An algebraic study of unitary one dimensional quantum cellular automata

Abstract

We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do not change the quantum cellular automata's computational power. The configurations we consider have finite but unbounded size.

18 pages, llncs. V1: full version. V2: essential results only, close to published version, with proofs.

References in corpus (4)

• On the absence of homogeneous scalar unitary cellular automata
• Reversible quantum cellular automata
• On Quantum Operations as Quantum States
• Unitarity in one dimensional nonlinear quantum cellular automata