Takayuki Nozaki

Ken Nakamura, Takayuki Nozaki

This paper proves that any quantum t-deletion-correcting codes also correct a total of t insertion and deletion errors under a certain condition. Here, this condition is that a set of quantum states is defined as a quantum error-correcting code if the error spheres of its states are disjoint, as classical coding theory. In addition, this paper proposes the quantum indel distance and describes insertion and deletion errors correcting capability of quantum codes by this distance.

Koki Sasaki, Ken Nakamura, Takayuki Nozaki

This paper focuses on Hagiwara codes, which are quantum deletion-correcting codes constructed by the quantum Reed-Solomon codes. Although Hagiwara codes can correct composite errors consisting of deletions and insertions, an efficient decoding algorithm to such errors remains an open problem. In this paper, we provide a decoding algorithm to such errors for Hagiwara codes.