Hyper Quantum Criticality – HyperQC is a major initiative with the aim of generating and controlling novel phases of correlated magnetic quantum matter, and of exploring them in high-precision experiments. A combination of new capabilities enabled by the development of instrumentation, pioneering ultra-fast studies and experiments on magnetic model materials will allow both the exploration of fundamental Hamiltonians and fully quantitative tests of quantum criticality in hyper-parameter space: temperature, magnetic field, pressure, energy, momentum and time.