Entanglement in the Quantum Game of Life

TL;DR

This paper explores the quantum dynamics of a spin chain modeled after Conway's game of life, revealing complex entanglement patterns and quantum behaviors distinct from classical patterns.

Contribution

It introduces a quantum analog of the game of life, analyzing entanglement evolution and identifying unique quantum phenomena not present in classical versions.

Findings

Chains can become fully entangled or exhibit oscillating entanglement structures

Quantum patterns differ significantly from classical ones in local observable dynamics

Discovery of a quantum blinker-like structure with no classical equivalent

Abstract

We investigate the quantum dynamics of a spin chain that implements a quantum analog of Conway's game of life. We solve the time-dependent Schr\"odinger equation starting with initial separable states and analyse the evolution of quantum correlations across the lattice. We report examples of evolutions leading to all-entangled chains and/or to time oscillating entangling structures and characterize them by means of entanglement and network measures. The quantum patterns result to be quite different from the classical ones, even in the dynamics of local observables. A peculiar instance is a structure behaving as the quantum analog of a blinker, but that has no classical counterpart.