Exotic equilibration dynamics on a 1-D quantum CNOT gate lattice

Understand

We consider the dynamics of local entropy and nearest neighbor mutual information of a 1-D lattice of qubits via the repeated application of nearest neighbor CNOT quantum gates.

• This is a quantum version of a cellular automaton.
• We analyze the entropy dynamics for different initial product states, both for open boundary conditions, periodic boundary conditions and we also consider the infinite lattice thermodynamic limit.
• The dynamics gives rise to fractal behavior, where we see the appearance of the Sierpinski triangle both for states in the computational basis and for operator dynamics in the Heisenberg picture.