Antimatter moves mass not space. Its a no-go because of all of the issues--time dilation? You need to move space, but we still haven't found a way to fully create negative energy.
I have no idea what that means. Care to clarify?
But there have been proposals for other ways of traveling through space, that involve manipulating space itself, so the distance between point A and point B are smaller. Think of wormholes, or similar. One such proposal is the Alcubierre drive, which warps space around it to cause the total distance traveled to get from point A to point B to be much smaller.
But such exotic drives require exotic forms of matter that we have no evidence of
IIRC The Alcubierre drive would require a significant fraction of the mass-energy of the entire universe to work.
We need a Douglas Adams-style infinite improbability drive!