No, we don't even know if warp drives are allowed by the laws of physics. We have a pretty good idea how to do hibernation: Saturate the tissue with some cryoprotectant and freeze it very quickly. The problem is that we don't have a cryoprotectant that is sufficiently non-toxic and we can't freeze anything as big as a human quickly enough.
Yeah and since nobody knows whether the exotic matter needed actually exists, we don't know whether bending spacetime in the required way is physically possible.
On the other hand, we can successfully freeze and thaw bunny kidneys.
