Publicação
A quantum algorithm for ray casting using an orthographic camera
| Resumo: | Quantum computing has the potential to provide better time complexities (than those achieved with classical computers) for challenging problems solved by classical comput ers or even provide a solution for problems out of reach of classical computers in terms of time complexity (where the time consumed for the resolution of the problem is not prac tical, e.g. thousands of years). Here we’re not solving an unsolvable problem but trying to improve its time complexity. There are several problems in rendering that are good can didates to being solved in a quantum fashion. Although previous research has proposed of theoretical ways of doing this, here we present a practical solution. This work takes a first step in applying quantum computing to one of the most fundamental operations in rendering: ray casting. This technique allows computing visibility between two points in a 3D model of the world which is described by a collection of geometric primitives. The algorithm returns, for a given ray, which primitive it intersects closest to its origin. Without a spatial acceleration structure, the complexity for this operation is O(N). The main goal of this work is to use the Grover’s Algorithm, a quantum search algorithm based on ampli tude amplification, to improve the complexity of this problem. This algorithm provides a quadratic speed up allowing for visibility evaluation for unstructured primitives in O( √ N) steps. Due to technological limitations associated with current quantum computers we had to simplify our problem’s structure and in this work the geometrical setup is limited to rectangles and parallel rays (orthographic projection). |
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| Autores principais: | Alves, Carolina Isabel Monteiro |
| Assunto: | Quantum computing Grover’s algorithm Complexity Ray casting Computação quântica Algoritmo de Grover Complexidade |
| Ano: | 2019 |
| 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 has the potential to provide better time complexities (than those achieved with classical computers) for challenging problems solved by classical comput ers or even provide a solution for problems out of reach of classical computers in terms of time complexity (where the time consumed for the resolution of the problem is not prac tical, e.g. thousands of years). Here we’re not solving an unsolvable problem but trying to improve its time complexity. There are several problems in rendering that are good can didates to being solved in a quantum fashion. Although previous research has proposed of theoretical ways of doing this, here we present a practical solution. This work takes a first step in applying quantum computing to one of the most fundamental operations in rendering: ray casting. This technique allows computing visibility between two points in a 3D model of the world which is described by a collection of geometric primitives. The algorithm returns, for a given ray, which primitive it intersects closest to its origin. Without a spatial acceleration structure, the complexity for this operation is O(N). The main goal of this work is to use the Grover’s Algorithm, a quantum search algorithm based on ampli tude amplification, to improve the complexity of this problem. This algorithm provides a quadratic speed up allowing for visibility evaluation for unstructured primitives in O( √ N) steps. Due to technological limitations associated with current quantum computers we had to simplify our problem’s structure and in this work the geometrical setup is limited to rectangles and parallel rays (orthographic projection). |
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