Team, Visitors, External Collaborators
Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Partnerships and Cooperations
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Section: New Results

Quantum Information

Participants : Simon Apers, Ivan Bardet, Xavier Bonnetain, Rémi Bricout, André Chailloux, Simona Etinski, Antonio Florez Gutierrez, Shouvik Ghorai, Antoine Grospellier, Lucien Grouès, Anthony Leverrier, Vivien Londe, María Naya Plasencia, Andrea Olivo, Jean-Pierre Tillich, André Schrottenloher, Christophe Vuillot.

Our research in quantum information focusses on several axes: quantum codes with the goal of developing better error-correction strategies to build large quantum computers, quantum cryptography which exploits the laws of quantum mechanics to derive security guarantees, relativistic cryptography which exploits in addition the fact that no information can travel faster than the speed of light and finally quantum cryptanalysis which investigates how quantum computers could be harnessed to attack classical cryptosystems.

Quantum codes

Protecting quantum information from external noise is an issue of paramount importance for building a quantum computer. It also worthwhile to notice that all quantum error-correcting code schemes proposed up to now suffer from the very same problem that the first (classical) error-correcting codes had: there are constructions of good quantum codes, but for the best of them it is not known how to decode them in polynomial time.

Two PhD theses have been defended this year within the project-team on this topic. First, Antoine Grospellier, co-advised by A. Leverrier and O. Fawzi (Ens Lyon), studied efficient decoding algorithms for quantum LDPC codes [13]. Beyond their intrinsic interest for channel-coding problems, such algorithms would be particularly relevant in the context of quantum fault-tolerance, since they would allow to considerably reduce the required overhead to obtain fault-tolerance in quantum computation. Vivien Londe, co-advised by A. Leverrier and G. Zémor (IMB), worked on the design of better quantum LDPC codes [14]: the main idea is to generalize the celebrated toric code of Kitaev by considering cellulations of manifolds in higher dimensions. A surprising result was that this approach leads to a much better behaviour than naively expected and a major challenge is to explore the mathematics behind this phenomenon in order to find even better constructions, or to uncover potential obstructions.

Lucien Grouès, who did an internship this summer in the project-team, has recently started a PhD with A. Leverrier and O. Fawzi on decoding quantum LDPC codes, and preliminary numerical results have already appeared in [62].

Ivan Bardet joined the project-team as a postdoc in March 2019, and will start a starting research position in 2020. His research focusses on the study of open-system dynamics as well as mixing times of Markovian dissipative evolutions with the goal of better understanding the lifetime of quantum memories.

Recent results:

Quantum cryptography

Quantum cryptography exploits the laws of quantum physics to establish the security of certain cryptographic primitives. The most studied one is certainly quantum key distribution, which allows two distant parties to establish a secret using an untrusted quantum channel. Our activity in this field is particularly focussed on protocols with continuous variables, which are well-suited to implementations. The interest of continuous variables for quantum cryptography was recently recognized by being awarded a 10 M€ funding from the Quantum Flagship and SECRET contributes to this project by studying the security of new key distribution protocols.

Recent results:

Quantum cryptanalysis of symmetric primitives and quantum algorithms

Symmetric cryptography seems at first sight much less affected in the post-quantum world than asymmetric cryptography: its main known threat seemed for a long time Grover's algorithm, which allows for an exhaustive key search in the square root of the normal complexity. For this reason, it was usually believed that doubling key lengths suffices to maintain an equivalent security in the post-quantum world. However, a lot of work is certainly required in the field of symmetric cryptography in order to “quantize” the classical families of attacks in an optimized way, as well as to find new dedicated quantum attacks. M. Naya Plasencia has been awarded an ERC Starting grant for her project named QUASYModo on this topic.

In parallel to this work, S. Apers is developing generic quantum algorithms solving combinatorial problems, notably in graphs. He also recently proposed a unified framework of quantum walk search, that will likely find applications in the context of quantum cryptanalysis.

Recent results: