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Optimizing quantum simulations and the DMRG method
Brandejs, Jan ; Pittner, Jiří (advisor)
Title: Optimizing quantum simulations and the DMRG method Author: Jan Brandejs Department: Department of Chemical Physics and Optics Supervisor: doc. Dr. rer. nat. Jiří Pittner, DSc., J. Heyrovský Institute of Physical Chemistry of the Czech Academy of Sciences Abstract: In this work, we explore the quantum information theoretical aspects of simulation of quantum systems on classical computers, in particular the many- electron strongly correlated wave functions. We describe a way how to reduce the amount of data required for storing the wavefunction by a lossy compression of quantum information. For this purpose, we describe the measures of quantum entanglement for the density matrix renormalization group method. We imple- ment the computation of multi-site generalization of mutual information within the DMRG method and investigate entanglement patterns of strongly correlated chemical systems. We present several ways how to optimize the ground state calculation in the DMRG method. The theoretical conclusions are supported by numerical simulations of the diborane molecule, exhibiting chemically interest- ing electronic structure, like the 3-centered 2-electron bonds. In the theoretical part, we give a brief introduction to the principles of the DMRG method. Then we explain the quantum informational...
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Emergence of space geometries from quantum entanglement
Lukeš, Petr ; Scholtz, Martin (advisor) ; Svítek, Otakar (referee) ; Švarc, Robert (referee)
MASTER THESIS Petr Lukeš Emergence of space geometries from quantum entanglement Institute of Theoretical Physics Supervisor of the master thesis: Mgr. Martin Scholtz, Ph.D. Study programme: Physics Study branch: Theoretical physics Prague 2019 Abstract: Connecting the field of Quantum Physics and General Relativity is one of the main interests of contemporary Theoretical Physics. This work attempts to find solution to simplified version of this problem. Firstly entropy is shown to be a good meeting point between the two different theories. Then some of entropy's less intuitive properties are shown, namely its dependence on area, not volume. This relation is studied from both Relativistic and Quantum viewpoint. After- wards there is a short description of a quantum model interpretable as geometry based on the information between its subsystems. Lastly, results of computations within this model are presented.
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Optimizing quantum simulations and the DMRG method
Brandejs, Jan ; Pittner, Jiří (advisor) ; Zamastil, Jaroslav (referee)
Title: Optimizing quantum simulations and the DMRG method Author: Jan Brandejs Department: Department of Chemical Physics and Optics Supervisor: doc. Dr. rer. nat. Jiří Pittner, DSc., J. Heyrovský Institute of Physical Chemistry of the Czech Academy of Sciences Abstract: In this work, we explore the quantum information theoretical aspects of simulation of quantum systems on classical computers, in particular the many- electron strongly correlated wave functions. We describe a way how to reduce the amount of data required for storing the wavefunction by a lossy compression of quantum information. For this purpose, we describe the measures of quantum entanglement for the density matrix renormalization group method. We imple- ment the computation of multi-site generalization of mutual information within the DMRG method and investigate entanglement patterns of strongly correlated chemical systems. We present several ways how to optimize the ground state calculation in the DMRG method. The theoretical conclusions are supported by numerical simulations of the diborane molecule, exhibiting chemically interest- ing electronic structure, like the 3-centered 2-electron bonds. In the theoretical part, we give a brief introduction to the principles of the DMRG method. Then we explain the quantum informational...
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