Identity Rules-Based Decomposition, Optimization, and Spin-Torque Modeling of Controlled V and V+ Gates for Quantum Full Adder

The quantum computing (QC) is emerging as one of the possibilities to replace the conventional computing to meet the complex computing challenges. Quantum gates are based on the quantum mechanical phenomena such as superposition and entanglement. Moreover, there are several ways to realize the reversible full adder representing one of the building blocks of the reversible computing. One of the ways to realize the reversible full adder is by using the controlled V and V+ gates. Spintronics is one of the quantum technologies to realize the reversible computing physically. Therefore, there is need of spin-torque based modelling of controlled V and V+ gates for the quantum computing applications in the reversible computing domain. In this paper, the controlled V and V+ gates are modelled for the spin-torque based qubit architecture through the optimization at elementary single-qubit rotation and two-qubit entanglement level. Therefore, the key innovation or unique contribution is to realize the controlled V and V+ gates by using the minimum number of the elementary operations (single- and two-qubits). Moreover, a quantum full adder (QFA) composed of controlled V and V+ gates, is optimized and realized with the spin-torque models of the controlled V and V+ gates to achieve fault tolerant fidelity. Therefore, the novelty is that the optimization of the controlled V and V+ gates for the reversible full adders is carried out by using the identity rules.