  The search for spontaneous pattern formation in equilibrium phases with
genuine quantum properties is a leading direction of current research. In this
work we investigate the effect of quantum fluctuations - zero point motion and
exchange interactions - on the phases of an ensemble of bosonic particles with
isotropic hard-soft corona interactions. We perform extensive path-integral
Monte Carlo simulations to determine their ground state properties. A rich
phase diagram, parametrized by the density of particles and the interaction
strength of the soft-corona potential, reveals supersolid stripes, kagome and
triangular crystals in the low-density regime. In the high-density limit we
observe patterns with 12-fold rotational symmetry compatible with periodic
approximants of quasicrystalline phases. We characterize these quantum phases
by computing the superfluid density and the bond-orientational order parameter.
Finally, we highlight the qualitative and quantitative differences of our
findings with the classical equilibrium phases for the same parameter regimes.
