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IEICE Communications Express

The first quantum error-correcting code for single deletion errors

Ayumu Nakayama, Manabu Hagiwara

Published Jan 1, 2020• 24 citations
Publisher

Abstract

A quantum error-correcting code for single deletion errors is provided. To the authors’ best knowledge, this is the first code for deletion errors.
DOI
10.1587/comex.2019xbl0154

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This paper serves as an introductory overview of quantum deletion error-correction codes, a burgeoning field within quantum coding theory. Covering foundational concepts, existing research, and open questions, it aims to be the first accessible resource on the subject. This paper contains basic definitions of terms so that readers can read it regardless of their background. This paper invites readers to explore this primer and take their initial steps into the realm of quantum deletion error-correcting codes research.
This manuscript is an extended abstract version of the paper entitled ``Quantum Deletion Codes derived from Classical Deletion Codes.'' The paper contributes to the fundamental theory for quantum deletion error-correcting codes. The paper proposes a code construction condition for a partition of classical deletion error-correcting codes to derive quantum deletion error-correcting codes. The construction methods in this paper give examples of quantum codes that can correct single-quantum deletion errors and have a code rate arbitrarily close to 1, while the previously known quantum deletion code rates are close to 0 for long length. This manuscript omits the proofs of the statements in the paper.
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