Entanglement in the quantum Game of Life

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 Schrodinger equation starting with initial separable states and analyze 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 in structures 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.

Automated summary

This study investigates the quantum dynamics of a spin chain that simulates Conway's Game of Life. By solving the time-dependent Schrodinger equation for separable initial states, the evolution of quantum correlations across the lattice is analyzed. Examples of evolutions resulting in entangled chains or oscillating entangling structures are reported and characterized using entanglement and network measures. The quantum patterns exhibit structures that differ significantly from classical ones, even in the dynamics of local observables. A notable example is a structure that behaves as a quantum analog of a blinker, but does not have a classical counterpart.