Distinctness of defect encoding schemes in color codes.

Tian-Hao Wei, Jia-Xuan Zhang, Jia-Ning Li +3 more

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.

Markus S. Kesselring, Fernando Pastawski, Jens Eisert +1 more

Clarice Dias de Albuquerque, Eduardo Brandani da Silva, Waldir Silva Soares

Manoj G. Gowda, Pradeep Kiran Sarvepalli

Twists are defects in the lattice which can be utilized to perform computations on encoded data. Twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes, and qubit subsystem color codes. They are known to exhibit projective non-Abelian statistics, which is exploited to perform encoded gates. In this paper, we initiate the study of twists in qudit color codes over the odd prime alphabet. Specifically, we present a systematic construction of twists in qudit color codes that permute both charge and color of the excitations. We also present a mapping between generalized Pauli operators and strings in the lattice. Making use of the construction, we give protocols to implement generalized Clifford gates using charge-and-color-permuting twists.

Manoj G. Gowda, Pradeep Kiran Sarvepalli

twists are defects in the lattice which can be utilized to perform computations on encoded data. twists have been studied in various classes of topological codes like qubit and qudit surface codes, qubit color codes and qubit subsystem color codes. they are known to exhibit projective non-abelian statistics which is exploited to perform encoded gates. in this paper, we initiate the study of twists in qudit color codes over odd prime alphabet. to the best of our knowledge, this is the first study of twists in qudit color codes. specifically, we present a systematic construction of twists in qudit color codes that permute both charge and color of the excitations. we also present a mapping between generalized pauli operators and strings in the lattice. making use of the construction, we give protocols to implement generalized clifford gates using charge-color permuting twists.

William J. Zeng, Benjamin J. Brown