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In this seminar, I will present our lattice QCD calculation of neutral meson mixing matrix elements, focusing on kaon and B-meson systems. I will discuss results for kaon mixing obtained with domain wall fermions at physical quark masses, using a non-perturbative renormalization. Additionally, I will outline ongoing work on B-meson mixing using a fully relativistic approach with multiple heavy-quark masses and lattice ensembles from the RBC/UKQCD and JLQCD collaborations. This high-precision determination of the mixing matrix elements will provide critical input for testing the Standard Model and constraining possible new physics.