Objectif As progress is made in implementing quantum computers, the question is looming: What will we do with them?This proposal is concerned with the theoretical computer science aspects of this question. Part of this question is concerned with quantum algorithms (WP1). We know of several examples of quantum algorithms with large speedups over the best known classical algorithms, such as Shor's poly-time integer factorization algorithm. While this is evidence that quantum computers will be useful once built, it does not tell us what quantum computers will be used for in practice (probably not much factoring). To ensure that quantum computer users are best able to make use of them, we will focus on developing general techniques for the design of quantum algorithms that can be easily applied by subject-matter experts in different fields to the problems that interest them.We will also consider the constraints of early quantum computers in our algorithm design. First, we would like to understand how the limited memory of early quantum computers will impact what they can do. Some of the most important techniques for designing quantum algorithms are already well-suited to the study of space-bounded computation, and we will generalize and improve these in WP1. To complement this, we will study lower bounds and complexity (WP2), focusing on space-bounded complexity classes, which have many relationships with other complexity classes. Second, since most early users will have to delegate their quantum computations, we would like to understand which quantum algorithms can still be used in various delegated or multiparty settings where some type of security is a consideration. We take the novel approach of using a quantum algorithmic model called span programs to design secure quantum computing protocols (WP3). It turns out that space-bounded models and secure quantum computation are very much related, and understanding this relationship is what ties this proposal together. Champ scientifique natural sciencescomputer and information sciencescomputational scienceengineering and technologyelectrical engineering, electronic engineering, information engineeringelectronic engineeringcomputer hardwarequantum computers Programme(s) HORIZON.1.1 - European Research Council (ERC) Main Programme Thème(s) ERC-2021-STG - ERC STARTING GRANTS Appel à propositions ERC-2021-STG Voir d’autres projets de cet appel Régime de financement HORIZON-AG - HORIZON Action Grant Budget-Based Institution d’accueil STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN Contribution nette de l'UE € 1 499 798,75 Adresse WINTHONTLAAN 2 3526 KV Utrecht Pays-Bas Voir sur la carte Région West-Nederland Utrecht Utrecht Type d’activité Research Organisations Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 499 798,75 Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN Pays-Bas Contribution nette de l'UE € 1 499 798,75 Adresse WINTHONTLAAN 2 3526 KV Utrecht Voir sur la carte Région West-Nederland Utrecht Utrecht Type d’activité Research Organisations Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 499 798,75