Essay: Reversible gates

Abstract – In this work we made a comparison between two techniques on the ground of Area, One is transistor implementation and other is QCA implementation of TR reversible gate. In the later section, we present a new-fangled design of the reversible adder and subtractor RSG gate. This gate can perform addition and subtraction operation simultaneously. This is a unique gate, before this we cannot perform both the operations concurrently. Here RSG is novel reversible gate which can be operated as Reversible Half Adder and Subtractor. The proposed gate is designed from 2X2 quantum gates such as CNOT , Controlled-V and Controlled ‘V+ gates. The reversible gate proposed in this work will be constructive in a number of digital signal processing applications where we need both the operations simultaneously.

Keywords’Reversible Computing, QCA, RSG, Quantum Computers, CNOT, Controlled-V and Controlled-V+ gates.

I. INTRODUCTION

Reversible logic is evolving as a favorable computing standard with applications in quantum computing, quantum dot cellular automata, optical computing, DNA computing, etc. Reversible circuits are information lossless circuits, in these unique output is generated for each input vector and vice versa. In a lucid manner there should be one to one mapping among inputs and outputs. Inputs and Outputs should be bijective in nature. In 1961 Landauer has proposed that for any irreversible logic computation each lost bit information causes kTln2 joules of heat dissipation, where k is Boltzmann’s constant and T is the absolute temperature at which computation is carried out[2].Further in 1973 Bennet postulated that energy dissipation will be null if computation is carried out in a reversible manner using reversible gates[3].One of the prime application of reversible logic is in quantum computing. A quantum computer operates on one, two or more two state quantum systems called as qubits. Each qubit is capable of representing 0 and 1 concurrently. The important parameters in the design and synthesis of reversible logic circuits are the quantum cost, delay and number of garbage outputs [4][5].The garbage outputs are unused outputs in reversible circuits which occur just to maintain the reversibility but do not implement any useful operations.

For any reversible gate to be used in quantum computing ,it should be transformed into its quantum gate implementation, then only it can be utilized in quantum computers. The quantum computing is the next step which will harness the power of atoms and molecules to perform memory and processing tasks .Quantum Computers have potential to accomplish certain calculations significantly faster than Si based computers. This computing is not limited to two states but this encodes the information as quantum bits or qubits which exist in superposition. Qubits represent atom, ion, photon or electron and their respective control devices that are working together to act as computer memory and processor.
Quantum Dot Cellular Automata (QCA)[12] was introduced in 1993 and verified in 1997[6].It is expected to achieve high device density, low power consumption and very high switching speed. QCA structure is constructed as an array of quantum cells, in this every cell has an electrostatic interaction with its neighboring cells. The basic circuits for QCA are majority gates, these gates work on the principle of majority input will win and become the output of circuit. In the literature many Majority gates are available these may be of three inputs, five inputs[14] and seven inputs[15] majority gate also.

There are many reversible gates available in the literature like Feynman Gate, Toffoli Gate[7],Peres Gate[8] etc. We have synthesized and simulated TR gate[1] using two different simulation environment to verify the logic, this kind of work is itself a unique because this type of comparison regarding reversible gates are never done before in the literature. A new reversible gate is proposed in this paper which can serve as adder and subtractor simultaneously.

The paper is organized as follows: section II presents the basic reversible gates and their quantum implementation; Section III presents the delay computation in reversible logic; Section IV presents experimental results of TR gate in different simulation environment; Section V presents proposed RSG gate and its quantum gate implementation; Section VI presents proposed design for reversible full adder and subtractor; Section VII provides discussion and conclusions.

II. BASIC REVERSIBLE GATES

The cost of reversible gate in terms of its quantum gates is called quantum cost [9].The quantum cost of all 1 x 1 and 2 x 2 gates are taken as unity[9], [10], [11].In simple words the

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