Implementation of Novel 2x2 Vedic Multiplier using QCA Technology

Advantages like working at high speed, scalability, and lower power consumption make QCA technology more feasible than modern CMOS technology. QCA Technology uses electrons’ Coulombic interaction and polarization to represent binary information 0 and 1. The present paper proposes a novel XOR Gate and a Half Adder design and uses them to implement a new 2x2 Vedic Multiplier on QCA technology. A 2x2 Vedic Multiplier multiplies two inputs, of two bits each, using Urdhva-Tiryakbhyam Vedic Sutra. The proposed circuit has a reduced cell count and Quantum cost compared Co-planar Vedic Multipliers to available in the literature. QCADesigner 2.0.3 is used for the simulation and verification of all three proposed circuits.


Introduction
The decline of Moore's law is going to bring an end to the CMOS era.As a result, the number of transistors placed on a single chip may not be increased any further in near future.Thus, modern technology may not achieve higher speed and computational power in the coming years [1].QCA (Quantum-dot Cellular Automata) Technology, introduced by C.S. Lent in 1993, overcomes such disadvantages by showcasing higher switching speed and lower energy dissipation.A QCA based circuit is a type of circuit that utilizes the properties of quantum dots to perform various functions.Quantum dots are tiny semiconductor particles that can be manipulated to create a range of electronic and optical properties.These properties make them ideal for use in a wide range of applications, including computing, communications, and sensing.One of the key advantages of QCA-based circuits is their ability to perform multiple functions simultaneously.This is known as parallel processing, and it allows for more efficient and faster computation.Additionally, QCA-based circuits are highly scalable, meaning that they can be easily expanded to include more functionality as needed.Another advantage of QCA-based circuits is their ability to operate at very low power levels.This is due to the fact that quantum dots can be manipulated at a molecular level, which allows for precise control of the circuit's energy consumption.This makes QCA-based circuits ideal for use in portable devices, such as smartphones and laptops, where power consumption is a major concern.QCA-based circuits also have the potential to revolutionize the field of cryptography.Quantum dots can be used to create highly secure encryption algorithms, making it nearly impossible for hackers to crack the code.This makes QCA-based circuits ideal for use in financial transactions, military communications, and other sensitive applications [2].Despite the many advantages of QCA-based circuits, there are also some limitations to consider.One of the main limitations is that QCA-based circuits are still in the early stages of development, and there is a lack of standardization in the field.This makes it difficult for manufacturers to create QCA-based products that are compatible with existing technology.Additionally, the cost of producing QCA-based circuits is currently quite high, which makes it difficult for them to be widely adopted in the consumer market.The fabrication of QCA devices is still a challenging task, and several feasibility issues need to be addressed.One of the primary challenges in QCA fabrication is the precise placement and alignment of the quantum dots.The size and shape of the quantum dots play a crucial role in determining the device's functionality and performance.Thus, the fabrication process must be capable of producing uniform and well-defined quantum dots.Various techniques, such as self-assembly, lithography, and chemical vapor deposition, have been proposed for the fabrication of quantum dots.Another challenge in QCA fabrication is the difficulty in connecting the quantum dots to the external circuitry.The interconnects must be designed and fabricated to ensure minimum crosstalk, minimum resistance, and minimum parasitic capacitance.Additionally, the interconnects must be compatible with the nanoscale dimensions of the QCA devices.Furthermore, the temperature and noise levels during QCA fabrication must be precisely controlled, as the performance of QCA devices is highly sensitive to temperature and noise.The fabrication process must be carried out in a cleanroom environment, and the equipment used must be capable of operating at ultra-low temperatures and with minimal noise.Despite these challenges, significant progress has been made in the fabrication of QCA devices in recent years.Researchers have demonstrated several working QCA devices, including basic logic gates, adders, multipliers, and memory elements.With continued research and development, it is expected that the feasibility of QCA fabrication will improve, and QCA technology will become a practical alternative to conventional semiconductor technology.

Basic QCA Cell
A QCA cell is the most basic element of QCA technology.It uses Coulombic interaction and Polarization effect to display binary information 0 and 1.It contains 4 Quantum dots and 2 electrons.There are two capacitors and two tunnelling junctions that allow electron to jump from one row to another.In order to minimize the Coulombic force, the electrons are oriented diagonally inside a QCA Cell [3].These two allowed diagonal states are named as binary 0 and 1.Based on the placement of Quantum dots, QCA cell can be of two types: 90° cells and 45° cells as shown in figure 1.The most important utilization of QCA Clocking, apart from synchronization, is wire crossing.Since each zone will be operated consecutively, zone 0 can be crossed with zone 2 and zone 1 can be crossed with zone 3 as they won't affect each other.Another way of wire crossing can be seen in figure 3 where we use 90° cells and 45° cells [5].

QCA Majority Gate
Majority gate is the most basic gate of QCA technology.It takes 3 input A, B and C and gives the majority polarized state of the inputs as output [6].

Proposed XOR Gate and Half Adder Design
We know that an XOR Gate is a logical gate that takes in two bits and returns TRUE if they have odd parity and FALSE if they have an even parity.
A XOR B= A ⊕ B= AB'+A'B We propose a new XOR gate for QCA circuits, as shown in figure 5.

Proposed 2x2 Vedic Multiplier
Vedic mathematics is a system of mathematics that is based on the ancient Indian texts known as the Vedas.It has been used to develop efficient algorithms for solving mathematical problems and has been applied in various fields such as computer science, cryptography and digital electronics.
Research on the application of Vedic mathematics in quantum-dot cellular automata (QCA) circuits has been an active area of research in recent years.A 2x2 Vedic Multiplier multiplies two inputs, of two bits each, using Urdhva-Tiryakbhyam Vedic sutra [7].
Input bits of A are taken as A0 and A1 and input bits of B are given as B0 and B1.STEP 1: Multiply the bits A0 and B0.

Simulation Results
Table 1 displays the output generated by simulation of the proposed Vedic Multiplier using QCA Designer and its comparison with desired output.Figure 9 depicts the simulation output in QCADesigner for a 2x2 Vedic Multiplier.The results are correct and are as expected.Our proposed design gives significant improvement in terms of area occupied and cycle count.The 2x2 multiplier can be extended to form multiplier in 4x4 or higher configuration.
The VLSI research community is exploring Quantum-dot Cellular Automata (QCA) as a nano-scale compute fabric due to the increasing difficulties in shrinking CMOS transistors.QCA is considered to be the most efficient platform among the various designing and implementation options available.However, the practical implementation of QCA is yet to be achieved.Nevertheless, designing and analysis using simulation can be continued to accelerate future developments.This is the current limitation of this technology.Once the fabrication of QCA cells is achieved, the designs already available can be utilized to obtain the desired results

Figure 2 .
Figure 2. QCA Clocking Cycles with four phases

Figure 4 .
Figure 4. QCA Majority Gate Figure 6 shows our proposed Half Adder using our new XOR gate.Half adder is a combinational circuit used to add two bits.It has two inputs viz.A and B; and two outputs viz.SUM and CARRY [8].SUM= A ⊕ B= AB'+A'B CARRY= A^B Our proposed QCA XOR Gate has 11 cells and the Half Adder circuit has 22 cells.

Table 1 :
Table 2 compares the Vedic Multiplier proposed in this work with other Multiplier designs available in the literature.Output of proposed Vedic Multiplier

Table 2 :
[2]parison of various Vedic MultipliersWe observe that the work done in references 8-11 has structures with Coplanar orientation.Our results show that the FoM i.e. the Quantum Cost has the least value of 0.27 in our structure.Structure by ref.12 has better Quantum Cost than our work but they use a Multilayer Orientation to generate a 2x2 Vedic Multiplier.QCA designs use fundamental Coulomb's law and polarizing effect to display binary information 0 and 1 on a QCA cell[2].Since the introduction, researchers have been working on implementing classic digital circuits on QCA Technology.This includes basic logic gates like NOT, AND, OR, XOR, and XNOR and combinational circuits such as Half adder, Full adder, and Multiplexer.In this work, we presented a 2 x 2 Vedic Multiplier with a new XOR gate design.We conclude that in the Co-Planar Orientation, our proposed Vedic Multiplier has the least cell-count.It also has the least value of Figure-of-Merit in terms of Quantum cost.To the best of our knowledge, only ref. 12 has better quantum Cost.However, the structured proposed by ref. 12 is of Multilayer orientation.