0804.4447v1. 

[2] Johannes G¨ utschow, Sonja Uphoff, Reinhard F. Werner, and Zolt´ an Zimbor´ as. Time asymptotics and entangle- ment generation of Clifford quantum celluar automata. To appear in Journal of Mathematical Physics , January 2010, 0906.3195. 

[3] Benjamin Schumacher and Reinhard F. Werner. Re- versible quantum cellular automata. Preprint , May 2004, quant-ph/0405174v1. 

[4] D.J. Shepherd, Torsten Franz, and Reinhard F. Werner. A universally programmable quantum cellular automa- ton. Physical Review Letters , 97, 2006, quant- ph/0512058v3. 

[5] Robert Raussendorf. A quantum cellular automaton for universal quantum computation. Physical Review A , 72, 2005, quant-ph/0412048v1. 

[6] Robert Raussendorf and Hans J. Briegel. A one- way quantum computer. Physical Review Letters , 86(22):5188–5191, May 2001. 

[7] Robert Raussendorf. Quantum computation via translation-invariant operations on a chain of qubits. 

Physical Review A , 72, 2005, quant-ph/0505122v2. 

[8] J. Fitzsimons and J. Twamley. Globally controlled quantum wires for perfect qubit transport, mirroring, and computing. Phys. Rev. Lett. , 97(9):090502, 2006, arXiv:quant-ph/0601120v2. 

[9] Daniel Gottesman. Stabilizer Codes and Quantum Er- ror Correction . PhD thesis, California Institute of Technology, Pasadena, California, May 1997, quant- ph/9705052v1. 

[10] David Fattal, Toby S. Cubitt, Yoshihisa Yamamoto, Sergey Bravyi, and Isaac L. Chuang. Entanglement in the stabilizer formalism. preprint , July 2004, quant- ph/0406168v1. 

[11] M. Fekete. ¨ Uber die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizien- ten. Mathematische Zeitschrift , 17:228–249, 1923. 

[12] J. Fitzsimons, L. Xiao, S. C. Benjamin, and J. A. Jones. Quantum information processing with delocalized qubits under global control. Phys. Rev. Lett. , 99(3):030501, 2007, arXiv:quant-ph/0606188v1. 

