# Work-sharing of qubits in topological error corrections

## TL;DR

This paper introduces a method to share qubits in topological error correction codes by adding SWAP gates, reducing wiring congestion and enabling fully 2D layouts for surface and color codes, simplifying fabrication.

## Contribution

The proposed method allows sharing of qubit roles via SWAP gates, transforming layouts to achieve fully 2D configurations, which was not previously possible.

## Key findings

- Reduces wiring congestion in topological codes
- Enables fully 2D qubit and control electrode layouts
- Improves fabrication simplicity and reliability

## 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.