Implementing gates in a continuous variable optical cluster state

Abstract

Continuous variable measurement-based quantum computation (MBQC) shows great potential for scalable quantum information processing. It has in recent years witnessed an increasing interest due to the simplicity in generating the foundational states – the cluster states – deterministically and in a scalable manner (1,2). There are still numerous steps to be taken towards realizing universal quantum computation but one of the critical steps is the realization of single and two-mode gates. In MBQC, quantum gates are implemented through simple Gaussian measurements of the cluster state: High-efficiency homodyne detection suffices to realize a complete gate set in the two-dimensional sub-space of the Gottesman-Kitaev-Preskill (GKP) qubits. GKP qubits are of particular interest as they allow for the implementation of non-Clifford gates via Gaussian transformation and they are error-correctable by Gaussian transformations (3). Here we present the execution of a complete set of measurement-based Gaussian single- and two-mode gates in a large two-dimensional cluster state (4). The fully programmable gates are also combined into a small-scaled circuit, demonstrating the programmability and flexibility of the setup. These demonstrations are critical steps towards realizing a universal quantum processor based on continuous variables. (1) Larsen et al, Science 366, 369 (2019) (2) Warit et al, Science 366, 373 (2019) (3) Larsen et al, arxiv:2101.03014 (4) Larsen et al, arxiv:2010.14422