Definition and evolution of quantum cellular automata with two qubits per cell

TL;DR

This paper defines and studies the evolution of quantum cellular automata with two qubits per cell, demonstrating their unitary evolution and periodic probability patterns through simulation.

Contribution

It introduces a new class of quantum cellular automata with two qubits per cell and analyzes their unitary evolution and periodic behavior.

Findings

Evolution is unitary for two-qubit cells

Probability distributions show periodic structures

One-qubit automata cannot have non-trivial unitary evolution

Abstract

Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical systems and processes. It is however known that except for the trivial case, unitary evolution of one-dimensional homogeneous quantum cellular automata with one qubit per cell is not possible. Quantum cellular automata that comprise two qubits per cell are defined and their evolution is studied using a quantum computer simulator. The evolution is unitary and its linearity manifests itself as a periodic structure in the probability distribution patterns.