2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (2010)
Sept. 23, 2010 to Sept. 26, 2010
Reversibility is one of the most important characteristics of microscopic mechanisms in physics. It is our aim in this paper to describe some classes of linear cellular automata(LCAs) that can be studied in terms of an associated reversibleLCA. We prove that any given LCA having as local transition map a row contraction can be dilated to a LCA having a local rule with isometric components. We finally show that a LCAsuch that its global transition function is a partial isometry has a quantum LCA power dilation which is reversible.
linear cellular automaton, reversibility, quantum computing, unitary operator, contraction, dilation, extension
A. Popovici and D. Popovici, "Dilatability to Quantum Linear Cellular Automata," 2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing(SYNASC), Timisoara, Romania, 2010, pp. 355-361.