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 open 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.

Figures (7)

• Figure 1: Quantum cellular automaton from dual-species atom arrays. (a) Two-species atom array (sketched on the left) modeled of system qubits (left most in red) and ancillary qubits (right most in green). System and ancillary qubits interact through the repeated application of the local quantum gate $G$. After a full sweep throughout the lattice, the ancilla qubits are measured and reinitialized and the sweep is repeated. (b) The gate $G$ is composed of two unitary gates: $U$ encodes coherent interactions within the system, $D$ induces ancilla-mitigated dissipation in the system. SWAP operations are inserted to stress the nearest-neighbor range of the gate $U$ and to ensure the final qubit order is consistent with the initial qubit order. (c) The full QCA update, consisting of sweep and ancilla reinitialization, implements a dissipative dynamics that can be expressed as a global Kraus map ${\cal K}$ that propagates the quantum state through time $\rho_{t+1} = {\cal K} [\rho_t]$.
• Figure 2: Average lattice occupation in finite-size NESS. (a) Phase diagram for a system of $N=30$ lattice sites with coherent transport induced by the gate $U(\pi/4)$ and bulk hopping probability $\tau =0.75$. The dashed line indicates the classical coexistence line separating the LD and HD phases and the solid line indicates the position of the transition to the MC phase in the classical model ($\omega =0$). Colored markers indicate parameter values we further study in Fig. \ref{['fig:LQU_and_Neg']} and colored lines indicate parameter ranges for the order parameter scalings in panels (b)-(d). Panel (b) shows the finite-size scaling of the average lattice occupation across the coexistence line ($\beta = 0.3$) and panels (c) and (d) show the finite-size scaling of the derivative of the average lattice occupation across the LD-MC ($\beta = 0.7$) and the HD-MC transition ($\alpha = 0.7$) respectively. All panels depict lattice sizes $N = 6,8,10,12,14,16,18,20,22,26,30$ encoded by the opacity of the lines with larger $N$ being more opaque.
• Figure 3: Quantum correlations. (a)-(c) Time evolution of the half-system entanglement negativity for $N=6,8,10,12,14$ in the MC, HD and LD phase respectively (see markers in Fig. \ref{['fig:PDq']}(a)). Panels (d) and (e) show the maximum two-site LQU and coherence with respect to the central bulk qubit across the HD-LD transition ($\beta=0.3$). Panels (f) and (g) show the derivative of the same quantities across the LD-MC transitions ($\beta =0.7$). All figures from panels (d)-(g) are plotted for $N=6,8,10,12,14,16,18,20,22,26,30.$
• Figure 4: Phase diagram from quantum correlations. Panels (a) and (b) show the two-site the coherence and LQU respectively, as described in the text, for the NESS that produced Fig. \ref{['fig:PDq']}(a).
• Figure S1: Circuit Diagram for the sequential update rule. The figure shows a circuit diagram for the sequential TASEP update with matrix product ansatz $\rho =\langle W| M^{\otimes N}|V\rangle$.