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000162779 005__ 20251017144631.0
000162779 0247_ $$2doi$$a10.1088/2632-2153/adf53d
000162779 0248_ $$2sideral$$a145237
000162779 037__ $$aART-2025-145237
000162779 041__ $$aeng
000162779 100__ $$aRoca-Jerat, Sebastián
000162779 245__ $$aA genetic algorithm to generate maximally orthogonal frames in complex space
000162779 260__ $$c2025
000162779 5060_ $$aAccess copy available to the general public$$fUnrestricted
000162779 5203_ $$aA frame is a generalization of a basis of a vector space to a redundant overspanning set whose vectors are linearly dependent. Frames find applications in signal processing and quantum information theory. We present a genetic algorithm that can generate maximally orthogonal frames (MOFs) of arbitrary size n in d-dimensional complex space. First, we formalize the concept of MOF and demonstrate that it depends on the choice of an energy function to weigh the different pairwise overlaps between vectors. Then, we discuss the relation between different energy functions and well-known frame varieties such as tight and Grassmannian frames and complex projective p-designs. Obtaining MOFs poses a global non-convex minimization problem. We discuss the relation with established numerical problems such as the Thomson problem and the problem of finding optimal packings in complex projective space. To tackle the minimization, we design a hybrid genetic algorithm that features local optimization of the parents. To assess the performance of the algorithm, we propose two visualization techniques that allow us to analyze the coherence and uniformity of high-dimensional frames. The genetic algorithm is able to produce highly-symmetric universal frames, such as equiangular tight frames, symmetric, informationally complete, positive operator-valued measurements and maximal sets of mutually unbiased bases, for configurations of up to d = 6 and n = 36, with runtimes of the order of several minutes on a regular desktop computer for the largest configurations.
000162779 536__ $$9info:eu-repo/grantAgreement/ES/CSIC/PTI-001$$9info:eu-repo/grantAgreement/ES/DGA/E09-17R-Q-MAD$$9info:eu-repo/grantAgreement/ES/MCIU/FPU20-07231$$9info:eu-repo/grantAgreement/ES/MICINN/CEX2023-001286-S$$9info:eu-repo/grantAgreement/EUR/MICINN/TED2021-131447B-C21
000162779 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es
000162779 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000162779 700__ $$0(orcid)0000-0003-2995-6615$$aRomán-Roche, Juan$$uUniversidad de Zaragoza
000162779 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica
000162779 773__ $$g6, 3 (2025), 035022 [20 pp.]$$tMachine Learning: Science and Technology$$x2632-2153
000162779 8564_ $$s3600813$$uhttps://zaguan.unizar.es/record/162779/files/texto_completo.pdf$$yVersión publicada
000162779 8564_ $$s733200$$uhttps://zaguan.unizar.es/record/162779/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000162779 909CO $$ooai:zaguan.unizar.es:162779$$particulos$$pdriver
000162779 951__ $$a2025-10-17-14:26:25
000162779 980__ $$aARTICLE