New construction of nine-qubit error-correcting code

TL;DR

This paper introduces two new nine-qubit quantum error-correcting codes and one three-qubit code, offering different performance characteristics and expanding options for optimizing quantum error correction.

Contribution

It presents novel nine-qubit and three-qubit error-correcting codes with unique properties, enhancing the design and application of quantum error correction schemes.

Findings

Two new nine-qubit codes with normal logical operators

One nine-qubit code suitable for high-wight bit-flip noise

One nine-qubit code suitable for high-wight phase-flip noise

Abstract

We report new construction of nine-qubit error-correcting code, which introduces two new nine-qubit codes and one new three-qubit code. Because both the new two nine-qubit codes have the normal logical operators, as opposed to the nine-qubit Shor code, it results in different performance when the three codes are applied in concatenated quantum error-correction. On the other hand, one of the two nine-qubit codes has the same stabilizer generators as the nine-qubit Shor code, they are more suitable for the high-wight bit-flip noise, and the other code has the different stabilizer generators, which is more suitable for the high-wight phase-flip noise. This work is enlightening to the construction of quantum error-correcting codes, and adds more options for optimizing the performance of quantum error-correction.