Lectures on quantum supreme matter

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These notes are based on lectures serving the advanced graduate education of the Delta Institute of Theoretical Physics in the Netherlands in autumn 2021. The goal is to explain in a language that can be understood by non-specialists very recent advances in quantum information and especially string theory suggesting the existence of entirely new forms of matter. These are metallic states characterized by an extremely dense many body entanglement, requiring the supremacy of the quantum computer to be completely enumerated. The holographic duality discovered in string theory appears to be a mathematical machinery capable of computing observable properties of such matter, suggesting the presence of universal general principles governing its phenomenology. The case is developing that these principles may well apply to the highly mysterious physical properties observed in the high temperature superconductors and other strongly interacting electron systems of condensed matter physics.