An Efficient Method to Decompose and Map MPMCT Gates That Accounts for Qubit Placement

Mixed-Polarity Multiple-Control Toffoli (MPMCT) gates are generally used to implement large control logic functions for quantum computation. A logic circuit consisting of MPMCT gates needs to be mapped to a quantum computing device that invariably has a physical limitation, which means we need to (1) decompose the MPMCT gates into one- or two-qubit gates, and then (2) insert SWAP gates so that all the gates can be performed on Nearest Neighbor Architectures (NNAs). Up to date, the above two processes have only been studied independently. In this work, we investigate that the total number of gates in a circuit can be decreased if the above two processes are considered simultaneously as a single step. We developed a method that inserts SWAP gates while decomposing MPMCT gates unlike most of the existing methods. Also, we consider the effect on the latter part of a circuit carefully by considering the qubit placement when decomposing an MPMCT gate. Experimental results demonstrate the effectiveness of our method.