Abstract
In this chapter we will consider a new approach to quantum computations. We shall discuss an algorithm introduced by Ohya and Volovich which can solve the NP-complete satisfiability (SAT) problem in polynomial time. The algorithm goes beyond the quantum Turing machine paradigm.
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
References
Accardi, L., Ohya, M.: Compound channels, transition expectations, and liftings. Appl. Math. Optim. 39, 33–59 (1999)
Accardi, L., Sabbadini, R.: On the Ohya–Masuda quantum SAT Algorithm. In: Antoniou, I., Calude, C.S., Dinneen, M. (eds.) Proceedings International Conference “Unconventional Models of Computations”. Springer, Berlin (2001)
Accardi, L., Lu, Y.G., Volovich, I.V.: Quantum Theory and Its Stochastic Limit. Springer, Berlin (2002)
Accardi, L., Fagnola, F.: Quantum interacting particle systems. In: Quantum Probability and White Noise Analysis, vol. 14. World Scientific, Singapore (2002)
Accardi, L., Ohya, M.: A stochastic limit approach to the SAT problem. Open Syst. Inf. Dyn. 11, 1–16 (2004)
Bennett, C.H., Bernstein, E., Brassard, G., Vazirani, U.: Strengths and weaknesses of quantum computing. SIAM J. Comput. 26, 1510–1523 (1997)
Bernstein, E., Vazirani, U.: Quantum complexity theory. In: Proc. of the 25th Annual ACM Symposium on Theory of Computing, pp. 11–22. ACM, New York (1993). SIAM J. Comput. 26, 1411 (1997)
Cleve, R.: An introduction to quantum complexity theory. In: Macchiavello, C., Palma, G.M., Zeilinger, A. (eds.) Collected Papers on Quantum Computation and Quantum Information Theory. World Scientific, Singapore (1999)
Czachor, M.: Notes on nonlinear quantum algorithm. Acta Phys. Slovaca 48, 157 (1998)
Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond., Ser. A 400, 96–117 (1985)
Fagnola, F., Rebolledo, R.: On the existence of stationary states for quantum dynamical semigroups. J. Math. Phys. 42(3), 1296–1308 (2001)
Garey, M., Johnson, D.: Computers and Intractability—A Guide to the Theory of NP-Completeness. Freeman, New York (1979)
Gu, J., Purdom, P.W., Franco, J., Wah, B.W.: Algorithms for the satisfiability (SAT) problem: a survey. DIMACS Ser. Discret. Math. Theor. Comput. Sci. 35, 19–151 (1996)
Iriyama, S., Ohya, M.: Rigorous estimation of the computational complexity for OMV SAT algorithm. Open Syst. Inf. Dyn. 15(2), 173–187 (2008)
Iriyama, S., Ohya, M.: Language classes defined by generalized quantum Turing machine. Open Syst. Inf. Dyn. 15(4), 383–396 (2008)
Ohya, M., Masuda, N.: NP problem in quantum algorithm. Open Syst. Inf. Dyn. 7(1), 33–39 (2000)
Ohya, M., Volovich, I.V.: Quantum computing, NP-complete problems and chaotic dynamics. In: Hida, T., Saito, K. (eds.) Quantum Information, pp. 161–171. World Scientific, Singapore (2000)
Ohya, M., Volovich, I.V.: Quantum computing and chaotic amplification. J. Opt. B 5(6), 639–642 (2003)
Ohya, M., Volovich, I.V.: New quantum algorithm for studying NP-complete problems. Rep. Math. Phys. 52(1), 25–33 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Ohya, M., Volovich, I. (2011). Quantum Algorithm III. In: Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems. Theoretical and Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0171-7_14
Download citation
DOI: https://doi.org/10.1007/978-94-007-0171-7_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0170-0
Online ISBN: 978-94-007-0171-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)