Quantum Walks on Quantum Cellular Automata Lattices: Towards a New Model for Quantum Computation

  • Ioannis G. KarafyllidisEmail author
  • Georgios Ch. Sirakoulis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11115)


Many physical problems cannot be easily formulated as quantum circuits, which are a successful universal model for quantum computation. Because of this, new models that are closer to the structure of physical systems must be developed. Discrete and continuous quantum walks have been proven to be a universal quantum computation model, but building quantum computing systems based on their structure is not straightforward. Although classical cellular automata are models of universal classical computation, this is not the case for their quantum counterpart, which is limited by the no-coning theorem and the no-go lemma. Here we combine quantum walks, which reproduce unitary evolution in space with quantum cellular automata, which reproduce unitary evolution in time, to form a new model of quantum computation. Our results show that such a model is possible.


Quantum cellular automata Quantum walks Quantum computing 


  1. 1.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  2. 2.
    Cybenco, G.: Reducing quantum computations to elementary unitary operations. Comput. Sci. Eng. 3, 27 (2001)CrossRefGoogle Scholar
  3. 3.
    Karafyllidis, I.G.: Quantum computer simulator based on the circuit model of quantum computation. IEEE Trans. Circuits Syst. I(52), 1590–1596 (2005)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Deutsch, D.: Quantum theory, the church-turing principle and the universal quantum computer. Proc. R. Soc. Lond. A. 400, 97–117 (1985)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997)CrossRefGoogle Scholar
  6. 6.
    Shor, P.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, pp. 124–134 (1994)Google Scholar
  7. 7.
    Aharonov, Y., Davidovich, L., Zagury, N.: Quantum random walks. Phys. Rev. A 48, 1687 (1993)CrossRefGoogle Scholar
  8. 8.
    Childs, A.M.: Universal computation by quantum walk. Phys. Rev. Lett. 102, 180501 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Lovett, N.B., Cooper, S., Everitt, M., Trevers, M., Kendon, V.: Universal quantum computation using the discrete-time quantum walk. Phys. Rev. Lett. 81, 042330 (2010)MathSciNetGoogle Scholar
  10. 10.
    Childs, A.M., Gosset, D., Webb, S.: Universal computation by multiparticle quantum walk. Science 339, 791–794 (2013)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Karafyllidis, I.G.: Definition and evolution of quantum cellular automata with two qubits per cell. Phys. Rev. A 70, 044301 (2004)CrossRefGoogle Scholar
  13. 13.
    Grössing, G., Zeilinger, A.: Quantum cellular automata. Complex Syst. 2, 197–208 (1988)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Meyer, D.: On the absence of homogeneous scalar unitary cellular automata. Phys. Lett. A 223, 337–340 (1996)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ioannis G. Karafyllidis
    • 1
    Email author
  • Georgios Ch. Sirakoulis
    • 1
  1. 1.Department of Electrical and Computer EngineeringDemocritus University of ThraceXanthiGreece

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