Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits

TL;DR

This paper introduces a non-reciprocal quantum circuit model controlled by a classical agent, revealing power-law entanglement growth and Hilbert space fragmentation, with distinct behaviors for different classical states.

Contribution

It presents a novel hybrid quantum-classical circuit model with kinetic constraints, leading to new entanglement dynamics and Hilbert space fragmentation phenomena.

Findings

For N=2, entanglement grows as L^{1/2}

For N≥3, entanglement grows as L^{0.57}

Classical control induces rich entanglement behaviors

Abstract

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.