In this paper, we discuss a construction method of quantum deletion error-correcting codes. First of all, we define deletion errors for quantum states, an encoder, a decoder, and two conditions which is expressed by only the combinatorial language. Then, we prove that quantum deletion error-correcting codes can be constructed by two sets that satisfy the conditions. In other words, problems that correct the deletion errors for quantum states are reduced to problems that find the sets satisfying the condition by this paper. Also, we performed experiment of the codes over IBM Quantum Experience.

中文翻译：

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单量子删除纠错码

在本文中，我们讨论了一种量子删除纠错码的构造方法。首先，我们定义了量子态的删除错误、编码器、解码器和仅由组合语言表达的两个条件。然后，我们证明了量子删除纠错码可以由两个满足条件的集合构成。换句话说，纠正量子态的删除错误的问题被简化为找到满足本文条件的集合的问题。此外，我们还通过 IBM Quantum Experience 对代码进行了实验。