Quantum Circuit Synthesis for Linear Nearest Neighbor Based on the Vector Transformation

Abstract

Abstract. In this paper, a synthesis method is proposed based on vector transformation for linear nearest neighbor quantum circuits. Its aim is to construct a linear nearest neighbor quantum circuit, and to reduce the quantum cost of the linear reversible circuit. The vector representation of the sequence of the circuit lines and qubits of quantum gate is given in this method. It realizes the nearest neighbor of the quantum circuit by moving the position of the qubits vector elements, and it does not cause confusion due to comparison and transformation of two vector elements in the circuit. The number of SWAP gates needed to make the quantum circuit nearest neighbors is given, and its correctness is proven. Compared with the current quantum circuit synthesis algorithms, the average optimization rate of the quantum cost is 39.69% for typical benchmark circuits. The algorithm can be applied to all quantum circuits of 2-qubit quantum gates, and can be used in large quantum circuits.