The reversible logic has promising applications in emerging computing paradigms, such as quantum computing, quantum dot cellular automata, optical computing, etc. In reversible logic gates, there is a unique one-to-one mapping between the inputs and outputs. To generate a useful gate function, the reversible gates require some constant ancillary inputs called ancilla inputs. Also to maintain the reversibility of the circuits some additional unused outputs are required that are referred to as the garbage outputs. The number of ancilla inputs, the number of garbage outputs and quantum cost plays an important role in the evaluation of reversible circuits. Thus minimizing these parameters are important for designing an efficient reversible circuit. Reversible circuits are of highest interest in optical computing, quantum dot cellular automata and quantum computing. The quantum gates perform an elementary unitary operation on one, two or more two-state quantum systems called qubits. Any unitary operation is reversible in nature, and hence, quantum networks are also reversible, to conclude the quantum computers must be built from reversible logic components. The main contribution of this dissertation is the design exploration and application of reversible circuits in emerging nanotechnologies. The emerging technologies explored in this work are 1) Optical quantum computing 2) Quantum computing. The first contribution of this dissertation is Mach-Zehnder interferometer based design of all optical reversible binary adder. The all optical reversible adder design is based on two new optical reversible gates referred as optical reversible gate I (ORG-I) and optical reversible gate II (ORG-II) and the existing all optical Feynman gate. The two new reversible gates ORG-I and ORGI-II have been proposed and can implement a reversible adder with a reduced optical cost which is equal to the number of MZI switches required, less propagation delay, and with zero overhead in terms of number of ancilla inputs and the garbage outputs. The proposed all optical reversible adder design based on the ORG-I and ORG-II reversible gates are compared and shown to be better than the other existing designs of reversible adder proposed in the non-optical domain in terms of number of MZI switches, delay, the number of ancilla inputs and the garbage outputs. The proposed all optical reversible adder will be a key component of an all optical reversible arithmetic logical unit (ALU), that is a quite essential component in a wide variety of optical signal processing applications. In the existing literature, the NAND logic based implementation is the only known implementation available for reversible gates and its functions. There is a lack of research in the direction of NOR logic based implementation of reversible gates and functions. The second contribution of this dissertation is the design of NOR logic based n-input and n-output reversible gates, one of which can be efficiently mapped into optical computing using the Mach-Zehnder interferometer (MZI), while the other can be mapped efficiently in optical computing using the linear optical quantum gates. The proposed reversible NOR gates work as a corresponding NOR counterpart of NAND logic based Toffoli gates. The proposed optical reversible NOR logic gates can implement the reversible boolean logic functions with less number of linear optical quantum logic gates with reduced optical cost and propagation delay compared to the implementation using existing optical reversible NAND gates. It is illustrated that an optical reversible gate library having both optical Toffoli gate and the proposed optical reversible NOR gate is superior compared to the library containing only the optical Toffoli gate: (i) in terms of number of linear optical quantum gates when implemented using linear optical quantum computing (LOQC), (ii) in terms of optical cost and delay when implemented using the Mach-Zehnder interferometer. The third contribution of this dissertation is a binary tree-based design methodology for a NxN reversible multiplier. The proposed binary tree-based design methodology for a NxN reversible multiplier performs the addition of partial products in parallel using the reversible ripple adders with zero ancilla bit and zero garbage bit; thereby, minimizing the number of ancilla and garbage bits used in the design. The proposed design methodology shows improvements in terms of number of ancilla inputs and garbage outputs compared to all the existing reversible multiplier designs. The methodology is also extended to the design of NxN reversible signed multiplier based on modified Baugh-Wooley multiplication methodology.

The reversible logic has the promising applications in emerging computing paradigm such as quantum computing, quantum dot cellular automata, optical computing, etc. In reversible logic gates there is a unique one-to-one mapping between the inputs and outputs. To generate an useful gate function the reversible gates require some constant ancillary inputs called ancilla inputs. Also to maintain the reversibility of the circuits some additional unused outputs are required that are referred as the garbage outputs. The number of ancilla inputs, number of garbage outputs and quantum cost plays an important role in the evaluation of reversible circuits. Thus minimizing these parameters are important for designing an efficient reversible circuit. Barrel shifter is an integral component of many computing systems due to its useful property that it can shift and rotate multiple bits in a single cycle. The main contribution of this thesis is a set of design methodologies for the reversible realization of reversible barrel shifters where the designs are based on the Fredkin gate and the Feynman gate. The Fredkin gate can implement the 2:1 MUX with minimum quantum cost, minimum number of ancilla inputs and minimum number of garbage outputs and the Feynman gate can be used so as to avoid the fanout, as fanout is not allowed in reversible logic. The design methodologies considered in this work targets 1.) Reversible logical right- shifter, 2.) Reversible universal right shifter that supports logical right shift, arithmetic right shift and the right rotate, 3.) Reversible bidirectional logical shifter, 4.) Reversible bidirectional arithmetic and logical shifter, 5) Reversible universal bidirectional shifter that supports bidirectional logical and arithmetic shift and rotate operations. The proposed design methodologies are evaluated in terms of the number of the garbage outputs, the number of ancilla inputs and the quantum cost. The detailed architecture and the design of a (8,3) reversible logical right-shifter and the (8,3) reversible universal right shifter are presented for illustration of the proposed methodologies.