Warm dense matter (WDM) is a thermodynamic regime typified by quantum degeneracy in the presence of significant thermal excitation. It occurs in certain astrophysical objects, planetary interiors, and inertial confinement fusion targets on their way to ignition. In fact, the properties of materials in these extreme conditions play a critical role in the hydrodynamic instabilities that limit the performance of inertial fusion energy designs. However, creating and studying WDM requires access to expensive and specialized experimental facilities that produce short-lived and non-uniform samples at low repetition rates. Thus computer simulations of WDM are especially valuable and they occupy a significant fraction of the operating cycles on some of the world’s largest supercomputers. However, even the best classical simulations are subject to severe uncertainties due to uncontrolled approximations that are difficult to quantify.