If you look at the output transistors of the two opamps arranged in a "bridged speaker" configuration, you'll notice that they look just like a H-bridge. There isn't anything particularly special about H-bridges - just add an opamp to linearize each side, and you'll see the power dissipation associated with linear amps, and the speaker will see a larger voltage swing across it.
If you want to the class D amplifier that audioguru mentioned, that'll probably be a bit trickier.