Boolean Function Decomposition Based on Grover Algorithm and Its Simulation Using Quantum Language Quipper

Abstract

Decomposition of functions is a general method frequently used in binary logic circuit synthesis, Data Mining and Machine Learning. Ashenhurst-Curtis (AC) decomposition belongs to one of the best known decomposition methods. However, it is really challenging to find the exact minimum AC decomposition for large functions because it requires many exhaust searches. In the hope that large scale quantum computers will be build in the future, we propose an quantum approach based on Grover algorithm to find the optimal AC decomposition in terms of partition theory. The detailed quantum circuit design was created and simulated using Quipper language. According to the experimental results, it is learnt that the quantum algorithm presented in this paper can decompose Boolean function successfully with almost 100% probability and iterations.