Bosonic systems for quantum computation and open-system probing

Considering an open system comprised of two coupled quantum harmonic oscillators, we study the system's response to unitary perturbations, as well as non-unitary perturbations, affecting the properties of the environment, e.g., its temperature and squeezing. We show that linear response, combined with a quantum probing approach, can provide valuable quantitative information about the perturbation and characteristics of the environment.

Secondly, we investigate bosonic quantum computation, which involves encoding discrete quantum information into continuous-variable quantum systems. CV quantum computation was introduced by Braunstein and Lloyd, who put forward a notion of universality that is independent of the encoding of the CV system. However, a proof that the Braunstein-Lloyd (BL) model allows for fault-tolerant computation is still missing.

Here, we provide evidence towards this objective, using the Gottesman-Kitaev-Preskill (GKP) encoding. We show how to generate GKP states from vacua by optimising a circuit comprised of a set of CV gates, deemed universal according to the BL notion. We compute the threshold value of the Glancy-Knill error probability for a fault-tolerant quantum memory from the known squeezing threshold for the concatenated GKP-surface code.

We demonstrate that our generated GKP states have error probabilities below this threshold, further corroborating our claim.<br>