Descripción del proyecto
Desarrollo de algoritmos eficientes para el procesamiento óptimo de información
Los altos costes indirectos relacionados con la corrección de los errores provocados por el ruido no deseado dificultan el aprovechamiento pleno de la teoría cuántica en la tecnología de la información. Aunque se ha avanzado en el diseño de mejores códigos de corrección de errores y esquemas tolerantes a fallos, todavía no se comprenden los límites de la comunicación en un medio cuántico ruidoso. El objetivo del proyecto financiado con fondos europeos AlgoQIP es desarrollar una teoría algorítmica de procesamiento óptimo de la información que vaya más allá del enfoque estadístico de la teoría de Shannon. Para ello, creará algoritmos eficientes que tomen como entrada la descripción de un modelo de ruido y como salida un método casi óptimo para una comunicación fiable bajo este modelo. Estos algoritmos tendrán aplicaciones directas en el desarrollo de tecnologías cuánticas.
Objetivo
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.
Ámbito científico
- 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
Programa(s)
Régimen de financiación
ERC-STG - Starting GrantInstitución de acogida
78153 Le Chesnay Cedex
Francia