Minimizing Reversible Circuits in the 2n Scheme Using Two and Three Bits Patterns

In this paper we present improvements to the cost of quantum circuits implemented with 2n-lines circuit implementation. The 2n-line circuit implementation is intended for the linear nearest neighbor quantum circuits and implements any quantum circuits in such manner that they can be directly mapped to quantum implementations. In this paper we propose a replacement strategy for 2- and 3-qubit patterns detected on the control lines. It is demonstrated that application of this strategy leads to a considerable reduction of circuit cost.