  We calculate the Drude weight in the superfluid (SF) and the supersolid (SS)
phases of hard core boson (HCB) model using stochastic series expansion (SSE).
We demonstrate from our numerical calculations that the normal phase of HCBs in
two dimensions can be an ideal conductor with dissipationless transport. In two
dimensions, when the ground state is a SF, the superfluid stiffness drops to
zero with a Kosterlitz-Thouless type transition at $T_{KT}$. The Drude weight,
though is equal to the stiffness below $T_{KT}$, surprisingly stays finite even
for temperatures above $T_{KT}$ indicating the non-dissipative transport in the
normal state of this system. In contrast to this in a three dimensional SF
phase, where the superfluid stiffness goes to zero continuously with a second
order phase transition at $T_c$, Drude weight also goes to zero at $T_c$ as
expected. We also calculated the Drude weight in a 2D SS phase, where the
charge density wave (CDW) order coexists with superfluidity. For the SS phase
we studied, superfluidity is lost via Kosterlitz-Thouless transition at
$T_{KT}$ and the transition temperature for the CDW order is larger than
$T_{KT}$. In striped SS phase where the CDW order breaks the rotational
symmetry of the lattice, for $T > T_{KT}$, the system behaves like an ideal
conductor along one of the lattice direction while along the other direction it
behaves like an insulator. In contrast to this, in star-SS phase, Drude weight
along both the lattice directions goes to zero along with the superfluid
stiffness and for $T > T_{KT}$ we have a finite temperature phase of a CDW
insulator.
