Robustness of a state with Ising topological order against local projective measurements
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929599957434368 |
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| author | Kumar, Sanjeev Tripathi, Vikram |
| author_facet | Kumar, Sanjeev Tripathi, Vikram |
| contents | 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 $γ$,) is resilient to such disturbances. Further, $γ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07866 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Robustness of a state with Ising topological order against local projective measurements Kumar, Sanjeev Tripathi, Vikram Strongly Correlated Electrons Quantum Physics 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 $γ$,) is resilient to such disturbances. Further, $γ$ 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. |
| title | Robustness of a state with Ising topological order against local projective measurements |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2403.07866 |