RESEARCH PAPER New efficient five-input majority gate for quantum-dot cellular automata Razieh Farazkish • Keivan Navi Received: 22 December 2011 / Accepted: 15 October 2012 / Published online: 30 October 2012 Ó Springer Science+Business Media Dordrecht 2012 Abstract A novel fault-tolerant five-input majority gate for quantum-dot cellular automata is presented. Quantum-dot cellular automata (QCA) is an emerging technology which is considered to be presented in future computers. Two principle logic elements in QCA are ‘‘majority gate’’ and ‘‘inverter.’’ In this paper, we propose a new approach to the design of fault-tolerant five-input majority gate by considering two-dimensional arrays of QCA cells. We analyze fault tolerance properties of such block five-input majority gate in terms of misalignment, missing, and dislocation cells. Some physical proofs are used for verifying five-input majority gate circuit layout and functionality. Our results clearly demonstrate that the redundant version of the block five-input majority gate is more robust than the standard style for this gate. Keywords Quantum-dot cellular automata  Majority gate  Fault-tolerant logic gates  Nanoelectronic circuits Introduction Current CMOS technology is going to approach a scaling limit in deep nanometer technologies (Navi et al. 2010a). The CMOS technology in nano-scales has some problems because of increase in amounts of variation in every aspect of a nanometer design. Quantum-dot cellular automata (QCA) is one of the promising new technologies that not only gives a solution at nano-scale, but also offers a new method of computation and information transformation (Orlov et al. 1997; Tougaw and Lent 1994). Two basic building block of QCA circuit are majority and inverter gates; hence, efficiently constructing QCA circuits using majority and inverter is of great interest (Azghadi et al. 2007; Farazkish et al. 2008, 2010, 2012; Navi et al. 2009, 2010a, b; Sayed- salehi et al. 2011; Zhang et al. 2004; Zhi et al. 2006). As already mentioned, one of the basic elements of QCA circuit is majority gate; majority gate can be used for implementing digital operations in a manner different from that of Boolean logic. Fault-tolerant design of QCA logic circuits is absolutely necessary for characterization of defective behavior of QCA circuits. In recent years, the fault tolerance properties of QCA circuits has been dem- onstrated by many researchers (Armstrong and Humphreys 2003a; Armstrong et al. 2003b; Beard 2006; Dalui et al. 2010; Farazkish et al. 2012; Fijany and Toomarian 2001). As majority gate is the basic element of QCA, this note investigates a new design for fault-tolerant five- R. Farazkish (&) Department of Computer Engineering, Science and Research Branch of Islamic Azad University, Tehran, Iran e-mail: r.farazkish@srbiau.ac.ir K. Navi Faculty of Electrical and Computer Engineering, Shahid Beheshti University G. C., Tehran, Iran e-mail: navi@sbu.ac.ir 123 J Nanopart Res (2012) 14:1252 DOI 10.1007/s11051-012-1252-3