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Create Date 30 October, 2023
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We present a summary of the state of the art of the most relevant quantum algorithms for mathematical research, including the problems they solve, as well as their advantages, limitations, and open issues.

This report aims to provide mathematic professionals with an accessible introduction to quantum computing, along with a summary of current quantum computing trends and open problems. It follows key principles: self-containment, a focus on mathematics, interdisciplinary coverage, brevity, transparency, and resource exploration. The report is divided into two parts, the first introducing quantum computing concepts, and the second presenting bibliographic resources, problems, and algorithms. It also addresses industry applications and the status of quantum computing in Spain, concluding with an alphabetical term index.