@article{ArrighiNesmeWerner2011, author = {Arrighi, Pablo and Nesme, Vincent and Werner, Reinhard F.}, title = {One-Dimensional quantum cellular automata}, series = {International journal of unconventional computing : non-classical computation and cellular automata}, volume = {7}, journal = {International journal of unconventional computing : non-classical computation and cellular automata}, number = {4}, publisher = {Old City Publishing Science}, address = {Philadelphia}, issn = {1548-7199}, pages = {223 -- 244}, year = {2011}, abstract = {We define and study quantum cellular automata (QCA). We show that they are reversible and that the neighborhood of the inverse is the opposite of the neighborhood. We also show that QCA always admit, modulo shifts, a two-layered block representation. Note that the same two-layered block representation result applies also over infinite configurations, as was previously shown for one-dimensional systems in the more elaborate formalism of operators algebras [18]. Here the proof is simpler and self-contained, moreover we discuss a counterexample QCA in higher dimensions.}, language = {en} }