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

• URL: http://arxiv.org/abs/2405.06021v1
• Date: Thu, 9 May 2024 18:00:05 GMT
• Title: Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits
• Authors: Kai Klocke, Joel E. Moore, Michael Buchhold,
• Abstract summary: We introduce a hybrid, non-reciprocal setup featuring a quantum circuit. The circuit is represented by a Majorana quantum chain controlled by a classical $N$-state Potts chain.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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