Cycle: XXXVII

PhD student: Andres Camilo Granda Arango

Roleo: R1 - First Stage Researcher

Supervisor: Prof. Giuseppe Sergioli

Co-supervisors: Dott. Gustavo Martin Bosyk, Dott. Federico Hernan Holik

I got my master degree in Physics at the University of Antioquia-Colombia, with a thesis entitled “Asymptotic quantum mechanics for N coupled oscillators”. Since then, I am a PhD scholar at the University of Cagliari. My field of research includes the fundamentals of quantum mechanics, particularly focused on the problem of how is the connection that exists between two apparently different theories: classical mechanics and quantum mechanics. My recent contributions are subject to the creation of a new mathematical formalism, called asymptotic quantum mechanics, based on probability density, asymptotic behaviors and Fourier transforms, which has allowed to recover classical probability densities plus quantum-like corrections in physical systems such as the harmonic oscillator, the hydrogen atom, particles enclosed in flat and spherical wells, free fall and recently in particles with relativistic characteristics. The current goal of my research is to incorporate machine learning. That is, using machine learning techniques, we will focus on the classification problem to try to discern whether certain states that a source has are intertwined or not, whether they exhibit coherence or not, or whether that particular quantum system was able to reach its classical limit.

THESIS' ABSTRACT

"Geometrical Aspects Of Resources Distribution In Quantum Random Circuits"
[Andrés Camilo Granda Arango (1), Giuseppe Sergioli (2), Federico Holik (3)
University of Cagliari, Via Is Mirrions 1, Cagliari, 09123, Italy, Universidad Nacional de La Plata, Instituto de Física, C.C. 727, La Plata, 1900, Argentina]

Quantum computing holds the promise of achieving computational advantages beyond classical capabilities. However, the fundamental reasons behind this advantage remain an open question. While entanglement and coherence have been suggested as key resources, results such as the Gottesmann-Knill theorem indicate that these features alone do not fully explain quantum speed-up. Recent studies have highlighted the role of quantum contextuality as a crucial element. In this thesis, we explore the distribution and robustness of quantum resources, particularly non-locality and entanglement, in quantum random circuits (QRC). Our study aims to quantify the extent to which different quantum devices can generate and sustain these resources under various conditions. To achieve this, we employ multiple quantifiers: the degree of violation of Svetlichny inequalities to assess genuine multipartite non-locality, and various entanglement measures such as Tangle, Concurrence, Von Neumann entropy, Negativity. Using a combination of theoretical simulations and experimental implementations on real quantum processors, we compare universal (Clifford + T) and non-universal (Clifford) sets of quantum gates, analyzing how they affect the distribution of quantum resources. Our findings reveal that while non-universal gates can generate highly entangled states, their distribution is restricted to discrete values, whereas universal gate sets provide a richer and more continuous resource distribution. Furthermore, we examine the impact of noise on resource distribution, showing that increased noise levels degrade non-local correlations and entanglement, thereby limiting the device’s computational capabilities. This study contributes to the ongoing discourse on quantum advantage and the certification of quantum processors. By providing a method to benchmark quantum devices based on fundamental physical principles rather than specific algorithmic performance, we propose a novel approach to evaluating a quantum processing unit’s (QPU) ability to generate a robust quantum state space. Our results suggest that the ability of a QPU to maintain high levels of non-locality and entanglement is critical for its performance, offering insights into the design and optimization of near-term quantum technologies.