Quantum Computing: 1-Way Quantum Automata
Languages generated with isolated cut-point by a class of bounded rational formal series are regular.
If a class of formal series is closed under f-complement, Hadamard product and convex linear combination, then the class of languages generated with isolated cut-point is closed under boolean operations.
We introduce a general model of 1-way quantum automata and we compare their behaviors with those of measure-once, measure-many and reversible 1-way quantum automata.
Keywordsformal power series quantum finite automata
Unable to display preview. Download preview PDF.
- 1.A. Ambainis and R. Freivalds. 1-way quantum finite automata: strengths, weaknesses and generalizations. In Proc. 39th Symposium on Foundations of Computer. Science, pp. 332–342, 1998.Google Scholar
- 2.A. Ambainis, A. Kikusts, and M. Valdats. On the class of languages recognizable by 1-way quantum finite automata. In Proc. 18th Annual Symposium on Theoretical. Aspects of Computer Science, LNCS 2010, Springer, pp. 305–316, 2001. Also as Technical Report quant-ph/0001005.Google Scholar
- 3.L. Baldi and G. Cerofolini. La Legge di Moore e lo sviluppo dei circuiti integrati. Mondo Digitale, 3:3–15, 2002 (in Italian).Google Scholar
- 5.J. Berstel and C. Reutenauer. Rational series and their languages. EATCS Monographs on Theoretical Computer Science, vol. 12, Springer-Verlag, 1988.Google Scholar
- 8.A. Brodsky and N. Pippenger. Characterizations of 1-way quantum finite automata. Technical Report TR-99-03, Department of Computer Science, University of British Columbia, 2000.Google Scholar
- 12.M. Golovkins and M. Kravtsev. Probabilistic Reversible Automata and Quantum Automata. In Proc. 8th International Computing and Combinatorics Conference, LNCS 2387, Springer, pp. 574–583, 2002Google Scholar
- 13.L. Grover. A fast quantum mechanical algorithm for database search. In Proc. 28th ACM Symposium on Theory of Computing, pp. 212–219, 1996.Google Scholar
- 14.J. Gruska. Quantum Computing. McGraw-Hill, 1999.Google Scholar
- 17.A. Kondacs and J. Watrous. On the power of quantum finite state automata. In 38th Symposium on Foundations of Computer Science, pp. 66–75, 1997.Google Scholar
- 18.M. Marcus and H. Minc. Introduction to Linear Algebra. The Macmillan Company, 1965. Reprinted by Dover, 1988.Google Scholar
- 19.M. Marcus and H. Minc. A Survey of Matrix Theory and Matrix Inequalities. Prindle, Weber & Schmidt, 1964. Reprinted by Dover, 1992.Google Scholar
- 20.G.E. Moore. Progress in Digital Integrated Electronics. In Digest of the 1975. International Electron Devices Meeting, IEEE, pp. 11–13, 1975.Google Scholar
- 22.A. Nayak. Optimal lower bounds for quantum automata and random access codes. In Proc. 40th Symposium on Foundations of Computer Science. pp. 369–376, 1999.Google Scholar
- 23.A. Paz. Introduction to Probabilistic Automata. Academic Press, 1971.Google Scholar
- 24.J.E. Pin. On languages accepted by finite reversible automata. In Proc. 14th. International Colloquium on Automata, Languages and Programming, LNCS 267, pp. 237–249. Springer-Verlag, 1987.Google Scholar
- 26.P. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing, 26:1484–1509, 1997. A preliminary version appeared in Proc. 35th IEEE Symp. on Foundations. of Computer Science, pp. 20–22, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
- 28.A. Salomaa and M. Soittola. Automata-theoretic aspects of formal power series. Texts and Monographs in Computer Science, Springer-Verlag, 1978.Google Scholar