  Event generators simulate particle interactions using Monte Carlo techniques,
providing the primary connection between experiment and theory in experimental
high energy physics. These software packages, which are the first step in the
simulation worflow of collider experiments, represent approximately 5 to 20% of
the annual WLCG usage for the ATLAS and CMS experiments. With computing
architectures becoming more heterogeneous, it is important to ensure that these
key software frameworks can be run on future systems, large and small. In this
contribution, recent progress on porting and speeding up the Madgraph5_aMC@NLO
event generator on hybrid architectures, i.e. CPU with GPU accelerators, is
discussed. The main focus of this work has been in the calculation of
scattering amplitudes and "matrix elements", which is the computational
bottleneck of an event generation application. For physics processes limited to
QCD leading order, the code generation toolkit has been expanded to produce
matrix element calculations using C++ vector instructions on CPUs and using
CUDA for NVidia GPUs, as well as using Alpaka, Kokkos and SYCL for multiple CPU
and GPU architectures. Performance is reported in terms of matrix element
calculations per time on NVidia, Intel, and AMD devices. The status and outlook
for the integration of this work into a production release usable by the LHC
experiments, with the same functionalities and very similar user interfaces as
the current Fortran version, is also described.
