[Paper Review] Entanglement dynamics and ergodicity breaking in a quantum cellular automaton

Kevissen Sellapillay, Alberto Verga+1 more|arXiv (Cornell University)|Jul 12, 2022

Quantum many-body systemsPhysics and Astronomy76 references11 citations

TL;DR

This paper investigates a quantum cellular automaton based on the PXP rule, demonstrating that ergodicity breaking extends beyond scar states to chaotic regions of the Hilbert space. Using chiral quasiparticles that propagate entanglement, the authors show nonlocal entanglement in nonthermal chaotic states, indicating potential utility for quantum computation despite the system's nonintegrable dynamics.

ABSTRACT

Ergodicity breaking is observed in the blockade regime of Rydberg atoms arrays, in the form of low entanglement eigenstates known as scars, which fail to thermalize. The signature of these states persists in periodically driven systems, where they coexist with an extensive number of chaotic states. Here we investigate a quantum cellular automaton based on the classical rule that updates a site if its two neighbors are in the lower state. We show that the breaking of ergodicity extends to chaotic states. The dynamical breaking of ergodicity is controlled by chiral quasiparticle excitations which propagate entanglement. Evidence of nonlocal entanglement is found, showing that these nonthermal chaotic states may be useful to quantum computation.

Motivation & Objective

• To investigate whether ergodicity breaking occurs not only in scar states but also within the chaotic sector of the Hilbert space.
• To explore the role of chiral quasiparticles in propagating entanglement and controlling dynamical ergodicity breaking.
• To determine whether nonthermal, chaotic states in the PXP automaton exhibit measurable nonlocal entanglement.
• To assess the potential of these nonergodic chaotic states as resources for quantum computation.

Proposed method

• The study employs a quantum cellular automaton based on the PXP rule, realized as a unitary evolution operator U(θ) using the Toffoli gate (rule 201) with a nonintegrable perturbation parameter θ.
• The dynamics are analyzed in the θ → π/2 limit, corresponding to the classical rule 201, which preserves the computational basis and supports domain wall excitations.
• Analytical and numerical methods are used to derive the dispersion relation of chiral quasiparticles and to compute entanglement entropy and inverse participation ratio (IPR) for initial states from the computational basis.
• The system's Hilbert space is constrained to forbid neighboring |1⟩qubits, reducing the dimension to Fibonacci number growth φ^N.
• Entanglement is quantified using von Neumann entropy and logarithmic negativity; state geometry is probed via IPR and level statistics.
• Numerical simulations track the evolution of initial computational basis states to assess ergodicity breaking across the Hilbert space.

Experimental results

Research questions

• RQ1 Does ergodicity breaking persist in chaotic states of a nonintegrable quantum cellular automaton?
• RQ2 Can chiral quasiparticles mediate nonlocal entanglement in a nonintegrable PXP automaton?
• RQ3 Do chaotic states with sub-Page-limit entanglement entropy and random matrix statistics exhibit nonergodic behavior?
• RQ4 Is there a partition of the Hilbert space into ergodic and nonergodic chaotic subspaces based on initial state structure?
• RQ5 Can nonthermal, long-range entangled chaotic states serve as useful resources for quantum computation?

Key findings

• Ergodicity breaking extends into the chaotic region of the Hilbert space, with nonthermal chaotic states exhibiting entanglement entropy below the Page limit.
• Chiral quasiparticles—domain walls and gliders—propagate entanglement at speeds ±2/3 and 1/3, respectively, and are responsible for dynamical entanglement spreading.
• Nonlocal entanglement is observed, indicating that chaotic states are not fully thermalized and may support long-range quantum correlations.
• Initial states with different quasiparticle content lead to distinct entanglement and IPR evolution, revealing a nonergodic partition of the Hilbert space.
• The vacuum orbit (|A⟩, |B⟩, |C⟩) supports a Z2 scar state with p = 0, confirming the existence of stable, nonthermal eigenstates.
• Numerical results show that even in the nonintegrable regime, chaotic states can retain memory of initial quasiparticle structure, suggesting robustness of nonergodicity.