Power-Law Entanglement and Hilbert Space Fragmentation in Nonreciprocal Quantum Circuits

Quantum circuits utilizing measurement to evolve a quantum wave function offer a new and rich playground to engineer unconventional entanglement dynamics. Here, we introduce a hybrid, nonreciprocal setup featuring a quantum circuit, whose updates are conditioned on the state of a classical dynamical agent. In our example the circuit is represented by a Majorana quantum chain controlled by a classical N- state Potts chain undergoing pair flips. The local orientation of the classical spins controls whether randomly drawn local measurements on the quantum chain are allowed or not. This imposes a dynamical kinetic constraint on the entanglement growth, described by the transfer matrix of an N- colored loop model. It yields an equivalent description of the circuit by an SU ( N )-symmetric Temperley-Lieb Hamiltonian or by a kinetically constrained surface growth model for an N- component height field. For N = 2 , we find a diffusive growth of the half-chain entanglement toward a stationary profile S(L) ( L ) L 1 = 2 for L sites. For N >= 3 , the kinetic constraints impose Hilbert space fragmentation, yielding subdiffusive growth toward S(L) ( L ) L 0 . 57 . This showcases how the control by a classical dynamical agent can enrich the entanglement dynamics in quantum circuits, paving a route toward novel entanglement dynamics in nonreciprocal hybrid circuit architectures.