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Many-body magic in strongly correlated systems

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Quantum resources have entered the many body stage over the last two decades. Apart from the prototypical case of entanglement, relatively little is known about how such resources relate to physical phenomena, a question that is of pivotal importance for the understanding of quantum simulators and computers as many-body systems. In this talk, I will show how magic – a type of resource that is fundamental in determining quantum advantage – is directly related to many-body phenomena. First, I will review recent developments in quantum information theory that have introduced stabilizer Renyi entropies as measures of magic. Based on that, I will present method(s) to measure magic in tensor network simulations, and illustrate a series of applications to many body systems, including: (a) how full-state magic and long-range magic behave in conformal field theories – illustrating the limit of the former, and the capabilities of the latter; (b) the scaling of magic in lattice gauge theories, both with and without dynamical matter; (c) how it is possible to have a distinct series of ‘complexity transitions’ in monitored quantum dynamics, and (d) how our computational tools are presently more advanced than the largest scale experimental demonstration of magic in Rydberg atom quantum simulators. I will conclude by commenting on the relevance of our findings for quantum computing, in particular, to determine which states are ultimately hard to realise in the context of quantum error correcting codes.

This talk is part of the Theory of Condensed Matter series.

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