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arXiv · 2403.07866

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

Sanjeev Kumar·Vikram Tripathi
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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.

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Sanjeev Kumar, Vikram Tripathi. 2024-03-12. Robustness of a state with Ising topological order against local projective measurements. https://doi.org/10.1103/physrevb.110.l161111

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