The properties of quantum materials are anomalously sensitive to external stimuli. At high-energy-density (HED) conditions, the orbital wavefunction overlap between neighboring sites in a crystal, then increases, in turn increasing the ratio of kinetic (inter-site charge hopping) to potential (on-site Coulomb repulsion) energy, providing a wealth of correlated electron phenomena, e.g., insulator-metal transitions, colossal magnetoresistance, valence fluctuations, superconductivity, superfludity, electrides, topological order, and quantum magnetic order (1-8). The occurrence of such a wide range of correlated electron phenomena arises from a delicate interplay between competing interactions that can be manipulated by tuning the energy density of matter in the HED regime, offering a raft of rich and unexplored phase space for the study of quantum phases of matter (see Figure). These conditions create a new quantum HED frontier, one that can transfer (harness) quantum properties to (at) high temperatures. This new HED quantum realm can be separated into two regimes: (1) core electron chemistry, and (2) the extreme compression states of hydrogen-rich systems (no core electrons), which leads to a new generation of hot superconductors.