Quantum Cloning by Cellular Automata
  We introduce a quantum cellular automaton that achieves approximate phase-covariant cloning of qubits. The automaton is optimized for 1-to-2N economical cloning. The use of the automaton for cloning allows us to exploit different foliations for improving the performance with given resources. 
G. M. D'Ariano, C. Macchiavello, M. Rossi
quant-ph