On quantum supervised learning and learning techniques for quantum error mitigation
(English) The development of quantum computers promises to drastically reduce the time required to solve certain computational problems. Among their most promising applications is the field of machine learning. However, significant uncertainty remains in this area. In particular, it is still unclear...
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| Tipo de recurso: | tesis doctoral |
| Fecha de publicación: | 2026 |
| 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:2117/457070 |
| Acceso en línea: | https://hdl.handle.net/2117/457070 https://dx.doi.org/10.5821/dissertation-2117-457070 |
| Access Level: | acceso abierto |
| Palabra clave: | supervised learning quantum computing quantum error mitigation quantum advantage quantum hypothesis testing 004 - Informàtica Àrees temàtiques de la UPC::Informàtica |
| Sumario: | (English) The development of quantum computers promises to drastically reduce the time required to solve certain computational problems. Among their most promising applications is the field of machine learning. However, significant uncertainty remains in this area. In particular, it is still unclear under which learning scenarios quantum algorithms will outperform their classical counterparts. This thesis aims to deepen our understanding of when quantum speed-ups can be expected in machine learning tasks. Specifically, we examine the connection between learning speed-ups and the more extensively studied phenomenon of quantum computational speed-up. We conclude that, in cases where the training set can be classically generated, the two are equivalent concepts, and we provide examples of such functions based on the prime factorization problem. Importantly, quantum machine learning is not only concerned with improving classical learning algorithms using quantum computation but also with learning from quantum data. In this context, we investigate a learning scenario in which the inputs to the target functions are quantum states, thereby generalizing the classical supervised learning framework. To this end, we first focus on the problem of quantum hypothesis testing, which can serve as a subroutine for both the problems of evaluating a function and learning a function. Specifically, we derive several sequential methods for solving the problem of quantum hypothesis testing, along with a lower bound on the resources required. This lower bound immediately implies corresponding lower bounds for the problems of learning and evaluating functions. Additionally, we develop a learning method based on the classical shadows technique. Finally, after exploring how quantum processes can aid learning tasks, we examine how classical learning techniques can, in turn, enhance quantum computing. In particular, we study how classical machine learning methods can be used to mitigate the effects of noise in quantum devices, with a focus on quantum error mitigation. Specifically, novel feature maps are proposed for the technique known as Clifford data regression. First, a theoretical justification for these feature maps is provided, followed by an analysis and a subsequent evaluation of their performance through numerical experiments. It is concluded that, for some of the proposed feature maps, a performance improvement is indeed achieved. |
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