Adaptive Deformation of Color Code in Square Lattices with Defects

TL;DR

This paper introduces a universal scheme for defect repair in color codes on square lattices, enhancing fault tolerance and resource efficiency in quantum error correction on defective hardware.

Contribution

It develops a systematic framework for handling defects in color codes, including repair methods and optimization schemes, supporting fault-tolerant quantum computing on imperfect hardware.

Findings

Proposed a universal superstabilizer scheme for stabilizer codes with defects.

Developed concrete repair methods for internal and ancilla qubit defects in color codes.

Achieved lower logical error rates with resource-efficient defect handling schemes.

Abstract

Quantum error correction is a crucial technology for fault tolerant quantum computing. On superconducting platforms, hardware defects in large scale quantum processors can disrupt the regular lattice structure of topological codes and impair their error correction capabilities. Although defect adaptive methods for surface codes have been extensively studied, other topological codes such as color codes still lack a systematic framework for handling defects. To address this issue, we propose a universal superstabilizer scheme applicable to data qubit defects in arbitrary stabilizer codes. Based on this scheme, we develop concrete repair methods for isolated defects of both internal data qubits and ancilla qubits in color codes defined on square lattices. Furthermore, for ancilla qubit defects, we present two optimization schemes. One scheme reuses neighboring ancilla qubits, and the other employs iSWAP gates. Unlike conventional approaches that directly disable neighboring data qubits and thus cause resource waste, both of our schemes avoid such waste and consequently achieve a lower logical error rate.Integrating the above techniques, we construct a comprehensive defect adaptive architecture for color codes to handle various defect clusters. We also show that our scheme supports a full transversal Clifford gate set and lattice surgery operations. These results provide a systematic theoretical pathway for deploying robust and low overhead color codes on defective quantum hardware.