XOR-AND-XOR Logic Forms for Autosymmetric Functions and Applications to Quantum Computing

We propose a new three-level XOR-AND-XOR form for autosymmetric functions, called XORAX expression. In general, Boolean function f over n variables is k-autosymmetric if it can be projected onto smaller fk, which depends on n-k only. show that expressions ease the reversible synthesis of producing compact networks, without inserting additional input lines. Autosymmetry occurs especially functions exhibit regular structure, as instance arithmetic functions. For this reason, networks might interesting quantum computing. Experimental results validate proposed approach.