Exact Results for Accepting Probabilities of Quantum Automata

One of the properties of Kondacs-Watrous model of quantum finite automata (QFA) is that the probability of the correct answer for a QFA cannot be amplified arbitrarily. In this paper, we determine the maximum probabilities achieved by QFAs for several languages. In particular, we show that any language that is not recognized by an RFA (reversible finite automaton) can be recognized by a QFA with probability at most 0.7726...

[1]  John Watrous,et al.  Space-Bounded Quantum Complexity , 1999, J. Comput. Syst. Sci..

[2]  Jozef Gruska,et al.  Descriptional Complexity Issues in Quantum Computing , 2000, J. Autom. Lang. Comb..

[3]  John G. Kemeny,et al.  Finite Markov chains , 1960 .

[4]  John Watrous,et al.  On the power of quantum finite state automata , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[5]  Arnolds Kikusts.  A small 1-way quantum finite automaton , 1998 .

[6]  M. Ben-Or,et al.  Limitations of Noisy Reversible Computation , 1996, quant-ph/9611028.

[7]  Massimo Pica Ciamarra.  Quantum Reversibility and a New Model of Quantum Automaton , 2001, FCT.

[8]  James P. Crutchfield,et al.  Quantum automata and quantum grammars , 2000, Theor. Comput. Sci..

[9]  John Watrous,et al.  Relationships between quantum and classical space-bounded complexity classes , 1998, Proceedings. Thirteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat. No.98CB36247).

[10]  Alex Brodsky,et al.  Characterizations of 1-Way Quantum Finite Automata , 2002, SIAM J. Comput..

[11]  Kathrin Paschen.  Quantum finite automata using ancilla qubits , 2000 .

[12]  Umesh V. Vazirani,et al.  Quantum complexity theory , 1993, STOC.

[13]  Ashwin Nayak,et al.  Optimal lower bounds for quantum automata and random access codes , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[14]  Andris Ambainis,et al.  1-way quantum finite automata: strengths, weaknesses and generalizations , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[15]  Andris Ambainis,et al.  On the Class of Languages Recognizable by 1-Way Quantum Finite Automata , 2001, STACS.

[16]  Andris Ambainis,et al.  Probabilities to Accept Languages by Quantum Finite Automata , 1999, COCOON.