An efficient conversion of quantum circuits to a linear nearest neighbor architecture

Several promising implementations of quantum computation rely on a Linear NearestNeighbor (LNN) architecture, which arranges quantum bits on a line, and allows neighborinteractions only. Therefore, several specific circuits have been designed on an LNNarchitecture. However, a general and efficient conversion method for an arbitrary circuithas not been established. Therefore, this paper gives an efficient conversion technique toconvert quantum circuits to an LNN architecture. When a quantum circuit is convertedto an LNN architecture, the objective is to reduce the size of the additional circuit addedby the conversion and the time complexity of the conversion. The proposed methodrequires less additional circuitry and time complexity compared with naive techniques.To develop the method, we introduce two key theorems that may be interesting on theirown. In addition, the proposed method also achieves less overhead than some knowncircuits designed from scratch on an LNN architecture.