Stable measurement-induced Floquet enriched topological order

• URL: http://arxiv.org/abs/2303.01533v2
• Date: Sat, 17 Feb 2024 18:03:21 GMT
• Title: Stable measurement-induced Floquet enriched topological order
• Authors: DinhDuy Vu, Ali Lavasani, Jong Yeon Lee, Matthew P. A. Fisher
• Abstract summary: Floquet code utilizes a periodic sequence of two-qubit measurements to realize the topological order. The code also possesses a time-crystal order - the $e-m$ transmutation after every cycle. We show that this transition is characterized by a divergent length scale.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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