Bosonic lattice codes

• Applicant: Professor Dr. Jens Eisert
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 545592371

Quantum computers offer great promise for solving currently intractable computational problems. However, to exploit delicate quantum effects, error correction schemes will be essential. While qubits are the most studied theoretical objects, including for the development of quantum error correcting codes, an alternative is to consider so-called bosonic systems. These are mathematically more complicated but describe a vast range of natural and engineered systems. In the past five years, experimental research in bosonic error has shown enormous progress, culminating with the first demonstration of a net gain in shielding encoded quantum information. This has been achieved with a particular class of codes known as Gottesman-Kitaev-Preskill (GKP) codes. Despite their promise, no single platform has proven substantially better than others and research efforts have focussed on specific implementations, either in cold atoms, superconducting or photonic setups. A full high-level description is then direly needed to compare different realizations between themselves and with the theoretically optimal performances. The BoLaCo project aims at developing such a common language based on the theory of lattices, and to use it for the analysis of GKP codes and comparison of experimental implementation. In particular, we will take advantage of the tools developed to study classical lattice codes for error correction and post-quantum cryptography, focussing on three main scientific work packages. The first will consist in exploring the mathematical structure of GKP codes, their relation to other codes and their performance in realistic, physically plausible scenarios. The second work package will be devoted to practical gadgets required for active error correcting schemes, namely constructing efficient algorithms for encoded state preparation, encoded computation and decoding. Finally, the third work package will explore the potential of GKP codes to devise cryptographic schemes. The scope of the project will also include to create a multi-disciplinary network including experimentalists and computer scientists to adopt and help develop an appropriate mathematical formalism that can be practically useful.

• DFG Programme: Research Grants
• International Connection: France
• Partner Organisation: Agence Nationale de la Recherche / The French National Research Agency
• Cooperation Partner: Professor Dr. Francesco Arzani