Variational Quantum Simulations of quantum many-body systems
Eigenstate thermalization hypothesis (ETH) suggests that any initial state defined in some small subset of the total Hilbert space will eventually spread to the whole Hilbert space under unitary time evolution. However, there is a class of quantum states violating the hypothesis - so-called quantum...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/408562 |
| Acceso en línea: | https://hdl.handle.net/2117/408562 |
| Access Level: | acceso abierto |
| Palabra clave: | Quantum Computing Eigenstate thermalization hypothesis Quantum simulation Quantum many-body physics Variational quantum algorithms Quantum many-body scars. Computació quàntica Àrees temàtiques de la UPC::Informàtica |
| Sumario: | Eigenstate thermalization hypothesis (ETH) suggests that any initial state defined in some small subset of the total Hilbert space will eventually spread to the whole Hilbert space under unitary time evolution. However, there is a class of quantum states violating the hypothesis - so-called quantum many-body scars (QMBS). In this thesis, we focus on two problems related to QMBS. The first problem refers to the probing of ETH violation via the Inverse Participation Ratio (IPR) - a measure characterizing the fraction of the total Hilbert space occupied by the given quantum state. We propose two quantum algorithms implemented on quantum circuits to probe the IPR of quantum systems without a need for full diagonalization of the system Hamiltonian. We use the proposed algorithms to study the time evolution of IPR during spin squeezing protocol, to characterize the QMBS state in the extended PXP model, and to indicate the critical transition. The second task in this thesis belongs to the Hamiltonian Learning problems i.e. finding the Hamiltonian of the many-body quantum system having access only to a set of time-evolved states. In particular, we consider access to time-evolved states under the Hamiltonian supporting the existence of QMBS states. With the help of Quantum Graph Recurrent Neural Networks (QGRNN) and the hybrid quantum-classical variational algorithm technique, we extract the matrix representation of the Hamiltonian from scarred states. |
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