Power-law entanglement and Hilbert space fragmentation in non-reciprocal quantum circuits
arxiv(2024)
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)∼ L^1/2 for L sites. For N≥3, the kinetic constraints
impose Hilbert space fragmentation, yielding subdiffusive growth towards
S(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 non-reciprocal hybrid circuit
architectures.
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