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Quantum computing has gained significant attention in recent years due to its potential to provide computational advantages in a huge range of scientific and industrial domains. In this seminar, we will present a short historical overview of the field, beginning with Feynman’s original conjectures and the foundational concepts of quantum bits. We will introduce key fault-tolerant quantum algorithms and motivate the challenges and goals of quantum computing. Then we will discuss the current state of the art, major industry players, and a critical view of the field’s promises versus its present limitations. We will conclude with an overview of the Quantum Spain initiative and describe the work being carried out at PIC within this national framework.