Stable measurement-induced Floquet enriched topological order
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916128947699712 |
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| author | Vu, DinhDuy Lavasani, Ali Lee, Jong Yeon Fisher, Matthew P. A. |
| author_facet | Vu, DinhDuy Lavasani, Ali Lee, Jong Yeon Fisher, Matthew P. A. |
| contents | The Floquet code utilizes a periodic sequence of two-qubit measurements to realize the topological order. After each measurement round, the instantaneous stabilizer group can be mapped to a honeycomb toric code, explaining the topological feature. The code also possesses a time-crystal order - the $e-m$ transmutation after every cycle, breaking the Floquet symmetry of the measurement schedule. This behavior is distinct from the stationary topological order realized in either random circuits or time-independent Hamiltonian. Therefore, the resultant phase belongs to the overlap between the classes of Floquet enriched topological orders and measurement-induced phases. In this work, we construct a continuous path interpolating between the Floquet and toric codes, focusing on the transition between the time-crystal and stationary topological phases. We show that this transition is characterized by a divergent length scale. We also add single-qubit perturbations to the model and obtain a richer two-dimensional parametric phase diagram of the Floquet code, showing the stability of the Floquet enriched topological order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_01533 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stable measurement-induced Floquet enriched topological order Vu, DinhDuy Lavasani, Ali Lee, Jong Yeon Fisher, Matthew P. A. Quantum Physics Statistical Mechanics The Floquet code utilizes a periodic sequence of two-qubit measurements to realize the topological order. After each measurement round, the instantaneous stabilizer group can be mapped to a honeycomb toric code, explaining the topological feature. The code also possesses a time-crystal order - the $e-m$ transmutation after every cycle, breaking the Floquet symmetry of the measurement schedule. This behavior is distinct from the stationary topological order realized in either random circuits or time-independent Hamiltonian. Therefore, the resultant phase belongs to the overlap between the classes of Floquet enriched topological orders and measurement-induced phases. In this work, we construct a continuous path interpolating between the Floquet and toric codes, focusing on the transition between the time-crystal and stationary topological phases. We show that this transition is characterized by a divergent length scale. We also add single-qubit perturbations to the model and obtain a richer two-dimensional parametric phase diagram of the Floquet code, showing the stability of the Floquet enriched topological order. |
| title | Stable measurement-induced Floquet enriched topological order |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2303.01533 |