A matrix representation method for decoders using majority gate characteristics in quantum-dot cellular automata

  • Feifei Deng
  • Guangjun Xie
  • Renjun Zhu
  • Yongqiang ZhangEmail author


Quantum-dot cellular automata (QCA) is a highly attractive alternative to CMOS for the future digital circuit design. Current methods for designing circuits in QCA, especially decoders, mainly refer to traditional CMOS circuit design methods, which do not make full use of the characteristics of QCA technology. For our purpose, the three-input majority gate in QCA is analyzed and a combinational logic gate that fully embodies the majority characteristics is then proposed. A matrix representation method for decoders using the logic gates is proposed, which combines matrix decomposition with majority characteristics. To verify the superiority of this method, a 2–4 and a 3–8 decoders are proposed and implemented in QCA. The proposed decoders have better physical properties in terms of area, latency, cell, gate count, power dissipation and cost function, compared with previous designs. In addition, a schematic diagram of a 4–16 decoder is also presented for demonstrating the scalability of this method. The experimental results show that this method is more suitable for the design of QCA decoders in contrast to previous methods, which can help to reduce the cost of QCA circuits.


Matrix decomposition Combinational logic gate Decoder Quantum-dot cellular automata 



This work is supported by the National Natural Science Foundation of China (No. 61271122).


  1. 1.
    Lent CS, Liu M, Lu Y (2006) Bennett clocking of quantum-dot cellular automata and the limits to binary logic scaling. Nanotechnology 17(16):4240–4251. CrossRefGoogle Scholar
  2. 2.
    Thapliyal H, Ranganathan N (2010) Reversible logic-based concurrently testable latches for molecular QCA. IEEE Trans Nanotechnol 9(1):62–69. CrossRefGoogle Scholar
  3. 3.
    International Technology Roadmap for Semiconductors (2011). Accessed 28 Oct 2011
  4. 4.
    Zhang Y, Xie G, Han J (2019) Serial concatenated convolutional code encoder in quantum-dot cellular automata. Nano Commun Netw. CrossRefGoogle Scholar
  5. 5.
    Santana-Bonilla A, Sandonas LM, Gutierrez R, Cuniberti G (2019) Exploring the write-in process in molecular quantum cellular automata: a combined modelingand first-principle approach. J Phys Condens Matter 31(40):9. CrossRefGoogle Scholar
  6. 6.
    Hariprasad A, Ijjada SR (2019) Quantum-dot cellular automata technology for high-speed high-data-rate networks. Circuits Syst Signal Process 38(11):5236–5252. CrossRefGoogle Scholar
  7. 7.
    Das K, De D, De M (2013) Realisation of semiconductor ternary quantum dot cellular automata. Micro Nano Lett 8(5):258–263. CrossRefGoogle Scholar
  8. 8.
    Perri S, Corsonello P, Cocorullo G (2014) Design of efficient binary comparators in quantum-dot cellular automata. IEEE Trans Nanotechnol 13(2):192–202. CrossRefGoogle Scholar
  9. 9.
    Debnath B, Das JC, De D (2018) Design of image steganographic architecture using quantum-dot cellular automata for secure nanocommunication networks. Nano Commun Netw 15:41–58. CrossRefGoogle Scholar
  10. 10.
    Amlani II, Orlov AO, Toth G, Bernstein GH, Lent CS, Snider GL (1999) Digital logic gate using quantum-dot cellular automata. Science 284(5412):289–291. CrossRefGoogle Scholar
  11. 11.
    Kianpour M, Sabbaghi-Nadooshan RA (2011) Novel modular decoder implementation in quantum-dot cellular automata (QCA). In: 2011 International Conference on Nanoscience, Technology and Societal Implications, pp 1–5.
  12. 12.
    Banerjee S, Bhattacharya J, Chatterjee R, Bagchi P, Mondal S, Bandyopadhyay R, Dutta R, Das P (2016) A novel design of 3 input 8 output decoder using quantum dot cellular automata. In: 2016 IEEE 7th Annual Information Technology, Electronics and Mobile Communication Conference (IEMCON), pp 1–6.
  13. 13.
    De D, Purkayastha T, Chattopadhyay T (2016) Design of QCA based programmable logic array using decoder. Microelectron J 55:92–107. CrossRefGoogle Scholar
  14. 14.
    Kumar M, Sasamal TN (2017) An optimal design of 2-to-4 decoder circuit in coplanar quantum-dot cellular automata. Energy Procedia 117:450–457CrossRefGoogle Scholar
  15. 15.
    Jeon J-C (2016) Low hardware complexity QCA decoding architecture using inverter chain. Int J Control Autom 9(4):347–358. CrossRefGoogle Scholar
  16. 16.
    Walus K, Dysart TJ, Jullien GA, Budiman RA (2004) QCADesigner: a rapid design and simulation tool for quantum-dot cellular automata. IEEE Trans Nanotechnol 3(1):26–31. CrossRefGoogle Scholar
  17. 17.
    Tougaw PD, Lent CS (1994) Logical devices implemented using quantum cellular automata. J Appl Phys 75(3):1818–1825. CrossRefGoogle Scholar
  18. 18.
    Lent CS, Isaksen B (2003) Clocked molecular quantum-dot cellular automata. IEEE Trans Electron Dev 50(9):1890–1896. CrossRefGoogle Scholar
  19. 19.
    Huang Y, Zhang S (2007) Complex matrix decomposition and quadratic programming. Math Oper Res 32(3):758–768. MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Lent CS, Tougaw PD (1997) A device architecture for computing with quantum dots. Proc IEEE 85(4):541–557. CrossRefGoogle Scholar
  21. 21.
    Csurgay AI, Porod W, Lent CS (2000) Signal processing with near-neighbor-coupled time-varying quantum-dot arrays. IEEE Trans Circuits Syst I Fundam Theory Appl 47(8):1212–1223. CrossRefGoogle Scholar
  22. 22.
    Srivastava S, Sarkar S, Bhanja S (2009) Estimation of upper bound of power dissipation in QCA circuits. IEEE Trans Nanotechnol 8(1):116–127. CrossRefGoogle Scholar
  23. 23.
    Srivastava S, Asthana A, Bhanja S, Sarkar S QCAPro—an error-power estimation tool for QCA circuit design. In: 2011 IEEE International Symposium of Circuits and Systems (ISCAS 2011), May 15, 2011–May 18, 2011, Rio de Janeiro, Brazil, 2011. Proceedings—IEEE International Symposium on Circuits and Systems. Institute of Electrical and Electronics Engineers Inc., pp 2377–2380.
  24. 24.
    Labrado C, Thapliyal H (2016) Design of adder and subtractor circuits in majority logic-based field-coupled QCA nanocomputing. Electron Lett 52(6):464–466. CrossRefGoogle Scholar

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

Authors and Affiliations

  • Feifei Deng
    • 1
  • Guangjun Xie
    • 1
  • Renjun Zhu
    • 1
  • Yongqiang Zhang
    • 1
    Email author
  1. 1.School of Electronic Science and Applied PhysicsHefei University of TechnologyHefeiChina

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