How Does Adiabatic Quantum Computation Fit into Quantum Automata Theory?

  • Tomoyuki YamakamiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11612)


Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the efficiency in solving the integer factoring and searching a database faster than any currently known classical computer algorithm. Adiabatic evolution of quantum systems have been studied as a potential means that physically realizes such quantum computation. Up to now, all the research on adiabatic quantum systems has dealt with polynomial time-bounded computation and little attention has been paid to, for example, adiabatic quantum systems consuming only constant memory space. Such quantum systems can be modeled in a form similar to quantum finite automata. This exposition dares to ask a bold question of how to make adiabatic quantum computation fit into the rapidly progressing framework of quantum automata theory. As our answer to this eminent but profound question, we first lay out a basic framework of adiabatic evolutionary quantum systems (AEQSs) with limited computational resources and then establish their close connection to quantum finite automata. We also explore fundamental structural properties of languages solved quickly by such adiabatic evolutionary quantum systems.


Adiabatic quantum computation Quantum finite automata Hamiltonian Schrödinger equation 


  1. 1.
    Aharonov, D., van Dam, W., Kemp, J., Landau, Z., Lloyd, S., Regev, O.: Adiabatic quantum computation is equivalent to standard quantum computation. SIAM J. Comput. 37(1), 166–194 (2007). Scholar
  2. 2.
    Ambainis, A., Beaudry, M., Golovkins, M., Çikusts, A., Mercer, M., Thérien, D.: Algebraic results on quantum automata. Theory Comput. Syst. 39, 165–188 (2006). Scholar
  3. 3.
    Ambainis, A., Yakaryilmaz, A.S.: Automata and quantum computing. CoRR abs/1507.01988 (2015).
  4. 4.
    Dam van, W., Mosca, M., Vazirani, U.: How powerful is adiabatic quantum computation? In: Proceedings of 42nd Annual Symposium on Foundations of Computer Science, FOCS 2001, pp. 279–287. IEEE Computer Society (2001).
  5. 5.
    Farhi, E., Goldstone, J., Gutmann, S., Lapan, J., Lundgren, A., Preda, D.: A quantum evolution algorithm applied to random instances of an NP-complete problem. Science 292, 472–476 (2001). Scholar
  6. 6.
    Farhi, E., Goldstone, J., Gutmann, S., Sipser., M.: Quantum computation by adiabatic evolution. CoRR abs/quant-ph/0001106 (2000).
  7. 7.
    Freivalds, R., Ozols, M., Mančinska, L.: Improved constructions of mixed state quantum automata. Theor. Comput. Sci. 410, 1923–1931 (2009). Scholar
  8. 8.
    Gruska, J.: Quantum Computing. McGraw-Hill (2000)Google Scholar
  9. 9.
    Kato, T.: On the adiabatic theorem of quantum mechanics. J. Phys. Soc. Jap. 5, 435–439 (1951)CrossRefGoogle Scholar
  10. 10.
    Kitaev, A., Shen, A., Vyalyi, M.: Classical and Quantum Computation. AMS, Providence (2002)CrossRefGoogle Scholar
  11. 11.
    Messiah, A.: Quantum Mechanics. Wiley, New York (1958)zbMATHGoogle Scholar
  12. 12.
    Moore, C., Crutchfield, J.P.: Quantum automata and quantum grammars. Theor. Comp. Sci. 237(1–2), 275–306 (2000). Scholar
  13. 13.
    Nakanishi, M.: Quantum pushdown automata with garbage tape. Int. J. Found. Comput. Sci. 29(3), 425–446 (2018). Scholar
  14. 14.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press (2000)Google Scholar
  15. 15.
    Yakaryilmaz, A., Say, A.C.C.: Unbounded-error quantum computation with small space bounds. Inf. Comput. 209(6), 873–892 (2011). Scholar
  16. 16.
    Yamakami, T.: Nonuniform families of polynomial-size quantum finite automata and quantum logarithmic-space computation with polynomial-size advice. In: Martín-Vide, C., Okhotin, A., Shapira, D. (eds.) LATA 2019. LNCS, vol. 11417, pp. 134–145. Springer, Cham (2019). Scholar

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© IFIP International Federation for Information Processing 2019

Authors and Affiliations

  1. 1.Faculty of EngineeringUniversity of FukuiFukuiJapan

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