Optimal Nonadditive Quantum Error-Detecting Code

TL;DR

This paper explores the design of optimal nonadditive quantum error-detecting codes with distance two, identifying maximal codeword codes for various qubit counts using graph-based methods.

Contribution

It introduces a method to find optimal nonadditive quantum error-detecting codes with maximal codewords for specific qubit numbers, expanding the understanding of quantum error detection.

Findings

Optimal codes found for n=5,6,8,10,12 qubits

Loop graphs assist in code construction for most cases

Identifies the limitations for n=7 case

Abstract

In this paper, we investigate the optimal nonadditive quantum error-detecting codes with distance two. The the numerical simulation shows that, with n being can be 5, 6, 7, 8, 10 and 12, such the n-qubit quantum error-detecting codes with maximal number of codewords can be found. Therein, except the n=7 case, the n-vertex loop graphs help find the optimal quantum codes.