Today's "It's is easy if you can turn the entire mass of Jupiter into energy" faster-than-light travel strategy is brought to you by the Telegraph online.
Just how long this might take may depend on your view of man's handling of energy over time. If water wheels or even fire counts as man's first successful effort at controlling outside energy, it took thousands or even tens of thousands of years for us to make much progress increasing that amount. However, if you start the clock at steam, it only took about a century to go from controlling the equivalent of a few dozen horses to controlling the equivalent of several million*. If we take that sort of progression and project it forward, maybe converting 2000,000,000,000,000,000,000,000,000 kilograms of matter into energy isn't completely out of the reach of the near future.