The Scientific World Journal

Volume 2015 (2015), Article ID 705056, 9 pages

http://dx.doi.org/10.1155/2015/705056

## A Customizable Quantum-Dot Cellular Automata Building Block for the Synthesis of Classical and Reversible Circuits

^{1}Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt^{2}School of Computer Science, University of Birmingham, Birmingham B15 2TT, UK

Received 7 May 2015; Accepted 28 June 2015

Academic Editor: Jitendra Nath Roy

Copyright © 2015 Ahmed Moustafa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Quantum-dot cellular automata (QCA) are nanoscale digital logic constructs that use electrons in arrays of quantum dots to carry out binary operations. In this paper, a basic building block for QCA will be proposed. The proposed basic building block can be customized to implement classical gates, such as XOR and XNOR gates, and reversible gates, such as CNOT and Toffoli gates, with less cell count and/or better latency than other proposed designs.

#### 1. Introduction

One of the challenging problems in the development of computation paradigms and systems is data loss [1]. Reversible computation is a possible solution to solve this problem by allowing the computation to be done at the logical level without data loss by establishing a one-to-one and onto mapping (bijection) between the inputs and outputs of the circuit, that is, the number of inputs equal to the number of outputs [1]. Efforts have been done in exploring the capabilities of emerging technologies to perform reversible computation.

A quantum-dot cellular automaton (QCA) is a promising emerging technology that works on novel paradigms such as synthesis of reversible gates [2]. QCA is a constructing nanoelectronic technology that gives another approach to computation at nano level [3]. Research and development in the field of electronic devices during the last decades made it possible for designers to increase the speed and decrease the size of the components and the power consumption. QCA is based upon the encoding of binary information in the electron charge configuration within quantum-dot cells. Computational power is provided by the Coulombic interaction between QCA cells. There is no current flow between cells and no outer source is delivered to singular internal cells [4]. Due to the reordering of electron positions, the physics of cell-to-cell interaction provides the local interconnections between cells [5, 6]. Lent and Tougaw in 1993 introduced the basic concepts of QCA [3, 7] as the computation with cellular automata consists of arrays of quantum-dot cells. The unique feature is that logic states are represented by a cell. A cell is a nanoscale device able to encode data by two-electron configuration. The cells must be aligned exactly at nanoscales to provide correct functionality; thus, the testing of these devices for misalignment and manufacturing errors has an important role for the correctness of circuits [8]. The relation between computation and data loss has been solved in QCA because it has very low power consumption which is a common property for QCA [9–11]. In [12–14], different QCA designs for XOR gate have been shown. In [2, 15, 16], designs for Toffoli gate have been proposed.

The aim of this paper is to propose QCA designs for classical and reversible gates using a basic building block. The basic building block can be customized to implement the required gate. Based on the proposed building block, QCA designs for classical gates such as XOR and XNOR will be proposed. Customization of the proposed building block makes it possible to extend the proposed design of the XOR gate to implement reversible gates such as CNOT and Toffoli gates. Moreover, the basic building block can be used to implement reversible circuits that contain more than one reversible gate. The proposed QCA circuits in this paper have been designed and simulated using the QCADesigner tool version 2.0.3 running the system with coherence simulation engine [17].

This paper is organized as follows. A literature review is presented in Section 2. A review of the QCA basics and clocking is given in Section 3. The proposed QCA for the XOR gate and reversible gates is shown in Section 4. Finally Section 5 concludes the paper.

#### 2. Literature Review

The design of QCA for reversible functions is gaining attention in the literature. Many designs for the XOR gate using QCA have been proposed. In 2012, Ahmad and Bhat [12] proposed two different designs for the XOR gate. The first design consists of 37 cells. It uses three MV (Majority Voting) gates; one MV gate is used as OR gate, while the second and third MV gates are used as AND gate. The second design has crossover and it consists of 30 cells; this design uses the same number of MV gates as in the first design. Both designs have 0.5 clock delay. In 2013, Beigh et al. [13] proposed seven different designs for the XOR gate. The first and seventh designs are the most efficient designs among the seven designs in terms of cell count and clock delay. The first design consists of 34 cells and has 1 clock delay. It uses four MV gates; one MV gate is used as OR gate, while the second, the third, and the fourth MV gates are used as AND gate. The seventh proposed design consists of 42 cells and has 0.5 clock delay. It uses three MV gates; one is used as OR gate, while the second and third MV gates are used as AND gate. In 2014, Santra and Roy [14] proposed a design of the XOR gate that consists of 30 cells and has 4 clock delay. It uses three MV gates; one is used as OR gate while the second and third MV gates are used as AND gate.

Many designs for Toffoli gate using QCA have been proposed. In 2008, Ma et al. [2] proposed QCA design of Toffoli gates that consists of 169 cells and has 4 clock delay. This design uses four MV gates. It is a complicated design due to the large number of cell count. In 2013, Bahar et al. [15] proposed two different designs for the Toffoli gate. The first design consists of 75 cells and has 1 clock delay. This design uses four MV gates; three MV gates are used as AND gate while the fourth MV gate is used as OR gate, while the second design consists of 48 cells with 1 clock delay, where it uses four MV gates; three MV gates are used as AND gate while the fourth MV gate is used as OR gate similar to their first design. In 2013, Rolih [16] proposed another design for the Toffoli gate using smaller number of cell count where the QCA design for the Toffoli gate consists of 44 cells and has 1 clock delay.

#### 3. QCA Basics

Before addressing the proposed layouts, it is important to review the basic properties of QCA. This section gives a brief overview of the device physics, basic logic gates, and clocking.

##### 3.1. Basic Quantum-Dot Construction

The computational elements and wires of an entire circuit are built through QCA devices. The basic component of a QCA device is a cell with four quantum dots placed in the corners and two free electrons. By applying sufficient local electric field on the tunneling junctions, the potential barriers control the transition of the mobile electrons to provide three states for the isolated cell. The first state is* null cell* which occurs when the barriers are lowered by decreasing the electric field; this allows electrons to be found on any dots. The second state is* positive polarization* () which occurs when the barriers are raised positively. The third state is* negative polarization* () that occurs when the barriers are raised negatively. The terms* positive polarization* and* negative polarization* are corresponding to binary logic values “1” and “0,” respectively. Figure 1 shows the basic QCA cells and their possible polarizations. Coulombic interactions between the cells are placed near each other to be forced into matching polarizations. More details for the QCA device physics can be found in [3].