Enhancing the quantum cost of Reed-Muller Based Boolean quantum circuits using genetic algorithms

Abstract

Abstract There is a direct equivalence between Boolean functions represented in Reed-Muller logic and Boolean Quantum Circuits. Different polarity Reed-Muller expansions will give different Boolean quantum circuits with different cost for the same Boolean function. For a given Boolean function with n variables there are 2n possible expansions. Searching for the expansion that gives a Boolean quantum circuit with minimum quantum cost within the search space is a hard problem for large n. This paper will use genetic algorithms to find the fixed/mixed polarity Reed-Muller expansion that gives a Boolean quantum circuit with minimum quantum cost to optimize the circuit realization of a given Boolean function.