Single Quantum Deletion Error-Correcting Codes

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 three conditions that are 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 experimented with the codes over IBM Quantum Experience.