Periodicity in quantum cellular automata

Abstract

Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures are based on 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 quantum bit (qubit) per cell is not possible because of the no-go lemma. In this paper, we define quantum cellular automata that comprise two qubits per cell and study their evolution using a quantum computer simulator. The evolution is unitary and its linearity manifests itself as a periodic structure in the probability distribution patterns. © 2012 Springer-Verlag Berlin Heidelberg.