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Explore the theoretical implications and practical applications of classically simulating quantum computations in this 49-minute lecture by Dr. Oliver Reardon-Smith from the Center for Theoretical Physics, PAS. Delve into the concept of quantifying non-classicality through "magic" resources required for implementation. Examine recent advancements extending results from Clifford/stabilizer subtheory to fermionic linear optics, with references to arXiv papers 2307.12912, 2307.12654, and 2307.12702. Gain insights into an underexplored framework for understanding quantum computations, and discover open questions in this field. Presented as part of the Warsaw colloquium for theoretical physics at CTP PAS on 2024-05-22.