Quantum Resource Distributions: Geometric Analysis and Computational Classification

Quantum computing is expected to outperform classical systems by harnessing intrinsically non-classical resources. Yet, the precise origin of this quantum advantage remains elusive. While entanglement and coherence have long been viewed as essential, results such as the Gottesman–Knill theorem demonstrate that these features alone are insufficient. Recent perspectives suggest that quantum contextuality and the geometric structure of state space may play fundamental roles. In this thesis, we investigate the distribution, robustness, and interplay of quantum resources—particularly genuine multipartite non-locality, entanglement, and quantum magic—within the framework of quantum random circuits. Using a combination of theoretical simulations and experimental implementations on real devices, we examine how these resources manifest across different gate sets, with and without noise. We develop a resource-centric methodology grounded in the violation of Mermin and Svetlichny inequalities, alongside entanglement measures such as tangle, concurrence, von Neumann entropy, and negativity. By comparing universal (Clifford+T) and non-universal (Clifford-only) architectures, we show that universal sets enable access to more expressive, statistically rich regions of Hilbert space, while Clifford circuits exhibit rigid, discretized distributions. Furthermore, we analyze how noise reshapes resource landscapes, suggesting that non-locality tends to degrade into Gaussian-like patterns under realistic conditions. Beyond simulation, we implement and benchmark our protocols on two quantum processors—IonQ's Aria-1 (trapped-ion, fully connected) and IQM's Garnet (superconducting, nearest-neighbor)—to assess their operational capacity to generate meaningful quantum correlations. These experiments highlight how connectivity and gate universality directly impact a device’s ability to explore high-dimensional quantum geometries. Altogether, this work offers a novel diagnostic framework for quantum devices rooted in the structure of quantum resource distributions. By shifting the perspective from algorithmic output toward a better understanding of the expressive reach of quantum circuits, we propose a new paradigm for certifying quantumness in the noisy, imperfect era of near-term quantum technologies. Extending this structural vision, the second part of the thesis investigates whether such quantum resources can also be recognized through computational inference. To this end, we design and apply a supervised quantum-inspired classifier based on the Pretty Good Measurement (PGM), capable of distinguishing among factorized, separable, entangled, and non-local quantum states. Using datasets labeled according to geometric and operational criteria, we assess the classifier’s ability to recover the underlying structure of the resource space. The results confirm that certain correlations—especially entanglement and non-locality—leave statistical signatures that are learnable, while others, like separability, remain more elusive. This reinforces the idea that quantum resources not only shape physical behavior but also define patterns of epistemic accessibility. The thesis thus bridges foundational questions with algorithmic realizations, offering a dual perspective on quantum resources: as measurable structures within Hilbert space, and as learnable features within computational models.