Publicação
Application of Tensor Networks On Text Universes
| Resumo: | According to Dirac, the main challenge is that the application of these fundamental laws results in equations that are too difficult to solve for the mathematical treatment of a significant portion of physics and the entirety of chemistry. Even with today’s most cutting-edge technological resources, simulating a quantum mechanical system is typi- cally a very difficult task; one of the primary reasons is related to the number of parame- ters required to represent a quantum state. This type of perspective when approaching complex mathematical situations in the field of physics still holds true today. Tensor Net- works can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe. The Density Matrix Renor- malization Group (DMRG), a tensor network method, is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This work aims to analyze the way in which Tensor Network Methods like MPS (Matrix Product State) and DMRG can be applied in order to achieve a more efficient examination of abstract universes with correlation between objects, specifically a text universe, and give a result which can be use to describe the system without the risk of high dimensionality and the use of great computational power. The possibility of applying these different methods for analysis can have an impact, not only in the field of condensed matter theory but on the study of black holes, quantum computing and the development of the holographic universe theory. |
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| Autores principais: | Capela, Afonso David dos Reis Caldeira de Cordeiro |
| Assunto: | Tensor Networks Matrix Product State Density Matrix Renormalization Group Quantum Mechanical System Quantum Computing |
| Ano: | 2022 |
| País: | Portugal |
| Tipo de documento: | dissertação de mestrado |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Nova de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório Institucional da UNL |
| Resumo: | According to Dirac, the main challenge is that the application of these fundamental laws results in equations that are too difficult to solve for the mathematical treatment of a significant portion of physics and the entirety of chemistry. Even with today’s most cutting-edge technological resources, simulating a quantum mechanical system is typi- cally a very difficult task; one of the primary reasons is related to the number of parame- ters required to represent a quantum state. This type of perspective when approaching complex mathematical situations in the field of physics still holds true today. Tensor Net- works can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe. The Density Matrix Renor- malization Group (DMRG), a tensor network method, is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This work aims to analyze the way in which Tensor Network Methods like MPS (Matrix Product State) and DMRG can be applied in order to achieve a more efficient examination of abstract universes with correlation between objects, specifically a text universe, and give a result which can be use to describe the system without the risk of high dimensionality and the use of great computational power. The possibility of applying these different methods for analysis can have an impact, not only in the field of condensed matter theory but on the study of black holes, quantum computing and the development of the holographic universe theory. |
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