arXiv subjects

Ayumu Nakayama

Publications and source records attributed to Ayumu Nakayama.

2 recordsLinked to original sources

arXiv2020

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 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.

quant-ph↗

arXiv2020

A Four-Qubits Code that is a Quantum Deletion Error-Correcting Code with the Optimal Length

This paper provides a new instance of quantum deletion error-correcting codes. This code can correct any single quantum deletion error, while our code is only of length 4. This paper also provides an example of an encoding quantum circuit and decoding quantum circuits. It is also proven that the length of any single deletion error-correcting codes is greater than or equal to 4. In other words, our code is optimal for the code length.

quant-ph↗