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Non-stabilizerness - also colloquially referred to as magic - is a resource for advantage in quantum computing and lies in the access to non-Clifford operations. Developing a comprehensive understanding of how non-stabilizerness can be quantified and how it relates to other quantum resources is crucial for studying and characterizing the origin of quantum complexity. In this presentation, I will establish a direct link between non-stabilizerness and entanglement spectrum flatness for a pure quantum state. This connection can be exploited to efficiently investigate non-stabilizerness, even in the presence of noise. Furthermore, I will illustrate a Monte Carlo approach applied to the probability distribution of Pauli strings to estimate non-stabilizerness, which is quantified by the Stabilizer Renyi Entropies (SREs). This will provide an insightful and efficient method for characterizing and analyzing the role of non-stabilizerness in quantum many-body systems. In particular, I will show the importance of magic in (a) one-dimensional systems, where the long-range magic displays strong signatures of conformal quantum criticality (Ising, Potts, and Gaussian), overcoming the limitations of full state magic, (b) in two-dimensional Z2 lattice gauge theories, where I will show the evidence that magic is able to identify the confinement-deconfinement transition, and displays critical scaling behavior even at relatively modest volumes.

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Emanuele Tirrito, SISSA
Seminar Room 0.03, ETP
Contact: Xhek Turkeshi