Innovative Approaches to Classical and Quantum Reflected Binary Code Generation using Pascal Triangle, Reversible N-Input C-Gate and Reversible N-Input Q-Gate

Abstract

There are numerous classical approaches employed by researchers in the generation of gray code sequences, however currently there is no straightforward method or model for generating quantum gray codes. This paper seeks to present three innovative approaches to generating quantum gray codes. The first approach employs the principle of the Pascal triangle and vectors which are very important concepts drawn from the field of algebra. The second approach known as the “N-input Reversible C-Gate” is based on a reversible XOR gate, a vital concept in classical circuit model of computation. The third approach known as “N-input Reversible Q-Gate” is based on a controlled NOT gate which is a key concept drawn from the field of quantum circuit model of computation. Finally, we assess the performance of the proposed and existing approaches by measuring execution time in terms of number of bits and comparing the results. The Pascal triangle approach to quantum gray code generation requires a longer time to execute as the number of bits rises, according to simulation data and results. The evaluation also shows that the N-input Reversible C-Gate and N-input Reversible Q-Gate gate performs faster than that of the Pascal triangle approach and some of the other existing algorithms.