Rattacaso, Davide (2023) Optimal parent Hamiltonians for many-body systems. [Tesi di dottorato]
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| Tipologia del documento: | Tesi di dottorato |
|---|---|
| Lingua: | English |
| Titolo: | Optimal parent Hamiltonians for many-body systems |
| Autori: | Autore Email Rattacaso, Davide davide.rattacaso@gmail.com |
| Data: | 9 Marzo 2023 |
| Numero di pagine: | 136 |
| Istituzione: | Università degli Studi di Napoli Federico II |
| Dipartimento: | Fisica |
| Dottorato: | Quantum Technologies (Tecnologie Quantistiche) |
| Ciclo di dottorato: | 35 |
| Coordinatore del Corso di dottorato: | nome email Tafuri, Francesco francesco.tafuri@unina.it |
| Tutor: | nome email Fazio, Rosario [non definito] Lucignano, Procolo [non definito] |
| Data: | 9 Marzo 2023 |
| Numero di pagine: | 136 |
| Parole chiave: | parent Hamiltonian; Hamiltonian learning; inverse problem; quantum resource theory; adiabatic quantum computation; quantum technologies; quantum process tomography |
| Settori scientifico-disciplinari del MIUR: | Area 02 - Scienze fisiche > FIS/03 - Fisica della materia |
| Depositato il: | 15 Mar 2023 09:48 |
| Ultima modifica: | 10 Apr 2025 13:41 |
| URI: | http://www.fedoa.unina.it/id/eprint/15152 |
Abstract
Given a quantum state, the inverse problem consists in the determination of a realistic Hamiltonian, called Parent Hamiltonian, that captures the physics of the system, i.e. a Hamiltonian having such state as an eigenstate or ground state or, in the case of time-dependent states, generating the observed time evolution. In the context of many-body quantum systems, the search for parent Hamiltonians is of profound interest from both theoretical and technological points of view, being a significant resource for quantum state preparation and verification of quantum devices. In this Ph.D. thesis, we propose an optimal solution for the time-dependent inverse problem, i.e. a method to find a realistic time-dependent Hamiltonian capable of generating a target time-dependent state by minimizing a suitable cost functional on a space of allowed interactions. We extend this approach to Hamiltonian learning of quantum devices, showing how it is possible to reconstruct the unknown Hamiltonian couplings of a synthetic quantum system from measurements on a single time-dependent quantum state and proving that the ergodic behavior of time-evolution is a resource for Hamiltonian learning. Finally, we consider the adiabatic limit of the time-dependent inverse problem to find local Hamiltonians having a target state as ground state. We define an inverse dynamics that, in the adiabatic limit, efficiently generates the unknown Hamiltonian. An additional part of the thesis is dedicated to the evolution of non-stabilizerness in integrable spin systems, with a focus on the transverse-field Ising model. Non-stabilizerness is a resource for quantum computation, encoding the inability to efficiently simulate a given evolution using a classical computer through the stabilizer formalism. It represents, along with entanglement, a necessary ingredient for quantum speed-up. We estimate how non-stabilizerness evolves after a quantum quench in subsystems of a large quantum system.
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