Right now, our rocket engines aren't good enough to fly really far into space. Our current engines are too heavy and can't go fast enough.
Antimatter could give us super powerful energy, but we can't make or store it easily. Even if we could use antimatter, we'd still need tons of fuel. Maybe using a special space scoop to collect fuel while moving might help.
Turning antimatter energy into rocket power isn't working well right now. We'd want a spaceship that can speed up at about half or one times Earth's gravity, but our current ion engines are way too weak.
Better space engines might be possible, but this could take hundreds of years to figure out.
Also, the whole world probably can't afford to build a giant spaceship right now. We'd need thousands of people to live on the ship for a trip that takes over 20 years. It would be like a floating city in space.
Maybe in thousands of years we might make a warp drive, but not anytime soon.