Nonequilibrium phases and quantum correlations in synthetic transport models

Abstract

Quantum devices featuring mid-circuit measurement and reset capabilities, such as quantum computers and dual-species Rydberg quantum simulators, enable the realization of quantum cellular automata. These systems evolve in discrete time following local updates implemented by unitary gates, and allow for the realization of both closed and synthetic dissipative dynamics. Here, we focus on quantum cellular automata that implement minimal models of classical and quantum transport. To illustrate our ideas, we focus on a discrete-time totally asymmetric simple exclusion process and investigate how coherent dynamical contributions allow for the emergence of quantum effects and correlations. We find that bipartite entanglement dominates the transient evolution, while stationary states can retain quantum correlations beyond entanglement. Our results suggest viable routes for realizing transport models on quantum devices and characterizing collective quantum correlations in strongly driven systems.

The paper asks how coherent hopping changes the phases and quantum correlations of a boundary-driven, discrete-time totally asymmetric simple exclusion process (TASEP). It constructs an ancilla-assisted quantum cellular automaton: nearest-neighbor unitary hopping is followed by stochastic rightward hopping implemented through ancilla interaction and reset, with particle injection and removal at the boundaries. The construction targets devices with mid-circuit measurement and reset; no experimental implementation is reported. Adaptive-bond-dimension TEBD simulations examine nonequilibrium steady states for chains up to $N=30$, primarily at stochastic hopping probability $\tau=0.75$ and coherent hopping angle $\omega=\pi/4$. Finite-size density curves and their derivatives support the persistence of low-density, high-density and maximum-current phases, with a discontinuous low–high-density transition and continuous transitions into the maximum-current phase. Coherent hopping reduces the maximum-current region. An increased local forward-transition probability, $\tau+(1-\tau)\sin^2\omega$, provides a qualitative interpretation. Half-chain negativity calculations up to $N=14$ show transient entanglement that eventually vanishes; its lifetime increases with size in the low- and high-density phases. Steady-state two-site reductions are separable but retain nonzero local quantum uncertainty and computational-basis coherence, whose parameter dependence tracks the phase structure. Partial-transpose moment tests at $N=30$ also detect no entanglement, although failure of this witness does not establish separability. The conclusions remain finite-size numerical observations: whether entanglement persists when the thermodynamic limit precedes the long-time limit is unresolved, and the main analysis concentrates on one coherent hopping strength.