Description du projet
De nouvelles techniques sous-tendent la conception d’algorithmes quantiques efficaces
La réussite du calcul quantique dépend essentiellement des avancées réalisées au niveau le plus fondamental. Les algorithmes quantiques efficaces peuvent avoir un impact considérable sur des problèmes importants à large portée, en résolvant les problèmes mathématiques plus rapidement que leurs homologues classiques. Bien que plusieurs algorithmes quantiques puissants soient connus, les techniques de base qu’ils utilisent sont rares. Le projet FoQaCiA, financé par l’UE, entend étendre la base théorique pour la conception d’algorithmes quantiques. Pour ce faire, les chercheurs étudieront quatre domaines de la phénoménologie quantique: la contextualité quantique, la non-classicalité et la suprématie quantique; la complexité des simulations classiques de calculs quantiques; l’arithmétique des circuits quantiques; et l’efficacité du calcul quantique tolérant aux fautes.
Objectif
In FoQaCiA, we will expand the theoretical basis for the design of quantum algorithms. Our view is that the future success of quantum computing critically depends on advances at the most fundamental level, and that large-scale investments in quantum implementations will only pay off if they can draw on additional foundational insights and ideas. While several powerful quantum algorithms are known, the basic techniques they employ are few and far between. Largely, it still remains to be discovered how to systematically harness the quantum for computation.
We study four areas of quantum phenomenology: (i) Quantum contextuality, non-classicality, and quantum advantage, (ii) Complexity of classical simulation of quantum computation, (iii) Arithmetic of quantum circuits, and (iv) Efficiency of fault-tolerant quantum computation.
These fields are chosen for two reasons. First, their progress is of great importance for the physical realisation and the broad applicability of quantum computation. Regarding (i), one of the simplest proofs of quantum contextuality, Mermin’s star, has recently been employed to prove (Bravyi, Gosset, König) that bounded-depth quantum circuits are more powerful than their classical analogues. We seek to expand this result beyond bounded depth. In (ii), we study the quantum speedup by shaving off the redundant part – the efficiently classically simulable. In (iii), we aim to provide more efficient techniques for gate and circuit synthesis, utilising the number-theoretic underpinnings of the problem. Regarding (iv), given the celebrated threshold theorem, and the fact that the error threshold is now known to be within reach of experiment, we will tackle the remaining challenge of reducing the cost of fault tolerance.
The second reason for selecting the above work areas is to mine them for foundational quantum mechanical structures and find related quantum algorithmic uses.
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HORIZON-RIA - HORIZON Research and Innovation ActionsCoordinateur
4715-330 Braga
Portugal