- Accelerate the ship be pointing lasers (or something that accelerates matter) at it from the launch point. Now one doesn't need to carry fuel and the rocket equation no longer applies.
- Use some form of ion engine where we accelerate particles to very high speed relative to chemical rockets. This makes the rocket equation very tame since so little of the mass (relatively speaking) is in propellant.
- Combine the above ion engine with some form of "ramjet" that takes hydrogen we collide with and turns it into fuel. This makes the rocket equation irrelevant since we don't carry our fuel (to the extent that we can get our fuel via the ramjet anyways).
Also as laumars says the 0.1% of annual energy usage was just a point of comparison because terwatts is such a foreign unit to most of us (including me) that it doesn't mean anything by itself.
The first rule of rocketry: For every ton you fire up add 10 tons to what you fire up.
There is a reason space is hard and that is that every ton you launch will require fuel to get into orbit. And now you have to accelerate the fuel for the majority of the way too so you need more fuel. But that also needs fuel ... etc.
Shooting up 0.1% of our annual energy usage will require an exponential amount of energy to get up.
The biggest rocket I ever build in KSP weighed in at 500'000 tons. With a 1 ton payload it only achieves about 250km/s acceleration. That's less than c/1000.
The Saturn V weighs 3'000 tons and has significantly less thrust (though NASA engines outperform KSP engines).
It's simply not realistic to achieve unless you manage to fire up the mentioned 0.1% of our current annual energy production PER ton of weight.
It doesn't seem likely to me that that is the case. The energy/time requirements to go the closest neighbouring star aren't really that high in the grand scheme of things. Accelerating one ton to c/10 takes 125 terrawatt hours, less than 0.1% of our current annual energy usage. We could then reach the nearest star/expolanet in ~40 years (taking a similar amount of energy to decelerate).
Obviously we aren't putting that much energy into a rocket tomorrow, but give it a few hundred years of technology development and it seems pretty reasonable.