An Efficient Method to Convert Arbitrary Quantum Circuits to Ones on a Linear Nearest Neighbor Architecture

A variety of quantum circuits have been designed. Most of them assume that arbitrary pairs of qubits can interact. However, several promising implementations of quantum computation rely on a Linear Nearest Neighbor (LNN) architecture, which arranges quantum bits on a line, and allows neighbor interactions only. Therefore, several specific circuits have been designed on an LNN architecture. However, a general and efficient conversion technique for an arbitrary circuit has not been established. Therefore, this paper gives an efficient method that converts an arbitrary quantum circuit to one on an LNN architecture. Our method achieves small overhead and time complexity compared with naive techniques. To develop the method, we introduce two key theorems that may be interesting on their own. In addition, our method also achieves smaller overhead for some known circuits designed on an LNN architecture.