An effervescent activity is developing worldwide around a new class of high-power laser and accelerator facilities that will soon lead to the realization of pioneering experiments. These will explore a new regime of particle-light and light-light interaction in which the dynamics of particles and/or plasmas is not only relativistic, but also greatly impacted by strong-field quantum electrodynamics (SF-QED) effects. The g4QED projects aims to produce, characterize, and optimize dense and bright photon sources, up to the GeV level, and to perform such experiments at the multi-beam laser facility Apollon, in France, and at the FACET-II facility at SLAC, US. To obtain such sources and conduct our experiments, a team of closely-working experimentalists, high-performance-simulation specialists and theoreticians follows an ambitious program structured in three experimental work-packages (WPs). Building up on the broad experience of the team, all three WPs explore original approaches to enter the largely unexplored SF-QED regime and drive high-energy (from sub-MeV to few GeV) gamma photon sources of unprecedented brightness. Synergies between all three approaches will allow to push forward an innovative program of experimental campaigns. The explored concepts are particularly promising since they are ideally suited to realize the first collisions between high-energy electron or gamma flashes and photons in the SF-QED regime. The experimental WPs are supported by two transversal WPs. The first aims to develop versatile diagnostics for high-energy photons and charged particles (electrons and positrons). The diagnostics will be designed to operate with high sensitivity in extreme environments. The second will provide the necessary theoretical and simulation support to help design and interpret the envisioned experimental program. Theoretical models will be supported by large-scale simulations using the most advanced particle-in-cell codes embarking SF-QED capabilities.
