ETRI Journal (Oct 2024)

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

  • Sang-Min Lee,
  • Ki-Sung Jin,
  • Soo-Cheol Oh,
  • Jin-Ho On,
  • Gyu-Il Cha

DOI
https://doi.org/10.4218/etrij.2024-0129
Journal volume & issue
Vol. 46, no. 5
pp. 759 – 773

Abstract

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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 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 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.

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