Stable measurement-induced Floquet enriched topological order

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.

arXiv comment6+8 pages, 13 figures

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• Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements
• Structured volume-law entanglement in an interacting, monitored Majorana spin liquid
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Competing automorphisms and disordered Floquet codes
• Noisy Monitored Quantum Circuits
• Phases of Floquet code under local decoherence
• Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics