Publicação
Quantum random walks: simulations and physical realizations
| Resumo: | Quantum computing is an emergent field that brings together Quantum Mechanics, Computer Science and Information Theory, which promises improvements to classical algorithms such as simulation of quantum systems, cryptography, data base searching and many others. Among these algorithms, quantum walks may provide a quadratic speed up when compared to their classical counterparts, allowing improvements to applications such as element distinctness, searching problems, matrix product verification and hitting times in graphs. The present work offers a general theoretical overview, simulation and circuit implementation of the coined, staggered and continuous-time quantum walk models. The first two chapters of this thesis are dedicated to the definition of the theoretical framework, simulation in Python and comparison of the aforementioned quantum walk models for the simple case of the dynamics in a line graph and for the search algorithm in a complete graph. This is then used as a benchmark for the final chapter, devoted to building and testing the circuits corresponding to models mentioned above in IBM’s Qiskit. A main contribution of this dissertation concerns the circulant graph approach to diagonal operators for continuous-time quantum walks. |
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| Autores principais: | Santos, Jaime Pereira |
| Assunto: | Quantum computing Quantum walks Python Qiskit Computação quântica Caminhadas quânticas |
| Ano: | 2021 |
| País: | Portugal |
| Tipo de documento: | dissertação de mestrado |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | Quantum computing is an emergent field that brings together Quantum Mechanics, Computer Science and Information Theory, which promises improvements to classical algorithms such as simulation of quantum systems, cryptography, data base searching and many others. Among these algorithms, quantum walks may provide a quadratic speed up when compared to their classical counterparts, allowing improvements to applications such as element distinctness, searching problems, matrix product verification and hitting times in graphs. The present work offers a general theoretical overview, simulation and circuit implementation of the coined, staggered and continuous-time quantum walk models. The first two chapters of this thesis are dedicated to the definition of the theoretical framework, simulation in Python and comparison of the aforementioned quantum walk models for the simple case of the dynamics in a line graph and for the search algorithm in a complete graph. This is then used as a benchmark for the final chapter, devoted to building and testing the circuits corresponding to models mentioned above in IBM’s Qiskit. A main contribution of this dissertation concerns the circulant graph approach to diagonal operators for continuous-time quantum walks. |
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