Viscardi, Michele (2026) Complexity, Entanglement and Stabilizer Entropy in Quantum Many-Body Systems. [Tesi di dottorato]

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Abstract

Quantum complexity arises from the interplay of entanglement and nonclassical resources beyond the stabilizer formalism, known as non-stabilizerness (or, more colloquially, \textit{magic}) . In particular, non-local magic—the magic component that cannot be generated or removed by local unitaries—has been put in connection with complex quantum behavior and quantum advantage. This thesis investigates the role of magic and its interplay with entanglement in quantum many-body systems, combining experimental, numerical, and theoretical approaches. We present the first experimental demonstration of non-local magic on a superconducting quantum processing unit. By directly characterizing intrinsic noise sources, we achieve quantitative agreement between theory and experiment without free parameters, and demonstrate independent control of local and non-local magic resources, paving the way for hardware-aware protocols in near-term quantum devices. We then provide a systematic study of quantum complexity in interacting spin systems by jointly analyzing stabilizer entropies and entanglement spectral properties, including antiflatness and capacity of entanglement. Across a broad class of models—such as XXZ, transverse-field XY models with and without Dzyaloshinskii–Moriya interactions, and cluster-based spin chains—we show that these quantities consistently distinguish quantum phases and accurately detect quantum phase transitions, revealing a deep connection between entanglement structure and non-stabilizerness in critical phenomena. Finally, we investigate the dynamical generation of complexity in quantum quenches, showing that free-fermion models retain a long-time gap from random-matrix-theory predictions, while non-integrable systems fully saturate complexity bounds. Together, these results establish magic-based and entanglement-spectral diagnostics as concrete, quantitative probes of quantum complexity, which are experimentally accessible and provide robust signatures of scrambling and thermalization.

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