Electric motors. I can't see how you'd get anywhere near the power that you need. Maybe you could have four huge gas turbines as power generators, running small electric motors...and you'd end up with an aviation Prius. Horrid in every way.
The gas turbine power plant that we used to operate consisted of 6 generators of 50MW each. Each generator had 2 P&W gas fired aero derivative turbines tacked onto them. Nominally of 25MW each.
To give you an idea of their power output and size these engines shared components with engines on older 707 turbo-jets and newer 737 engines.
I would imagine that an A380 engine could easily run a 100MW generator. And the ones that I've seen at Avalon and down at Mortlake are friggin' huge in comparison. And those are rated in hundreds of megawatts.
So, putting all this into perspective, an electric motor driving a fan to give that sort of thrust or propulsion would weigh 50t or more. Not to mention the cabling, and of course, the generator source, which, in this case, would be something like a RR Trent 900 connected to an equally heavy generator...
Or 4 of them...
And if they decide to burn anything that burns but is susceptible to temperatures, then the cost of trace heating, not to mention the risks involved in using such technology, surely would be prohibitive?
For better or for worse, we're stuck with the status quo, I would think. At least until we run out of the stuff...