Representation of Boolean Quantum Circuits as Reed-Muller Expansions

In this paper we show that there is a direct correspondence between Boolean quantum operations and certain forms of classical (non-quantum) logic known as Reed-Muller expansions. This allows us to readily convert Boolean circuits into their quantum equivalents. A direct result of this is that the problem of synthesis and optimization of Boolean quantum circuits can be tackled within the field of Reed-Muller logic.