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QI: Fachverband Quanteninformation

QI 2: Quantum Computing and Algorithms I

QI 2.6: Vortrag

Montag, 20. September 2021, 12:00–12:15, H5

Gottesman-Kitaev-Preskill bosonic error correcting codes: a lattice perspective — Jonathan Conrad, •Francesco Arzani, and Jens Eisert — Freie Universität Berlin, Arnimallee 14, 14195 Berlin

Bosonic error correcting codes (ECC) protect the state of a finite-dimensional quantum system by embedding it in the infinite-dimensional Hilbert space of an ensemble of harmonic oscillators. Gottesman-Kitaev-Preskill (GKP) codes are a class of bosonic ECC that rely on translation symmetries of the code-states to detect and correct common errors affecting physical realizations of harmonic oscillators (e.g. photon loss in electromagnetic modes). For example, imposing the correct symmetries on a single oscillator restricts the state-space to that of a qubit. To achieve better noise resilience, the code can be concatenated with a qubit-level ECC. This allows to directly apply the machinery developed for qubits. However, the translation symmetries also establish a formal connection with lattices, which is not fully exploited by usual approaches to concatenated codes (CC). Furthermore, CC are special cases, which are not guaranteed to be optimal given the underlying bosonic nature of the system.

We examine general GKP codes, including concatenated GKP codes, through the lens of lattice theory to understand the structure of this class of stabilizer codes. We derive formal bounds on code parameters, show how different decoding strategies are related and point to natural resource savings that have remained hidden in previous approaches.