Design and evaluation of clocked nanomagnetic logic conservative Fredkin gate

  • Ali Akbar Dadjouyan
  • Samira SayedsalehiEmail author
  • Reza Faghih Mirzaee
  • Somayyeh Jafarali Jassbi


Nanomagnetic logic (NML) has recently been proposed as an attractive and promising implementation of QCA and also as a possible alternative to the CMOS technology. With this emerging technology, it is possible to process and store binary information according to the magnetization state of nanomagnets. Similar to other nanotechnologies, NML circuits are also sensitive to fabrication variations and thermal fluctuations. Therefore, it is highly consequential to improve the testability of these circuits. Circuits based on conservative logic inherently enhance test performance. In this paper, the Fredkin gate, which is one of the most famous conservative reversible gates has been designed and simulated in NML by considering the physical properties of nanomagnets. It can be used to design other testable and ultra-low-power NML circuits as well. OOMMF physical simulation tool is used to simulate and validate the proposed gate at room temperature. The results indicate the correct functionality of the design.


Nanotechnology Field-coupled nanocomputing Nanomagnetic logic Conservative logic Reversible logic Fredkin gate NML clocking 



  1. 1.
    Cowburn, R., Welland, M.: Room temperature magnetic quantum cellular automata. Science 287(5457), 1466–1468 (2000)CrossRefGoogle Scholar
  2. 2.
    Csaba, G., Imre, A., Bernstein, G.H., Porod, W., Metlushko, V.: Nanocomputing by field-coupled nanomagnets. IEEE Trans. Nanotechnol. 99(4), 209–213 (2002)CrossRefGoogle Scholar
  3. 3.
    Csaba, G., Lugli, P., Csurgay, A., Porod, W.: Simulation of power gain and dissipation in field-coupled nanomagnets. J. Comput. Electron. 4(1–2), 105–110 (2005)CrossRefGoogle Scholar
  4. 4.
    Vacca, M., Graziano, M., Di Crescenzo, L., Chiolerio, A., Lamberti, A., Balma, D., Canavese, G., Celegato, F., Enrico, E., Tiberto, P.: Magnetoelastic clock system for nanomagnet logic. IEEE Trans. Nanotechnol. 13(5), 963–973 (2014)CrossRefGoogle Scholar
  5. 5.
    Stamps, R.L., Breitkreutz, S., Åkerman, J., Chumak, A.V., Otani, Y., Bauer, G.E., Thiele, J.-U., Bowen, M., Majetich, S.A., Kläui, M.: The 2014 magnetism roadmap. J. Phys. D Appl. Phys. 47(33), 333001 (2014)CrossRefGoogle Scholar
  6. 6.
    Siddiq, M.A., Niemier, M.T., Csaba, G., Orlov, A.O., Hu, X.S., Porod, W., Bernstein, G.H.: A nanomagnet logic field-coupled electrical input. IEEE Trans. Nanotechnol. 12(5), 734–742 (2013)CrossRefGoogle Scholar
  7. 7.
    Dingler, A., Kurtz, S., Niemier, M., Hu, X.S., Csaba, G., Nahas, J., Porod, W., Bernstein, G., Li, P., Sankar, V.K.: Making non-volatile nanomagnet logic non-volatile. In: DAC Design Automation Conference 2012. IEEE (2012)Google Scholar
  8. 8.
    Imre, A., Csaba, G., Ji, L., Orlov, A., Bernstein, G., Porod, W.: Majority logic gate for magnetic quantum-dot cellular automata. Science 311(5758), 205–208 (2006)CrossRefGoogle Scholar
  9. 9.
    Niemier, M., Crocker, M., Hu, X.S.: Fabrication variations and defect tolerance for nanomagnet-based QCA. In: IEEE International Symposium on Defect and Fault Tolerance of VLSI Systems, 2008. DFTVS’08. IEEE (2008)Google Scholar
  10. 10.
    Shah, F.A., Csaba, G., Niemier, M.T., Hu, X.S., Porod, W., Bernstein, G.H.: Error analysis for ultra dense nanomagnet logic circuits. J. Appl. Phys. 117(17), 17A906 (2015)CrossRefGoogle Scholar
  11. 11.
    Spedalieri, F.M., Jacob, A.P., Nikonov, D.E., Roychowdhury, V.P.: Performance of magnetic quantum cellular automata and limitations due to thermal noise. IEEE Trans. Nanotechnol. 10(3), 537–546 (2011)CrossRefGoogle Scholar
  12. 12.
    Vacca, M., Cairo, F., Turvani, G., Riente, F., Zamboni, M., Graziano, M.: Virtual clocking for nanomagnet logic. IEEE Trans. Nanotechnol. 15(6), 962–970 (2016)CrossRefGoogle Scholar
  13. 13.
    Fredkin, E., Toffoli, T.: Conservative logic. Int. J. Theor. Phys. 21(3–4), 219–253 (1982)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Swaminathan, G., Aylor, J., Johnson, B.: Concurrent testing of VLSI circuits using conservative logic. In: Proceedings, 1990 IEEE International Conference on Computer Design: VLSI in Computers and Processors, 1990. ICCD’90. IEEE (1990)Google Scholar
  15. 15.
    Laundauer, R.: Irreversibility and heat generation in the computational process. IBM J. Res. Dev. 5, 183–191 (1961)CrossRefGoogle Scholar
  16. 16.
    Bennett, C.H.: Logical reversibility of computation. IBM J. Res. Dev. 17(6), 525–532 (1973)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Patel, K.N., Hayes, J.P., Markov, I.L.: Fault testing for reversible circuits. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 23(8), 1220–1230 (2004)CrossRefGoogle Scholar
  18. 18.
    Thapliyal, H., Ranganathan, N.: Reversible logic-based concurrently testable latches for molecular QCA. IEEE Trans. Nanotechnol. 9(1), 62–69 (2009)CrossRefGoogle Scholar
  19. 19.
    Ma, X., Huang, J., Metra, C., Lombardi, F.: Reversible gates and testability of one dimensional arrays of molecular QCA. J. Electron. Test. 24(1–3), 297–311 (2008)CrossRefGoogle Scholar
  20. 20.
    Kianpour, M., Sabbaghi-Nadooshan, R.: Novel 8-bit reversible full adder/subtractor using a QCA reversible gate. J. Comput. Electron. 16(2), 459–472 (2017)CrossRefGoogle Scholar
  21. 21.
    Aharoni, A.: Introduction to the Theory of Ferromagnetism, vol. 109. Clarendon Press, Oxford (2000)Google Scholar
  22. 22.
    O’Handley, R.C.: Modern Magnetic Materials: Principles and Applications. Wiley, Hoboken (1999)Google Scholar
  23. 23.
    Csaba, G., Porod, W.: Simulation of field coupled computing architectures based on magnetic dot arrays. J. Comput. Electron. 1(1–2), 87–91 (2002)CrossRefGoogle Scholar
  24. 24.
    Varga, E., Niemier, M.T., Csaba, G., Bernstein, G.H., Porod, W.: Experimental realization of a nanomagnet full adder using slanted-edge magnets. IEEE Trans. Magn. 49(7), 4452–4455 (2013)CrossRefGoogle Scholar
  25. 25.
    Azghadi, M.R., Kavehie, O., Navi, K.: A novel design for quantum-dot cellular automata cells and full adders (2012). arXiv:1204.2048
  26. 26.
    Akeela, R., Wagh, M.D.: A five-input majority gate in quantum-dot cellular automata. In: NSTI Nanotech (2011)Google Scholar
  27. 27.
    Navi, K., Farazkish, R., Sayedsalehi, S., Azghadi, M.R.: A new quantum-dot cellular automata full-adder. Microelectron. J. 41(12), 820–826 (2010)CrossRefGoogle Scholar
  28. 28.
    Navi, K., Sayedsalehi, S., Farazkish, R., Azghadi, M.R.: Five-input majority gate, a new device for quantum-dot cellular automata. J. Comput. Theor. Nanosci. 7(8), 1546–1553 (2010)CrossRefGoogle Scholar
  29. 29.
    Roohi, A., Khademolhosseini, H., Sayedsalehi, S., Navi, K.: A symmetric quantum-dot cellular automata design for 5-input majority gate. J. Comput. Electron. 13(3), 701–708 (2014)CrossRefGoogle Scholar
  30. 30.
    Parish, M., Forshaw, M.: Physical constraints on magnetic quantum cellular automata. Appl. Phys. Lett. 83(10), 2046–2048 (2003)CrossRefGoogle Scholar
  31. 31.
    Niemier, M.T., Varga, E., Bernstein, G.H., Porod, W., Alam, M.T., Dingler, A., Orlov, A., Hu, X.S.: Shape engineering for controlled switching with nanomagnet logic. IEEE Trans. Nanotechnol. 11(2), 220–230 (2012)CrossRefGoogle Scholar
  32. 32.
    Kurtz, S., Varga, E., Siddiq, M., Niemier, M., Porod, W., Hu, X., Bernstein, G.: Non-majority magnetic logic gates: a review of experiments and future prospects for ‘shape-based’ logic. J. Phys.: Condens. Matter 23(5), 053202 (2011)Google Scholar
  33. 33.
    Graziano, M., Chiolerio, A., Zamboni, M.: A technology aware magnetic QCA NCL-HDL architecture. In: 9th IEEE Conference on Nanotechnology, 2009. IEEE-NANO 2009. IEEE (2009)Google Scholar
  34. 34.
    Graziano, M., Vacca, M., Chiolerio, A., Zamboni, M.: An NCL-HDL snake-clock-based magnetic QCA architecture. IEEE Trans. Nanotechnol. 10(5), 1141–1149 (2011)CrossRefGoogle Scholar
  35. 35.
    Csaba, G., Lugli, P., Becherer, M., Schmitt-Landsiedel, D., Porod, W.: Field-coupled computing in magnetic multilayers. J. Comput. Electron. 7(3), 454–457 (2008)CrossRefGoogle Scholar
  36. 36.
    Riente, F., Turvani, G., Vacca, M., Roch, M.R., Zamboni, M., Graziano, M.: Topolinano: a cad tool for nano magnetic logic. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 36(7), 1061–1074 (2017)CrossRefGoogle Scholar
  37. 37.
    Lamberti, A., Laurenti, M., Balma, D., Enrico, E., Celegato, F., Tiberto, P., Boarino, L., Zamboni, M.: Electric clock for nanomagnet logic circuits. Field-Coupled Nanocomput. Paradig. Progr. Perspect. 8280, 73 (2014)Google Scholar
  38. 38.
    Alam, M.T., Siddiq, M.J., Bernstein, G.H., Niemier, M., Porod, W., Hu, X.S.: On-chip clocking for nanomagnet logic devices. IEEE Trans. Nanotechnol. 9(3), 348–351 (2010)CrossRefGoogle Scholar
  39. 39.
    Turvani, G., Riente, F., Graziano, M., Zamboni, M.: A quantitative approach to testing in quantum dot cellular automata: Nanomagnet logic case. In: 2014 10th Conference on Ph.D. Research in Microelectronics and Electronics (PRIME). IEEE (2014)Google Scholar
  40. 40.
    Siddiq, M.A.J.: Clock Line and Field-Coupled Input for Nanomagnet Logic. University of Notre Dame, Notre Dame (2014)Google Scholar
  41. 41.
    Butler, K.C., Bernstein, G.H., Csaba, G., Porod, W., Hu, X.S., Niemier, M.: Contiguous clock lines for pipelined nanomagnet logic. J. Comput. Electron. 13(3), 763–768 (2014)CrossRefGoogle Scholar
  42. 42.
    Carlton, D.B., Emley, N.C., Tuchfeld, E., Bokor, J.: Simulation studies of nanomagnet-based logic architecture. Nano Lett. 8(12), 4173–4178 (2008)CrossRefGoogle Scholar
  43. 43.
    Niemier, M., Bernstein, G.H., Csaba, G., Dingler, A., Hu, X., Kurtz, S., Liu, S., Nahas, J., Porod, W., Siddiq, M.: Nanomagnet logic: progress toward system-level integration. J. Phys.: Condens. Matter 23(49), 493202 (2011)Google Scholar
  44. 44.
    Donahue, M.J.: OOMMF user’s guide, version 1.0 (1999)Google Scholar
  45. 45.
    Landau, L., Lifshitz, E.: On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. In: Pitaevski, L.P. (ed.) Perspectives in Theoretical Physics, pp. 51–65. Elsevier (1992)Google Scholar
  46. 46.
    Gilbert, T.L.: A phenomenological theory of damping in ferromagnetic materials. IEEE Trans. Magn. 40(6), 3443–3449 (2004)MathSciNetCrossRefGoogle Scholar
  47. 47.
    Lemcke, O.: Implementation of Temperature in Micromagnetic Simulations. Interdisciplinary Nanoscience Center Hamburg, University of Hamburg, Hamburg, Germany (2004). Accessed 2019

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Ali Akbar Dadjouyan
    • 1
  • Samira Sayedsalehi
    • 2
    Email author
  • Reza Faghih Mirzaee
    • 3
  • Somayyeh Jafarali Jassbi
    • 1
  1. 1.Department of Computer Engineering, Science and Research BranchIslamic Azad UniversityTehranIran
  2. 2.Department of Computer Engineering, South Tehran BranchIslamic Azad UniversityTehranIran
  3. 3.Department of Computer Engineering, Shahr-e-Qods BranchIslamic Azad UniversityTehranIran

Personalised recommendations