Error stabilized logical qubits in qudit generalizations of the monitored Kitaev model

• URL: http://arxiv.org/abs/2509.16758v1
• Date: Sat, 20 Sep 2025 17:48:10 GMT
• Title: Error stabilized logical qubits in qudit generalizations of the monitored Kitaev model
• Authors: Aayush Vijayvargia, Ezra Day-Roberts, Onur Erten,
• Abstract summary: We study the monitored dynamics of qudit generalizations of the Kitaev model on the honeycomb and square lattices.<n>Our results reveal a rich interplay between quantum spin liquids and monitored circuit dynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Monitored dynamics in quantum circuits provide tunable platforms for the realization of novel non-equilibrium phases. Motivated by recent advances in monitored Kitaev circuits, we investigate the monitored dynamics of the qudit ($d=4$) generalizations of the Kitaev model on the honeycomb and square lattices. In the absence of additional perturbations, the measurement-only dynamics of these models map onto multi-flavor loop models and display either critical or area-law entanglement scaling. Magnetic field terms couple different flavors and when measured with sufficiently large probability, they enhance the stability of the area-law phase that hosts the logical qubits. In a circuit picture, these terms correspond to single-qubit measurements and can be interpreted as errors. We also examine the impact of two-qubit measurements that commute with the plaquette operator, which induce effective non-quadratic interactions between Majorana fermions. These interactions can drive a transition to a volume-law-entangled phase and, for sufficiently strong coupling, stabilize a distinct area-law phase with an additional logical qubit for the square lattice model. Our results reveal a rich interplay between quantum spin liquids and monitored circuit dynamics, highlighting new mechanisms for engineering and controlling entanglement phases in multi-flavor Majorana systems.

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