Noise analysis and error correction on experimentally accessible continuous variable cluster states
Creators: name: Walshe, Blayney
Publisher: name: RMIT University
Year: 2024
Subjects: classificationCode: 510803
subject: Quantum information, computation and communication

description: Quantum computing promises to revolutionise many industries by overcoming problems that are out of reach of classical computation, even were we to scale up our current capabilities immensely. Fields of research such as medicine, materials design, and anything requiring complex simulations hope to benefit from quantum computers.

Continuous variable quantum computing is a promising architecture that overcomes many of the problems associated with other quantum computing architectures. Room tem- perature operation, immense scalability, and the utilisation of common optical components are all reasons to choose continuous variable quantum computing in the optical regime. However, continuous-variable quantum computing comes with its own challenges. It relies on logical states that are not noise free (and cannot be, due to finite energy constraints). Gottesman, Kitaev, and Preskill (GKP) error correction uses noisy logical states to convert continuous variable noise into a probability for a logical error. Despite this, in order for continuous-variable quantum computation to be fault-tolerant it needs high quality GKP states, which are challenging to produce.

Within this body of work I address the noise that impacts continuous-variable quantum computation. I reduce the reported squeezing level required to reach certain gate-noise levels. When those levels are low enough to meet the error correction threshold of a quantum error correction code, continuous-variable quantum computation is fault-tolerant with that code. First I demonstrate how to perform GKP error correction on physically realisable continuous-variable cluster states. I show that both gates and error correction can be performed at the same time, reducing the number of modes required to perform a fault- tolerant gate operation. Then, I extend those results to two-mode gates and demonstrate single-step two-mode gates in the quad rail lattice, a scalable continuous-variable cluster state that allows for universal quantum computation. I further expand my findings into a whole class of scalable, universal cluster states beyond the quad rail lattice, called macronode-based cluster states. In doing so, I reduce the requirements on the quality of GKP resource required to achieve fault-tolerance to a minimum for all macronode-based cluster states that are constructed by a balanced four splitter, a type of linear-optical network classified within this body of work. I apply these findings to a further set of macronode-based cluster states that are constructed by incomplete versions of the balanced four splitter.

Beyond the main results, this thesis also contains many smaller tools that have proved invaluable to me throughout my research, and which can serve others in their investigation into continuous-variable quantum computation. These include previously unknown de- compositions of Gaussian unitary gates, the generalised teleported gate arising from the combination of any two arbitrary states via a beam splitter, and alternate ways to arrange macronode-based cluster states to find more efficient uses of them.