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Designing a Turing-complete cellular automata system using quantum-dot cellular automata

Journal of Computational Electronics volume 19, pages 1337–1343 (2020)Cite this article

Abstract

The quantum-dot cellular automata (QCA) computing paradigm is used to implement Rule 110, a unique one-dimensional cellular automata (CA) that has been proven to be Turing complete. A Turing complete architecture is capable of universal computing, which means that it could be used to implement any arbitrary computation. The optimized design of a single Rule 110 cell is presented, first using Boolean algebra and then by the use of QCA cells. This is followed by simulations to verify the correct behavior of the device and a method for efficiently filling a two-dimensional region with a one-dimensional CA device.

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References

  1. Lent, C.S., Tougaw, P.D., Porod, W.: Bistable saturation in coupled quantum dots for quantum cellular automata. Appl. Phys. Lett. 62(7), 714–716 (1993)

    Article  Google Scholar 

  2. Lent, C.S., Tougaw, P.D., Porod, W.: Bistable saturation in coupled quantum-dot cells. J. Appl. Phys 74(5), 3558–3566 (1993)

    Article  Google Scholar 

  3. Perez-Martinez, F., Farrer, I., Anderson, D., Jones, G.A.C., Ritchie, D.A., Chorley, S.J., Smith, C.G.: Demonstration of a quantum cellular automata cell in a GaAs⁄AlGaAs heterostructure. Appl. Phys Lett. 91(3), 032102 (2007)

    Article  Google Scholar 

  4. Purkayastha, T., Deah, D., Das, K., Ghatak, S.: Towards quantum dot and device implementation with InP–GaAs–InP nanostructure. Nanomater. Energy 5(1), 20–27 (2016)

    Article  Google Scholar 

  5. Cao, L., Altomare, F., Guo, H., Feng, M., Chang, A.M.: Coulomb blockade correlations in a coupled single-electron device system. Solid State Commun. 296, 12–16 (2019)

    Article  Google Scholar 

  6. Lapinte, C., Makhoul, R., Hamon, P., Roisnel, T., Hamon, J.: A tetrairon dication featuring tetraethynylbenzene bridging ligand: a molecular prototype of quantum‐dot cellular automata. Chem. Eur. J (2020). https://doi.org/10.1002/chem.202000910

    Article  Google Scholar 

  7. Christie, J., Forrest, R., Corcelli, S., Wasio, N., Quardokus, R., Brown, R., Kandel, A., Lu, Y., Lent, C.S., Henderson, K.: Synthesis of a neutral mixed-valence diferrocenyl carborane for molecular quantum-dot cellular automata applications. Angew. Chem. 127, 15668–15671 (2015)

    Article  Google Scholar 

  8. Graziano, M., Wang, R., Roch, M., Ardesi, Y., Riente, F., Piccinini, G.: Characterisation of a bis-ferrocene molecular QCA wire on a non-ideal gold surface. Micro Nano Lett. 14, 22–27 (2019)

    Article  Google Scholar 

  9. Ardesi, Y., Pulimeno, A., Graziano, M., Riente, F., Piccinini, G.: Effectiveness of molecules for quantum cellular automata as computing devices. J. Low Power Electron. Appl. 8, 24–42 (2018)

    Article  Google Scholar 

  10. Blair, E.: Electric-field inputs for molecular quantum-dot cellular automata circuits. IEEE Trans. Nanotechnol. 18, 453–460 (2019)

    Article  Google Scholar 

  11. Haughan, K., Niemier, M.T., Porod, W., Csaba, G.: Cellular automata designs for out of plane nanomagnet logic. In: Proceedings of the 2014 International Workshop on Computational Electronics, pp. 1–4 (2014)

  12. Tougaw, P.D., Lent, C.S.: Logical devices implemented using quantum cellular automata. J. Appl. Phys. 75(3), 1818–1825 (1994)

    Article  Google Scholar 

  13. Lent, C.S., Tougaw, P.D.: A device architecture for computing with quantum dots. Proc. IEEE 85(4), 541–557 (1997)

    Article  Google Scholar 

  14. Lent, C.S., Tougaw, P.D., Porod, W., Bernstein, G.H.: Quantum cellular automata. Nanotechnology 4(1), 49–57 (1993)

    Article  Google Scholar 

  15. Wood, J.D., Tougaw, D.: Matrix multiplication using quantum-dot cellular automata to implement conventional microelectronics. IEEE Trans. Nanotechnol. 10(5), 1036–1042 (2010)

    Article  Google Scholar 

  16. Tougaw, D., Khatun, M.: A scalable signal distribution network for quantum-dot cellular automata. IEEE Trans. Nanotechnol. 12, 215–224 (2013)

    Article  Google Scholar 

  17. Schiff, J.L.: Cellular Automata: A Discrete View of the World. Wiley, New York (2011)

    Google Scholar 

  18. Hadeler, K.-P., Müller, J.: Cellular Automata: Analysis and Applications. Springer, Berlin (2017)

    Book  Google Scholar 

  19. Ilachinski, A.: Cellular Automata: A Discrete Universe. World Scientific Publishing, Singapore (2001)

    Book  Google Scholar 

  20. Jackson, J.D.: Classical Electrodynamics. Wiley, New York (1975)

    MATH  Google Scholar 

  21. Cook, M.: Universality in elementary cellular automata. Complex Syst. 15(1), 1–40 (2004)

    MathSciNet  MATH  Google Scholar 

  22. Wolfram, S.: A New Kind of Science. Wolfram Media, Oxfordshire (2002)

    MATH  Google Scholar 

  23. Baldwin, A.T., Will, J., Tougaw, D.: Using the full quantum basis set to simulate quantum-dot cellular automata devices. J. Comput. Electron. 18(4), 982–987 (2019)

    Article  Google Scholar 

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Acknowledgements

This work was supported by the Leitha and Willard Richardson Professorship of Engineering and the Richardson Summer Research Fellowship, both of which are provided through the Valparaiso University College of Engineering.

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  1. Valparaiso University, Valparaiso, USA

    Douglas Tougaw & Jeffrey D. Will

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  1. Douglas Tougaw
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  2. Jeffrey D. Will
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Correspondence to Douglas Tougaw.

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Tougaw, D., Will, J.D. Designing a Turing-complete cellular automata system using quantum-dot cellular automata. J Comput Electron 19, 1337–1343 (2020). https://doi.org/10.1007/s10825-020-01518-1

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  • DOI: https://doi.org/10.1007/s10825-020-01518-1

Keywords

  • Nanoelectronics
  • Quantum-dot cellular automata (QCA)
  • Turing complete
  • Rule 110
  • Cellular automata