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

TL;DR

This paper introduces the Octo-Rail Lattice, a four-dimensional cluster state for fault-tolerant quantum computing, combining topological error correction with scalable optical implementation using time multiplexing.

Contribution

It presents a novel four-dimensional cluster state design that enables fault-tolerant quantum computation with scalable, static optical components and integrates topological error correction codes.

Findings

Achieves fault-tolerance with 9.75 dB squeezing threshold.

Compatible with GKP qunaught states and surface code.

Scalable setup with linear size growth in dimensions.

Abstract

Macronode cluster states are promising for fault-tolerant continuous-variable quantum computation, combining gate teleportation via homodyne detection with the Gottesman-Kitaev-Preskill code for universality and error correction. While the two-dimensional Quad-Rail Lattice offers flexibility and low noise, it lacks the dimensionality required for topological error correction codes essential for fault tolerance. This work presents a four-dimensional cluster state, termed the Octo-Rail Lattice, generated using time-domain multiplexing. 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 optical components allowing for a straight-forward implementation. Analysis demonstrates that the Octo-Rail Lattice, when combined with GKP qunaught states and the surface code, exhibits noise performance compatible with a fault-tolerant threshold of 9.75 dB squeezing. This ensures universality and fault-tolerance without requiring additional resources such as other non-Gaussian states or feed-forward operations. This finding implies that the primary challenge in constructing an optical quantum computer lies in the experimental generation of these highly non-classical states. Finally, a generalisation of the design to arbitrary dimensions is introduced, where the setup size scales linearly with the number of dimensions. This general framework holds promise for applications such as state multiplexing and state injection.