Bounded light cone and robust topological order out of equilibrium
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866917918009196544 |
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| author | Zeng, Yu Hamma, Alioscia Zhang, Yu-Ran Cao, Jun-Peng Fan, Heng Liu, Wu-Ming |
| author_facet | Zeng, Yu Hamma, Alioscia Zhang, Yu-Ran Cao, Jun-Peng Fan, Heng Liu, Wu-Ming |
| contents | The ground state degeneracy of topologically ordered gapped Hamiltonians is the bedrock for self-correcting quantum memories, which are unfortunately not stable away from equilibrium even at zero temperature. This plague precludes practical robust self-correction since stability at zero temperature is a prerequisite for finite-temperature robustness. In this work, we show that the emergence of a bounded light cone renders the unitary time evolution a quasi-adiabatic continuation that preserves topological order, with the initial ground space retaining its macroscopic distance at all times as a quantum code. We also show how bounded light cones can emerge through suitable perturbations in Kitaev's toric code and honeycomb model. Our results suggest that topological orders and self-correcting quantum memories can be dynamically robust at zero temperature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13839 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bounded light cone and robust topological order out of equilibrium Zeng, Yu Hamma, Alioscia Zhang, Yu-Ran Cao, Jun-Peng Fan, Heng Liu, Wu-Ming Quantum Physics The ground state degeneracy of topologically ordered gapped Hamiltonians is the bedrock for self-correcting quantum memories, which are unfortunately not stable away from equilibrium even at zero temperature. This plague precludes practical robust self-correction since stability at zero temperature is a prerequisite for finite-temperature robustness. In this work, we show that the emergence of a bounded light cone renders the unitary time evolution a quasi-adiabatic continuation that preserves topological order, with the initial ground space retaining its macroscopic distance at all times as a quantum code. We also show how bounded light cones can emerge through suitable perturbations in Kitaev's toric code and honeycomb model. Our results suggest that topological orders and self-correcting quantum memories can be dynamically robust at zero temperature. |
| title | Bounded light cone and robust topological order out of equilibrium |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2208.13839 |