Lower cost quantum gate realizations of multiple-control Toffoli gates

A systematic method is presented for realizing multiple-control Toffoli gates using elementary quantum gates. Results are presented showing that for the NOT, controlled-NOT and the two square root of NOT gates, the method produces circuits as good and in certain cases better than those known to date. A major feature of the work reported here is that in addition to the previously studied cases of one and the maximum required ancillary lines, the presented method covers all cases in between. The approach is general and can be directly applied to other sets of elementary gates.