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

TL;DR

This paper introduces a four-qubit quantum deletion error-correcting code that is optimal in length, capable of correcting any single deletion error, and provides explicit encoding and decoding circuits.

Contribution

It presents the first known four-qubit quantum deletion error-correcting code with proven optimal length and explicit circuit implementations.

Findings

The code corrects any single quantum deletion error.

The code length of 4 is proven to be optimal.

Explicit encoding and decoding circuits are provided.

Abstract

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.