Work sharing of qubits in topological error corrections

Abstract

Topological error-correcting codes, such as surface codes and color codes, are promising because quantum operations are realized by two-dimensionally (2D) arrayed quantum bits (qubits). However, physical wiring of electrodes to qubits is complicated, and 3D integration for the wiring requires further development of fabrication technologies. Here, we propose a method to reduce the congestion of wiring to qubits by just adding a SWAP gate after each controlled-NOT (CNOT) gate. SWAP gates exchange roles of qubits. Then, the roles of qubits are shared between different qubits. We found that our method transforms the qubit layout and reduces the number of qubits that cannot be accessed two-dimensionally. We show that fully 2D layouts including both qubits and control electrodes can be achieved for surface and color codes of minimum sizes. This method will be beneficial to simplifications of fabrication process of quantum circuits in addition to improvements of reliability of qubit system.