Structured volume-law entanglement in an interacting, monitored Majorana spin liquid

Abstract

Monitored quantum circuits allow for unprecedented dynamical control of many-body entanglement. Here we show that random, measurement-only circuits, implementing the competition of bond and plaquette couplings of the Kitaev honeycomb model, give rise to a structured volume-law entangled phase with subleading $L\ln L$ liquid scaling behavior. This interacting Majorana liquid takes up a highly-symmetric, spherical parameter space within the entanglement phase diagram obtained when varying the relative coupling probabilities. The sphere itself is a critical boundary with quantum Lifshitz scaling separating the volume-law phase from proximate area-law phases, a color code or a toric code. An exception is a set of tricritical, self-dual points exhibiting effective (1+1)d conformal scaling at which the volume-law phase and both area-law phases meet. From a quantum information perspective, our results define error thresholds for the color code in the presence of projective error and stochastic syndrome measurements. We show that an alternative realization of our model circuit can be implemented using unitary gates plus ancillary single-qubit measurements only.

arXiv comment4.5 + 3 pages; 4 + 8 figures

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• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Exact, Average, and Broken Symmetries in a Simple Adaptive Monitored Circuit
• Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout