A lot of physical phenomea are modelled by Hamiltonian systems, which are entirely determinated by a real function called the Hamiltonian, which represents the energy of the system. One of the major property of the flow is that it is a symplectomorphism, i.e. an application which preserves a differential 2-form called the symplectic form or symplectic structure of the phase space over time. When numerically solving Hamiltonian equations, taking this property into account using methods that preserve the symplectic structure ensures better stability over long time and physical consistency [1]. When using a neural network to solve a Hamiltonian equation while preserving the symplectic structure, a specific architecture must be considered, using symplectic layers. A well-known symplectic architecture used to learn Hamiltonian ODEs was proposed in [2]. Here, we propose a way to extend this framework to Hamiltonian PDEs and propose two architectures of symplectic neural operators. We compare the performance with non-symplectic neural operators for wave equation in a heterogeoous medium and the Korteweg-de Vries equation. [1] Hairer E., Lubich C., Wanner G., \emph{Geometric numerical integration}, second edition, Berlin, Springer, 2006. [2] Jin P., Zhang Z., Zhu A., Tang Y., Karniadakis G., \emph{SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems}, Neural Networks, vol. 132, PP. 166-179, 2020.