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.
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Amoroso, S., Pratt, Y.N.: Decision procedures for surjectivity and injectivity of parallel maps for tesselations structures. J. Comp. Syst. Sci. 6, 448–464 (1972)
Arrighi, P.: Algebraic characterizations of unitary linear quantum cellular automata, arXiv:quant-ph/0512040
Boykett, T.: Efficient exhaustive enumeration of reversible one dimensional cellular automata. Theoretical Computer Science (2004)
Dürr, C., LêThanh, H., Santha, M.: A decision procedure for well formed quantum cellular automata. Random Structures and Algorithms 11, 381–394 (1997)
Dürr, C., Santha, M.: A decision procedure for unitary quantum linear cellular automata. SIAM J. of Computing 31(4), 1076–1089 (2002)
Feynman, R.P.: Quantum mechanical computers. Found. Phys. 16, 507–531 (1986)
Hoyer, P.: Note on linear quantum cellular automata (manuscript)
Ibarra, O.H., Jiang, T.: On the computing power of one-way cellular arrays. In: ICALP, pp. 550–562 (1987)
Landauer, R.: Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5(183) (1961)
Meyer, D.A.: Unitarity in one dimensional nonlinear quantum cellular automata, arXiv:quant-ph/9604011
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)
Pedersen, J.: Cellular automata as algebraic systems. Complex Systems 6, 237–250 (1992)
Schumacher, B., Werner, R.F.: Reversible quantum cellular automata, arXiv:quant-ph/0405174
Van Dam, W.: Quantum Cellular Automata, Master thesis, Department of Mathematics and Computer Science, University of Nijmegen, The Netherlands (1996)
Watrous, J.: On one dimensional quantum cellular automata. Complex Systems 5(1), 19–30 (1991)
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© 2006 Springer-Verlag Berlin Heidelberg
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Arrighi, P. (2006). Algebraic Characterizations of Unitary Linear Quantum Cellular Automata. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_11
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DOI: https://doi.org/10.1007/11821069_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37791-7
Online ISBN: 978-3-540-37793-1
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