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

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

Blog Article

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 crystal beaded candle holder logical flip-and-shift operations.The estimated space-time cost for a logical Hadamard operation with a code distance d is 5d2 + 3d2.

The efficiency enhancement of the proposed method is approximately four times greater than those of previous approaches, regardless of the code distance.Unlike the color touch 7/97 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.