  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, non-reciprocal 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 towards a stationary
profile $S(L)\sim L^{1/2}$ for $L$ sites. For $N\ge3$, the kinetic constraints
impose Hilbert space fragmentation, yielding subdiffusive growth towards
$S(L)\sim L^{0.57}$. 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 non-reciprocal hybrid circuit
architectures.
