Figure 1: (a) A classical system of Brownian spheres may crystallize at low temperatures if cooled slowly. By contrast, a bi-disperse system (i.e., consisting of two different kinds of hard spheres) such as the one shown cannot crystallize and will jam into a glass at high densities and low temperatures. Similarly, a rapidly cooled system of hard spheres does not have enough “time” to crystallize and forms a glass instead. Using the mapping of [7], it is seen that the quantum analog of the classical hard-sphere Brownian system is that of spheres with sticky interactions. In the classical hard-sphere limit, only pair interactions appear in the corresponding quantum system. (b) The pair potential in the corresponding quantum system given by Biroli et al. [1] (for two values of $\lambda$, a parameter that adjusts how hard the classical potential is, where $r$ is the interparticle distance and $\sigma$ is the sphere diameter) and the corresponding phase diagrams, shown in (c). Top: The solid curve indicates the classical Brownian hard-sphere phase diagram (pressure $P$ versus volume fraction $\varphi$) for uniform annealed systems wherein spheres forming a liquid at low densities pack into a face-centered-cubic (FCC) crystal structure at high densities. The dashed curve shows the phase diagram of a rapidly quenched or bi-disperse system in which crystallization is thwarted and the system becomes a glass instead [random close packing (RCP)]. Bottom: The corresponding quantum phases obtained by the map of [7]. The liquid-to-solid transition of the classical Brownian sphere system maps into a superfluid to supersolid transition. Similarly, the superfluid to superglass transition constitutes an analog of the classical liquid to glass transition. [ Panels (b) and (c) adapted from Biroli et al. [1].]