Extremal Magic States from Symmetric Lattices

Extremal Magic States from Symmetric Lattices arXiv:submit/6539486 [quant-ph] 13 Jun 2025 Misaki Ohta and Kazuki Sakurai We have stored the following files on Zenodo: Data of 4,320 shortest vectors of the Barnes-Wall lattice, classified by entanglement (concurrence). Data of 61,440 second shortest vectors of the Barnes-Wall lattice, classified by entanglement (concurrence). Programming files related to magic for 2- and 3-qubit systems, and 1-qutrit systems. Programming files related to entanglement (concurrence) for 2- and 3-qubit systems. Lists of physically distinct (up to phase equivalence) maximally magic states for 2- and 3-qubit systems, and 1-qutrit systems. Lists of physically distinct (up to phase equivalence) stabilizer states for 2- and 3-qubit systems. A PDF file containing the programming code. Coordinates of the 1st to 4th shortest vectors of the E8 lattice