Brodoloni, Luca (2025) Neural quantum Monte Carlo simulations for disordered systems and quantum simulators. [Tesi di dottorato]

Documento PDF phd_thesis-final.pdf Download (4MB)

Abstract

This thesis extends the applicability of the self-learning Projector Quantum Monte Carlo (PQMC) framework, a method that intrinsically employs a neural quantum state to enhance its performance, to a range of complex quantum systems beyond testbed models. We begin by detailing the theoretical foundations of Projective Quantum Monte Carlo (PQMC) and its enhancement through Neural Quantum States. The self-learning PQMC scheme is described, where a Restricted Boltzmann Machine is iteratively trained on the walker population to approximate the ground state. This method is rigorously benchmarked, showing exact convergence for the 1D Transverse Field Ising Model. The power of this neural-guided approach is then demonstrated on a variety of challenging problems involving disorder and frustration. We enable the high-precision study of quantum phase transitions in the 2D Edwards-Anderson spin glass and in amorphous systems of Rydberg atoms, providing key insights into their critical properties and glassy phases. Furthermore, the framework is applied to unravel the influence of geometry and interaction range on phase transitions in frustrated triangular lattices, specifically revealing exotic phases and the emergence of clock phases via an order-by-disorder mechanism for both short and power-law interactions. The research also include a hybrid quantum-classical pipeline in which experimental data from a Rydberg atom quantum computer are used to guide the PQMC algorithm, leading to a substantial performance increase validated against more standard benchmarks. This work suggests a general protocol for leveraging current quantum devices to enhance classical simulations. Finally, we provide an investigation of the energy gap distributions of spin glasses. We develop a high-performance, GPU-accelerated exact diagonalization code to study finite-size scaling in the Sherrington-Kirkpatrick and Edwards-Anderson models. This foundational study is then extended to larger scales via a novel PQMC-based gap estimator, suggesting the emergence of heavy-tailed gap distributions in two-dimensional spin glass models. This investigation is useful to understand the behaviors and limitations in the context of adiabatic quantum computing.

Downloads

Actions (login required)

Modifica documento