Dynamical Decomposition and Mapping of MPMCT Gates to Nearest Neighbor Architectures

Abstract

We usually use Mixed-Polarity Multiple-Control Toffoli (MPMCT) gates to realize large control logic functions for quantum computation. A logic circuit consisting of MPMCT gates needs to be mapped to a quantum computing device that has some physical limitation; (1) we need to decompose MPMCT gates into one or two-qubit gates, and then (2) we need to insert SWAP gates such that all the gates can be performed on Nearest Neighbor Architectures (NNAs). Up to date, the above two processes have been independently studied intensively. This paper points out that we can decrease the total number of the gates in a circuit if the above two processes are considered dynamically as a single step; we propose a method to inserts SWAP gates while decomposing MPMCT gates unlike most of the existing methods. Our additional idea is to consider the effect on the latter part of a circuit carefully by considering the qubit layout when composing an MPMCT gate. We show some experimental results to confirm the effectiveness of our method.