Abstract
Foundations of the theory of quantum Turing machines are investigated. The protocol for the preparation and the measurement of quantum Turing machines is discussed. The local transition functions are characterized for fully general quantum Turing machines. A new halting protocol is proposed without augmenting the halting qubit and is shown to work without spoiling the computation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. Church, Am. J. Math. 58, 345 (1936).
A. M. Turing, Proc. Lond. Math. Soc. Ser. 2 42, 230 (1936).
C. H. Papadimitriou, Computational Complexity (Addison-Wesley, Reading, MA, 1994).
R. P. Feynman, Inter. J. Theor. Phys. 21, 467 (1982).
D. Deutsch, Proc. R. Soc. Lond. A 400, 97 (1985).
D. Deutsch, Proc. R. Soc. Lond. A 425, 73 (1989).
P. Benioff, J. Stat. Phys. 22, 563 (1980).
E. Bernstein and U. Vazirani, SIAM J. Comput. 26, 1411 (1997).
A. Yao, in Proceedings of the 34th Annual Symposium on foundations of Computer Science, edited by S. Goldwasser, p. 352 (IEEE Computer Society Press, Los Alamitos, CA, 1993).
P. W. Shor, in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser, p. 124 (IEEE Computer Society Press, Los Alamitos, CA, 1994).
J. M. Myers, Phys. Rev. Lett. 78, 1823 (1997).
M. Ozawa, Phys. Rev. Lett. 80, 631 (1998).
H. Nishimura and M. Ozawa, “Computational complexity of uniform quantum circuit families and quantum Turing machines,” (in preparation).
N. Linden and S. Popescu, “The halting problem for quantum computers,” (e-print: quant-ph/9806054).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Kluwer Academic Publishers
About this chapter
Cite this chapter
Ozawa, M. (2002). Quantum Turing Machines: Local Transition, Preparation, Measurement, and Halting. In: Kumar, P., D’Ariano, G.M., Hirota, O. (eds) Quantum Communication, Computing, and Measurement 2. Springer, Boston, MA. https://doi.org/10.1007/0-306-47097-7_32
Download citation
DOI: https://doi.org/10.1007/0-306-47097-7_32
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-306-46307-5
Online ISBN: 978-0-306-47097-4
eBook Packages: Springer Book Archive