The Octo-Rail lattice: a four-dimensional cluster state design

Abstract: Macronode cluster states are a natural candidate to implement fault-tolerant continuous-variable quantum computation in the optical context. They achieve universality with built-in error correction by combining gate teleportation via homodyne detection with the Gottesman-Kitaev-Preskill code. Out of the different macronode designs, the two-dimensional Quad-Rail lattice was shown to exhibit favorable properties regarding flexibility and noise. However, it lacks the dimensionality to run topological error correction codes needed to achieve fault-tolerance.
In this work, we use time-domain-multiplexing to generate a four-dimensional cluster state called the Octo-Rail lattice. This new macronode design combines the noise properties and flexibility of the Quad-Rail lattice with the possibility to run various topological error correction codes including surface and color codes. Besides, the presented experimental setup is easily scalable and includes only static components allowing for a straight-forward implementation.
We are able to show, that a source of GKP qunaught states with a squeezing above the threshold of 10.1 dB is sufficient to render our design universal and fault-tolerant, without the need for any further resources such as non-Gaussian states or feed-forward operations. Consequently, we can conclude, that the remaining difficulty in building an optical quantum computer lies in the experimental generation of these highly non-classical states.
Finally, we introduce a generalisation of our design to arbitrary dimensions, where the setup size scales linearly with the number of dimensions. We believe that this general scheme will prove useful in applications such as state multiplexing and state injection.

This seminar is part of a visit sponsored by WACQT’s Guest Researcher Programme (GRP).