Abstract
In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in an observation as the squared magnitude of its amplitude. We give an efficient algorithm which decides if a linear quantum cellular automaton is well-formed. The complexity of the algorithm is O(n 2) if the input automaton has continuous neighborhood.
This research was supported by the ESPRIT Working Group 7097 RAND.
The French-Hungarian Research Program “Balaton” n∘94026 of the Ministère des Affaires Etrangères.
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References
S. Amoroso and Y. Patt, Decision Procedures for Surjectivity and Injectivity of Parallel Maps for Tessellation Structures, Journal of Computer and System Sciences 6, 448–464, 1972.
A. Berthiaume and G. Brassard, The Quantum Challenge to Structural Complexity Theory, Proceeding of the 7th IEEE Conference on Structure in Complexity Theory, 132–137, 1992.
R. Bellman, On a routing problem, Quarterly of Applied Mathematics, 16(1):87–90, 1958.
M. Biafore, Can Computers Have Simple Hamiltonians? MIT Physics of Computation Seminar ftp://im.lcs.mit.edu/poc/biafore, 1994.
E. Bernstein and U. Vazirani, Quantum complexity theory, Proceeding of the 25th ACM Symposium on the Theory of Computing, 11–20, 1993.
T. Cormen, C. Leiserson and R. Rivest, Introduction to Algorithms, The MIT Press, 1990.
D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer, Proceeding of the Royal Society of London, A400:97–117, 1985.
D. Deutsch and R. Jozsa, Rapid solution of problems by quantum computation, Proceeding of the Royal Society of London, A439:553–558, 1992.
R. Feynman, Simulating physics with computers, International Journal of Theoretical Physics 21 467–488, 1982.
R. Feynman, Quantum Mechanical Computers, Foundations of Physics 16, 507, 1986.
L. Ford and D. Fulkerson, Flows in Networks, Princeton University Press, 1962.
R. Jozsa, Characterizing classes of functions computable by quantum parallelism, Proceeding of the Royal Society of London, A435:563–574, 1991.
S. Lloyd, A potentially realizable Quantum Computer, Science 261, 1569–1571, 1993.
S. Lloyd, Envisioning a Quantum Supercomputer, Science 263, 695, 1994.
N. Margolus, Parallel Quantum Computation, MIT Physics of Computation Seminar ftp://im.lcs.mit.edu/poc/margyolus, 1994.
D. Simon, On the Power of Quantum Computation, Proceeding of the 34th IEEE Symposium on Foundations of Computer Science, 116–123, 1994.
P. Shor, Algorithms for Quantum Computation: Discrete Log and Factoring Proceeding of the 26th ACM Symposium on the Theory of Computing, 124–134, 1994
K. Sutner, De Bruijn graphs and cellular automata, Complex Systems, 5:19–30, 1991.
R. Tarjan, Depth first search and linear graph algorithms, SIAM Journal on Computing, 1(2):146–160, 1972.
J. Watrous, On one dimensional quantum cellular automata, Proceeding of the 36th IEEE Symposium on Foundations of Computer Science, 528–537, 1995.
A. Yao, Quantum circuit complexity, Proceeding of the 34th IEEE Symposium on Foundations of Computer Science, 352–361, 1993.
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© 1996 Springer-Verlag Berlin Heidelberg
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Dürr, C., Lê Thanh, H., Santha, M. (1996). A decision procedure for well-formed linear quantum cellular automata. In: Puech, C., Reischuk, R. (eds) STACS 96. STACS 1996. Lecture Notes in Computer Science, vol 1046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60922-9_24
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DOI: https://doi.org/10.1007/3-540-60922-9_24
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