Quantum Resources in Quantum Technologies: From Quantum Optimization to Many-Body Physics

Significant progress has been made in quantum technologies over the past decade. Despite this success, a central question remains: to what extent quantum resources are being exploited. This question is crucial not only for benchmarking quantum systems but also to unlock their full potential. This thesis analyses the role of quantum resources spanning quantum optimization algorithms to quantum many-body systems. First, we show how squeezing establishes a natural connection between the Quantum Approximate Optimization Algorithm and quantum metrology, revealing the role of quantum correlations and providing a benchmarking method for quantum-optimization devices. Further, we study multipartite entanglement in quantum optimization and demonstrate its presence on quantum hardware. However, entanglement alone is insufficient for a quantum advantage, as stabilizer states—though highly entangled—are classically simulable. We therefore study the role of nonstabilizerness in quantum optimization. Building on such resources, we further examine how they manifest in disordered systems. We show the emergence of non-Markovianity in disorder-averaged dynamics. Moreover, we examine complexity-resources across chaotic to integrable regimes in random-matrix models, highlighting the need for a multifaceted approach in quantum simulation. These investigations provide a deeper understanding of quantum technologies, from optimization to simulation, and lay the foundation for future developments toward quantum advantage.