the ground state of a weakly Zeeman perturbed honeycomb Kitaev model to environment induced decoherence effects mimicked by random local projective measurements. Our findings show the nonabelian Ising topological order, as quantified by a tripartite mutual information (the topological entanglement entropy $\gamma$,) is resilient to such disturbances. Further, $\gamma$ is found to evolve smoothly from a topologically ordered state to a distribution of trivial states as a function of rate of measurement (temperature). We assess our model by contrasting it with the Toric Code limit of the Kitaev model, whose ground state has abelian $Z_2$ topological order, and which has garnered greater attention in the literature of fault-tolerant quantum computation. The findings reveal the topological order in the Toric Code limit collapses rapidly as opposed to our model where it can withstand higher measurement rates.

References in corpus (20)

• Non-Abelian Anyons and Topological Quantum Computation
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Minimally Entangled Typical Thermal State Algorithms
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Relating out-of-time-order correlations to entanglement via multiple-quantum coherences
• Measurement as a shortcut to long-range entangled quantum matter
• Growth of entanglement entropy under local projective measurements
• Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
• Intrinsic Gap of the nu=5/2 Fractional Quantum Hall State
• Topological transitions with continuously monitored free fermions
• Shortest Route to Non-Abelian Topological Order on a Quantum Processor
• Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer
• Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain
• Readout of Majorana Qubits
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Entanglement Phases in large-N hybrid Brownian circuits with long-range couplings
• Measurement-induced phase transitions in the toric code
• Counterdiabatic route for preparation of state with long-range topological order
• Dynamics of entanglement in systems of identical fermions undergoing decoherence
• Sudden death of entanglement in fermionic systems under collective decoherence