In this study, we first use a three-qubit system as an example to demonstrate the construction of quantum circuits for the eight maximally entangled basis vectors, subsequently extending the approach to N-qubit systems. We employ a random-number approach to generate maximally entangled basis vectors and their corresponding circuits, while also detailing the required number of single-qubit and CNOT gates. This approach not only provides a solid theoretical foundation but also establishes a practical technique for technological applications, bypassing the difficulty of storing large-scale encoding data.
@article{arxiv.2510.02685,
title = {Construction of the Complete Set of Maximally Entangled Basis Vectors for N-Qubit Systems},
author = {Chi-Chuan Hwang},
journal= {arXiv preprint arXiv:2510.02685},
year = {2025}
}