Tuning entanglement phases and topological memory in the measurement-only Kitaev model with single and multi-qubit checks

Abstract: Quantum circuits provide an emerging controllable platform to realize novel dynamical non-equilibrium phases including topologically ordered states. The Kitaev model has become a cornerstone of quantum magnetism due to its quantum spin liquid ground state and rich phase diagram. The Kitaev model has also been treated in the monitored circuit setting, giving rise to topological area-law and critical-law entanglement entropy phases. In this article, we study the evolution of its phase diagram under the addition of new terms, motivated by their effects in the Kitaev model. We find that a single-qubit term, analogous to a magnetic field, leads to a trivial state in the high field limit, but with an additional intermediate volume-law phase. A three-qubit operator that commutes with the flux operators has the opposite effect: it stabilizes the critical-law phase against the short ranged area-law entanglement. We also employ a four-qubit plaquette commuting operator that simultaneously measures two opposite identical-type bonds on a plaquette. This generates a distinct volume-law phase and preserves the plaquette fluxes and associated topological order, yielding extensive entanglement while coexisting with the topological memory characteristic of the area-law phase. We quantitatively locate phase boundaries using stabilizer (Clifford) simulations together with tripartite mutual information and entanglement entropy measures. Our results highlight the rich phase diagram accessible from the measurement-only Kitaev model as well as suggesting rules relating the newly added operators to the phases they promote.