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From the perspective of quantum many-body physics, the Floquet code ofHastings and Haah can be thought of as a measurement-only version of the Kitaevhoneycomb model where a periodic sequence of two-qubit XX, YY, and ZZmeasurements dynamically stabilizes a toric code state with two logical qubits.However, the most striking feature of the Kitaev model is its intrinsicfractionalization of quantum spins into an emergent gauge field and itinerantMajorana fermions that form a Dirac liquid, which is absent in the Floquetcode. Here we demonstrate that by varying the measurement strength of thehoneycomb Floquet code one can observe features akin to the fractionalizationphysics of the Kitaev model at finite temperature. Introducing coherent errorsto weaken the measurements we observe three consecutive stages that revealqubit fractionalization (for weak measurements), the formation of a Majoranaliquid (for intermediate measurement strength), and Majorana pairing togetherwith gauge ordering (for strong measurements). Our analysis is based on amapping of the imperfect Floquet code to random Gaussian fermionic circuits(networks) that can be Monte Carlo sampled, exposing two crossover peaks. Withan eye on circuit implementations, our analysis demonstrates that the Floquetcode, in contrast to the toric code, does not immediately break down to atrivial state under weak measurements, but instead gives way to a long-rangeentangled Majorana liquid state.

Qubit fractionalization and emergent Majorana liquid in the honeycomb Floquet code induced by coherent errors and weak measurements