Bosonic systems for quantum computation and open-system probing

Abstract

Quantum technologies commonly operate on finite-dimensional systems, such as qubits, also known as discrete-variable (DV) systems. Continuous-variable (CV) bosonic systems, which occupy an infinite-dimensional Hilbert space, present a promising alternative. That is the focus of this thesis, which has two main goals. Firstly, we look at probing bosonic systems, to gain information about their dynamics and interaction with their environment. We employ linear response theory, which was recently extended to encompass physical situations where an open quantum system evolves toward a non-equilibrium steady-state. We use the framework put forward by Konopik and Lutz to go beyond unitary perturbations of the dynamics. 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.

Thesis embargoed until 31st December 2025.

Date of Award	Dec 2024
Original language	English
Awarding Institution	Queen's University Belfast
Sponsors	Engineering and Physical Sciences Research Council
Supervisor	Alessandro Ferraro (Supervisor) & Mauro Paternostro (Supervisor)