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The authors study the quantum dynamics of a (2+1) D monitored random circuit involving local projective measurements, inspired by the physics of the Kitaev quantum spin liquid. A Majorana parton description of the dynamics reveals a close connection between the entanglement dynamics of quantum trajectories and the 3D classical fully packed loop model. The authors uncover a critical phase where quantum trajectories exhibit long-range entanglement with a logarithmic (L log L) violation of the area law, and a topologically ordered phase reminiscent of the toric code phase.
Lavasani et al. (Fri,) studied this question.