Description du projet
Développer des algorithmes efficaces pour un traitement optimal de l’information
L’importance des ressources requises pour corriger les erreurs liées au bruit indésirable entravent l’exploitation de la théorie quantique dans les technologies de l’information. Bien que des progrès aient été accomplis pour concevoir de meilleurs codes de correction des erreurs et des systèmes tolérants aux pannes, les facteurs limitant les communications sur un support propice au bruit quantique ne sont toujours pas compris. Le projet AlgoQIP, financé par l’UE, vise à élaborer une théorie algorithmique du traitement optimal de l’information qui va au-delà de l’approche statistique de la théorie de Shannon. Il y parviendra en développant des algorithmes efficaces qui recevront en entrée la description d’un modèle de bruit, et renverront en sortie une méthode quasi optimale pour une communication fiable dans le cadre de ce modèle. Ces algorithmes auront des applications directes dans le développement des technologies quantiques.
Objectif
In the road towards quantum technologies capable of exploiting the revolutionary potential of quantum theory for information technology, a major bottleneck is the large overhead needed to correct errors caused by unwanted noise. Despite important research activity and great progress in designing better error correcting codes and fault-tolerant schemes, the fundamental limits of communication/computation over a quantum noisy medium are far from being understood. In fact, no satisfactory quantum analogue of Shannon’s celebrated noisy coding theorem is known.
The objective of this project is to leverage tools from mathematical optimization in order to build an algorithmic theory of optimal information processing that would go beyond the statistical approach pioneered by Shannon. Our goal will be to establish efficient algorithms that determine optimal methods for achieving a given task, rather than only characterizing the best achievable rates in the asymptotic limit in terms of entropic expressions. This approach will address three limitations — that are particularly severe in the quantum context — faced by the statistical approach: the non-additivity of entropic expressions, the asymptotic nature of the theory and the independence assumption.
Our aim is to develop efficient algorithms that take as input a description of a noise model and output a near-optimal method for reliable communication under this model. For example, our algorithms will answer: how many logical qubits can be reliably stored using 100 physical qubits that undergo depolarizing noise with parameter 5%? We will also develop generic and efficient decoding algorithms for quantum error correcting codes. These algorithms will have direct applications to the development of quantum technologies. Moreover, we will establish methods to compute the relevant uncertainty of large structured systems and apply them to obtain tight and non-asymptotic security bounds for (quantum) cryptographic protocols.
Champ scientifique
- natural sciencesphysical sciencesquantum physics
- natural sciencescomputer and information sciencescomputer securitycryptography
- engineering and technologyelectrical engineering, electronic engineering, information engineeringelectronic engineeringcomputer hardwarequantum computers
- natural sciencescomputer and information sciencesdata sciencedata processing
Programme(s)
Thème(s)
Régime de financement
ERC-STG - Starting GrantInstitution d’accueil
78153 Le Chesnay Cedex
France