Quantum entangled breathers in Goldilocks quantum cellular automata*

We conducted robustness studies of quantum entangled breathers (QEBs) to evaluate their stability. QEBs are an emergent dynamical structure appearing in a continuous time generalization of Goldilocks quantum cellular automata. This system is a qubit spin chain on which sites evolve according to a local unitary operator if and only if 2 or 3 sites in a 5 site neighborhood are spin-up. The QEB is a quantum entangled generalization of a discrete breather or excited bright soliton on a lattice, a famous and robust classical solution to nonlinear wave equations. We consider four sources of noise: uniform and non-uniform spatial noise in the state; uniform spectral noise in the state; perturbations to the closed system Hamiltonian; and open quantum system evolution including T₁ and T₂ decoherence processes. We find that QEBs present a robust signal of quantum complexity in a simple system that can be studied on a wide variety of quantum simulators.