Changing the Gate Order for Optimal LNN Conversion

While several physical realization schemes have been proposed for future quantum information processing, most known facts suggest that quantum information processing should have intrinsic limitations; physically realizable operations would be only interaction between neighbor qubits. To use only such physically realizable operations, we need to convert a general quantum circuit into one for an so-called Linear Nearest Neighbor (LNN) architecture where any gates should be operated between only adjacent qubits. Thus, there has been much attention to develop efficient methods to design quantum circuits for an LNN architecture. Most of the existing researches do not consider changing the gate order of the original circuit, and thus the result may not be optimal. In this paper, we propose a method to convert a quantum circuit into one for an LNN architecture with the smallest number of SWAP gates. Our method improves the previous result for Approximate Quantum Fourier Transform (AQFT) by the state-of-the-art design method.