Optimal execution of logical Hadamard with low‐space overhead in rotated surface code

• Published in: ETRI journal
• Main Authors: Lee, Sang‐Min, Jin, Ki‐Sung, Oh, Soo‐Cheol, On, Jin‐Ho, Cha, Gyu‐Il
• Format: Journal Article
• Language: English
• Published: 15.10.2024
• ISSN: 1225-6463; 2233-7326
• DOI: 10.4218/etrij.2024-0129

Abstract Fault‐tolerant quantum computation requires error‐correcting codes that enable reliable universal quantum operations. This study introduces a novel approach that executes the logical Hadamard with low‐space requirements while preserving the original definition of logical operators within the framework of the rotated surface codes. Our method leverages a boundary deformation method to rotate the logical qubit transformed by transversal Hadamard. Following this, the original encoding of the logical qubit is reinstated through logical flip‐and‐shift operations. The estimated space–time cost for a logical Hadamard operation with a code distance d is 5 d 2 + 3 d 2 . The efficiency enhancement of the proposed method is approximately four times greater than those of previous approaches, regardless of the code distance. Unlike the traditional method, implementing a logical Hadamard requires only two patches instead of seven. Furthermore, the proposed method ensures the parallelism of quantum circuits by preventing interferences between adjacent logical data qubits.