Classically Time-Controlled Quantum Automata

  • Alejandro Díaz-CaroEmail author
  • Marcos Villagra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11324)


In this paper we introduce classically time-controlled quantum automata or CTQA, which is a slight but reasonable modification of Moore-Crutchfield quantum finite automata that uses time-dependent evolution operators and a scheduler defining how long each operator will run. Surprisingly enough, time-dependent evolutions provide a significant change in the computational power of quantum automata with respect to a discrete quantum model. Furthermore, CTQA presents itself as a new model of computation that provides a different approach to a formal study of “classical control, quantum data” schemes in quantum computing.


Quantum computing Quantum finite automata Time-dependent unitary evolution Bounded error Cutpoint language 



The authors thank Abuzer Yakaryılmaz for comments and discussions on a preliminary version of this paper.


  1. 1.
    Ambainis, A., Freivalds, R.: 1-way quantum finite automata: Strengths, weaknesses and generalizations. In: Proceedings of the 39th Annual Symposium on Foundations of Computer Science (FOCS), pp. 332–341 (1998)Google Scholar
  2. 2.
    Ambainis, A., Watrous, J.: Two-way finite automata with quantum and classical states. Theor. Comput. Sci. 287(1), 299–311 (2002)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Brodsky, A., Pippenger, N.: Characterizations of 1-way quantum finite automata. SIAM J. Comput. 31(5), 1456–1478 (2002)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Díaz-Caro, A.: A lambda calculus for density matrices with classical and probabilistic controls. In: Chang, B.Y.E. (ed.) Programming Languages and Systems (APLAS 2017). Lecture Notes in Computer Science, vol. 10695, pp. 448–467. Springer, Cham (2017)CrossRefGoogle Scholar
  5. 5.
    Green, A.S., Lumsdaine, P.L., Ross, N.J., Selinger, P., Valiron, B.: Quipper: a scalable quantum programming language. In: ACM SIGPLAN Notices (PLDI 2013), vol. 48, no. 6, pp. 333–342 (2013)CrossRefGoogle Scholar
  6. 6.
    Knill, E.H.: Conventions for quantum pseudocode. Technical report LA-UR-96-2724, Los Alamos National Laboratory (1996)Google Scholar
  7. 7.
    Moore, C., Crutchfield, J.P.: Quantum automata and quantum grammars. Theor. Comput. Sci. 237(1–2), 275–306 (2000)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Nishimura, H., Yamakami, T.: An application of quantum finite automata to interactive proof systems. J. Comput. Syst. Sci. 75(4), 255–269 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Paykin, J., Rand, R., Zdancewic, S.: Qwire: a core language for quantum circuits. In: Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages, POPL 2017, pp. 846–858. ACM, New York (2017)Google Scholar
  10. 10.
    Say, A.C.C., Yakaryılmaz, A.: Quantum finite automata: a modern introduction. In: Calude, C.S., Freivalds, R., Kazuo, I. (eds.) Computing with New Resources. LNCS, vol. 8808, pp. 208–222. Springer, Cham (2014). Scholar
  11. 11.
    Say, A., Yakaryilmaz, A.: Magic coins are useful for small-space quantum machines. Quantum Inf. Comput. 17(11–12), 1027–1043 (2017)MathSciNetGoogle Scholar
  12. 12.
    Selinger, P.: Towards a quantum programming language. Math. Struct. Comput. Sci. 14(4), 527–586 (2004)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Selinger, P., Valiron, B.: A lambda calculus for quantum computation with classical control. Math. Struct. Comput. Sci. 16(3), 527–552 (2006)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Villagra, M., Yamakami, T.: Quantum and reversible verification of proofs using constant memory space. In: Dediu, A.-H., Lozano, M., Martín-Vide, C. (eds.) TPNC 2014. LNCS, vol. 8890, pp. 144–156. Springer, Cham (2014). Scholar
  15. 15.
    Villagra, M., Yamakami, T.: Quantum state complexity of formal languages. In: Shallit, J., Okhotin, A. (eds.) DCFS 2015. LNCS, vol. 9118, pp. 280–291. Springer, Cham (2015). Scholar
  16. 16.
    Yamakami, T.: One-way reversible and quantum finite automata with advice. Inf. Comput. 239, 122–148 (2014)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zheng, S., Qiu, D., Gruska, J.: Power of the interactive proof systems with verifiers modeled by semi-quantum two-way finite automata. Inf. Comput. 241, 197–214 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Departamento de Ciencia y TecnologíaUniversidad Nacional de QuilmesBernal, Buenos AiresArgentina
  2. 2.Instituto de Ciencias de la ComputaciónCONICET-Universidad de Buenos AiresBuenos AiresArgentina
  3. 3.Núcleo de Investigación y Desarrollo TecnológicoUniversidad Nacional de AsunciónAsunciónParaguay

Personalised recommendations