Resources, symmetry, and complexity in quantum algorithms

• Grant number: 25/17993-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2025
• End date: November 30, 2028
• Field of knowledge: Physical Sciences and Mathematics - Physics
• Principal Investigator: Diogo de Oliveira Soares Pinto
• Grantee: Tatiana Rossafa Pauletti
• Host Institution: Instituto de Física de São Carlos (IFSC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project aims to investigate how fundamental quantum resources - such as entanglement, coherence, magic, and fidelity - influence the performance of variational quantum algorithms (VQAs), with emphasis on the structure of parameterized circuits (PQCs) with symmetry. The first part of this work will consist of a structural analysis, without coupling to specific Hamiltonians, aiming to evaluate the expressiveness of the circuits and the complexity associated with the preparation of quantum states. In this stage, group symmetry will be explored as a computational resource, allowing to restrict the search space and improve the navigability of the optimization process, in scenarios with and without noise (modeled by Kraus operators). In the second stage, symmetric variational circuits will be applied to the simulation of strongly correlated systems, described by the one-dimensional Fermi-Hubbard model with spin, external potential, and independent control of magnetization and density. Because they admit exact solutions via Lieb-Wu equations, these systems allow rigorous validation of variational architectures in different electronic correlation regimes. The goal is not to reproduce previously explored architectures, but rather to test hypotheses developed throughout the project regarding the relationship between quantum resources and variational efficiency. Thus, we will propose architectures based on theoretical criteria, with symmetry-protected complexity, greater noise tolerance and practical applicability in NISQ devices.