Projektbeschreibung
Entwicklung von effizienten Algorithmen zur optimalen Informationsverarbeitung
Der hohe Aufwand, der zum Korrigieren von Fehlern notwendig ist, die durch ungewolltes Rauschen verursacht werden, verhindert die Anwendung der Quantentheorie in der Informationstechnologie. Obwohl es Fortschritte bei der Entwicklung besserer Fehlerkorrekturcodes und fehlertoleranter Schemata gibt, bestehen noch immer Wissenslücken zu den Grenzen der Kommunikation über ein von Rauschen geprägtes Quantenmedium. Das EU-finanzierte Projekt AlgoQIP möchte eine algorithmische Theorie für eine optimale Informationsverarbeitung aufstellen, die über den statistischen Ansatz der Theorie von Shannon hinausgeht. Dazu sollen effiziente Algorithmen entwickelt werden, bei denen die Beschreibung eines Rauschmodells eingegeben und eine nahezu optimale Methode für eine zuverlässige Kommunikation unter diesem Modell ausgegeben werden. Diese Algorithmen werden eine direkte Anwendung in der Entwicklung von Quantentechnologien finden.
Ziel
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.
Wissenschaftliches Gebiet
- 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
Programm/Programme
Thema/Themen
Finanzierungsplan
ERC-STG - Starting GrantGastgebende Einrichtung
78153 Le Chesnay Cedex
Frankreich