Local Transition Functions of Quantum Turing Machines

Masanao Ozawa; Harumichi Nishimura

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 34, Issue: 5, page 379-402
  • ISSN: 0988-3754

Abstract

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Foundations of the notion of quantum Turing machines are investigated. According to Deutsch's formulation, the time evolution of a quantum Turing machine is to be determined by the local transition 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.

How to cite

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Ozawa, Masanao, and Nishimura, Harumichi. "Local Transition Functions of Quantum Turing Machines." RAIRO - Theoretical Informatics and Applications 34.5 (2010): 379-402. <http://eudml.org/doc/222093>.

@article{Ozawa2010,
abstract = { Foundations of the notion of quantum Turing machines are investigated. According to Deutsch's formulation, the time evolution of a quantum Turing machine is to be determined by the local transition 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. },
author = {Ozawa, Masanao, Nishimura, Harumichi},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Quantum Turing machines; transition functions; multi-tape quantum Turing machines.; quantum Turing machines},
language = {eng},
month = {3},
number = {5},
pages = {379-402},
publisher = {EDP Sciences},
title = {Local Transition Functions of Quantum Turing Machines},
url = {http://eudml.org/doc/222093},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Ozawa, Masanao
AU - Nishimura, Harumichi
TI - Local Transition Functions of Quantum Turing Machines
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 5
SP - 379
EP - 402
AB - Foundations of the notion of quantum Turing machines are investigated. According to Deutsch's formulation, the time evolution of a quantum Turing machine is to be determined by the local transition 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.
LA - eng
KW - Quantum Turing machines; transition functions; multi-tape quantum Turing machines.; quantum Turing machines
UR - http://eudml.org/doc/222093
ER -

References

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  1. P. Benioff, 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.  
  2. E. Bernstein and U. Vazirani, Quantum complexity theory. SIAM J. Comput.26 (1997) 1411-1473.  Zbl0895.68042
  3. D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. Roy. Soc. London Ser. A400 (1985) 97-117.  Zbl0900.81019
  4. D. Deutsch, Quantum computational networks. Proc. Roy. Soc. London Ser. A425 (1989) 73-90.  
  5. R.P. Feynman, Simulating physics with computers. Internat. J. Theoret. Phys.21 (1982) 467-488.  
  6. J. Gruska, Quantum Computing. McGraw-Hill, London (1999).  
  7. M. Hirvensalo, On quantum computation. Ph.D. Thesis, Turku Center for Computer Science, Finland (1997).  Zbl1061.81009
  8. 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  
  9. C.H. Papadimitriou, Computational Complexity. Addison-Wesley, Reading, MA (1994).  
  10. 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.  
  11. 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.  

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