Codeword Stabilized Codes from m-Uniform Graph States
Abstract
An m-uniform quantum state on n qubits is an entangled state in which every m-qubit subsystem is maximally mixed. Starting with an m-uniform state realized as the graph state associated with an m-regular graph, and a classical [n,k,d \ge m+1] binary linear code with certain additional properties, we show that pure [[n,k,m+1]]_2 quantum error-correcting codes (QECCs) can be constructed within the codeword stabilized (CWS) code framework. As illustrations, we construct pure [[2^{2r}-1,2^{2r}-2r-3,3]]_2 and [[(2^{4r}-1)^2, (2^{4r}-1)^2 - 32r-7, 5]]_2 QECCs. We also give measurement-based protocols for encoding into code states and for recovery of logical qubits from code states.
Cite
@article{arxiv.2405.06142,
title = {Codeword Stabilized Codes from m-Uniform Graph States},
author = {Sowrabh Sudevan and Sourin Das and Thamadathil Aswanth and Nupur Patanker and Navin Kashyap},
journal= {arXiv preprint arXiv:2405.06142},
year = {2025}
}
Comments
A shorter version of this manuscript is available in the Proceedings of the 2024 International Symposium on Information Theory (ISIT 2024)