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Beyond Shannon: Algorithms for optimal information processing

Project description

Developing efficient algorithms for optimal information processing

The large overhead needed to correct errors caused by unwanted noise hinders the exploitation of quantum theory in information technology. Although there has been progress in designing better error-correcting codes and fault-tolerant schemes, the limits of communication over a quantum noisy medium are still not understood. The EU-funded AlgoQIP project aims to build an algorithmic theory of optimal information processing that goes beyond the statistical approach of Shannon’s theory. It will achieve this by developing efficient algorithms that take as input a description of a noise model and output a near-optimal method for reliable communication under this model. These algorithms will have direct applications in the development of quantum technologies.

Objective

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.

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Programme(s)

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Topic(s)

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Funding Scheme

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ERC-STG - Starting Grant

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Call for proposal

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(opens in new window) ERC-2019-STG

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Host institution

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE
Net EU contribution

Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.

€ 1 492 733,00
Address
DOMAINE DE VOLUCEAU ROCQUENCOURT
78153 Le Chesnay Cedex
France

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Total cost

The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.

€ 1 492 733,00

Beneficiaries (1)

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