Efficient Constructions for Simulating Multi Controlled Quantum Gates

Stefan Balauca, Andreea Arusoaie

Abstract: Multi Controlled Gates, with Multi Controlled Toffoli as primary example are a building block for a lot of complex quantum algorithms in the domains of discrete arithmetic, cryptography, machine learning, and image processing. However, these gates cannot be physically implemented in quantum hardware and therefore they need to be decomposed into many smaller elementary gates. In this work we analyse previously proposed circuit constructions for MCT gates and describe 6 new methods for generating MCT circuits with efficient costs, less restrictions, and improved applicability.