BEGIN:VCALENDAR VERSION:2.0 PRODID:Icfo X-PUBLISHED-TTL:P1W BEGIN:VEVENT UID:69d4b43145b62 DTSTART:20240412T090000Z SEQUENCE:0 TRANSP:OPAQUE LOCATION:ICFO Auditorium and Online (Teams) SUMMARY:ICFO | JOANA FRAXANET MORALES CLASS:PUBLIC DESCRIPTION:In recent years\, the evolution of quantum technologies has res ulted in an unprecedented control over individual quantum particles and ma ny-body systems. This remarkable progress has given rise to a new era\, ma rked by the convergence of classical and quantum methodologies to investig ate fundamental questions concerning the nature of quantum matter\, improv ing our understanding of the role of entanglement in solid-state systems o r the mechanisms behind high-energy physics. From analog quantum simulator s to digital quantum computers\, these advancements hold potential across diverse domains.\nThis thesis explores the interplay between classical and quantum methods in understanding topological phases of matter. We concent rate on three distinct directions: non-conventional topological supercondu ctors\, interaction-induced topological phases in ultracold atom quantum s imulators\, and applications of variational quantum algorithms. Each traje ctory relies on the combination of different techniques with the aim of un derstanding and characterizing topological phenomena in different settings .\nExploring non-conventional topological superconductors involves extendi ng the paradigmatic Kitaev chain model by incorporating additional terms i n the Hamiltonian such as long-range interactions and quasi-periodic poten tials. This investigation is relevant to better understand the impact of r eal-world conditions on the both the topological and localization properti es of systems hosting non-local Majorana modes\, which are promising candi dates for topological quantum computation.\nIn the realm of interacting sy stems\, we explore the realization of interaction-induced topological phas es in systems of ultracold atoms in optical lattices\, both \;in one a nd two dimensions. The remarkable control and versatility of such platform s enable the simulation of both theoretical topological models and strongl y correlated physics. Notably\, the interplay between interactions and top ology can give rise to intriguing phenomena\, such as delocalized fraction al charges and gapless topological phases\, challenging existing intuition . We employ advanced numerical methods based on tensor networks to benchma rk the experimental proposals that open the door to the realization and de tection of novel many-body phases of matter\, including topological quantu m critical points and a higher-order topological Peierls insulator in Bose -Hubbard models with long-range interactions.\nVariational quantum algorit hms\, conversely\, have the potential to efficiently tackle a wide range o f problems\, including ground state search\, phase classification or acces sing topological invariants. Despite current limitations in trainability a nd scalability\, these hybrid classical-quantum algorithms provide practic al insights into current quantum hardware capabilities and can inspire fut ure architectures. We explore the application of variational quantum algor ithms to shed light on topological phenomena\, raising questions about the ir ability to discern topological phase transitions and compute topologica l invariants in situations where classical approaches fail.\nThis thesis p resents a comprehensive exploration of distinct approaches to topological quantum matter by leveraging quantum technologies and quantum-inspired cla ssical algorithms. Our results not only advance our understanding of quant um systems but also pave the way for the realization and discovery of nove l physics extending to quantum information processing\, materials science\ , and beyond. DTSTAMP:20260407T073721Z END:VEVENT END:VCALENDAR