Fibonacci many-body scars in a decorated Rule-54 quantum cellular automaton

TL;DR

This paper introduces a method to construct exact quantum many-body scars using the intrinsic soliton structure of the Rule-54 quantum cellular automaton, revealing new insights into weak ergodicity breaking.

Contribution

It presents a novel qubit-level approach to engineer exact scars based on the automaton's soliton structure, expanding understanding of nonthermal eigenstates in quantum systems.

Findings

Exact scars grow with Fibonacci combinatorics.

Scar fraction remains exponentially small in Hilbert space.

Finite-size simulations show Page-like entanglement and rapid growth.

Abstract

Quantum many-body scars provide a controlled form of weak ergodicity breaking, in which structured nonthermal eigenstates coexist with a thermalizing many-body spectrum. We introduce a qubit-level route to exact scars based on the intrinsic soliton structure of the Rule-54 quantum cellular automaton. A hard-core dimer sector of Rule 54 supplies an exactly translatable protected skeleton, while local projector-controlled decorations are invisible on this skeleton and nontrivial outside it. The protected dynamics is therefore reducible to finite translation orbits, whose Fourier modes form exact Floquet eigenstates with sub-volume-law entanglement. The number of exact scars grows with Fibonacci combinatorics, whereas their fraction in the full qubit Hilbert space remains exponentially small. Finite-size simulations show Page-like eigenstate entanglement, rapid entanglement growth, fidelity decay, and circular unitary ensemble quasienergy statistics in the decorated complement. This construction demonstrates that exact many-body scars can be engineered from native finite-orbit structures of an interacting reversible automaton, and provides a direct starting point for digital quantum simulation of scarred cellular-automaton dynamics.