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Local Transition Functions of Quantum Turing Machines

Published online by Cambridge University Press:  15 April 2002

Masanao Ozawa  and
Harumichi Nishimura
Masanao Ozawa
Affiliation:
Graduate School of Human Informatics, School of Informatics and Sciences, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan; (mozawa@math.human.nagoya-u.ac.jp) CREST, Japan Science and Technology.
Harumichi Nishimura
Affiliation:
CREST, Japan Science and Technology. Graduate School of Human Informatics, School of Informatics and Sciences, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan; (anishi@info.human.nagoya-u.ac.jp)
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Abstract

Foundations of the notion of quantum Turing machines areinvestigated. According to Deutsch's formulation, the time evolution of a quantum Turing machine is to be determined by the localtransition function. In this paper, the local transition functions are characterized for fully general quantum Turing machines, including multi-tape quantum Turing machines, extending the results due to Bernstein and Vazirani.

Keywords

Quantum Turing machinestransition functionsmulti-tape quantum Turing machines.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 34 , Issue 5 , September 2000 , pp. 379 - 402
Copyright
© EDP Sciences, 2000

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References

Benioff, P., The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines. J. Statist. Phys. 22 (1980) 563-591. CrossRef
Bernstein, E. and Vazirani, U., Quantum complexity theory. SIAM J. Comput. 26 (1997) 1411-1473. CrossRef
Deutsch, D., Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. Roy. Soc. London Ser. A 400 (1985) 97-117. CrossRef
Deutsch, D., Quantum computational networks. Proc. Roy. Soc. London Ser. A 425 (1989) 73-90. CrossRef
Feynman, R.P., Simulating physics with computers. Internat. J. Theoret. Phys. 21 (1982) 467-488. CrossRef
J. Gruska, Quantum Computing. McGraw-Hill, London (1999).
M. Hirvensalo, On quantum computation. Ph.D. Thesis, Turku Center for Computer Science, Finland (1997).
H. Nishimura and M. Ozawa, Computational complexity of uniform quantum circuit families and quantum Turing machines. Theoret. Comput. Sci. (to appear). Available at the LANL quantum physics e-print archive at http://xxx.lanl.gov/archive/quant-ph/9906095
C.H. Papadimitriou, Computational Complexity. Addison-Wesley, Reading, MA (1994).
P.W. Shor, Algorithms for quantum computation: Discrete logarithms and factoring, in Proc. 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser. IEEE Computer Society Press, Los Alamitos, CA (1994) 124-134.
A. Yao, Quantum circuit complexity, in Proc. 34th Annual Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, CA (1993) 352-361.