It might be that abundant energy solutions for the future might involve bold leaps from where we are now.
Bold leaps might be required but it appears that some of the technological approaches listed currently have dubious status. Some are mere ideas with little research to support them currently. Some have dubious research whereby it is not at all clear if the proposed approaches actually work, or if they do work they lack convincing scientific proof - which requires replication by other scientists in the appropriate area of expertise.
This does not necessarily mean that such approaches will not work, but it does mean that extensive scientific testing and evaluation might be needed to demonstrate that such approaches are viable. In some cases the cost and duration of such validation exercises might be beyond the scope of the XPRIZE challenge. For example, even the relatively promising high temperature nuclear fusion process being demonstrated by ITER involves billions of dollars and a project that spans decades!
Having said that many of the XPRIZE submissions for an abundant energy solution might seem dubious from some perspectives - even the winning submission. So some thought might have to go into the design of the challenge with regard to this aspect.
Innovative Solutions: No New Energy Required
We all agree that the deployment of an abundant, clean, affordable energy source would benefit all, and the environment. To do this we do need an innovation solution. This topic is very interesting to me because my job, and much of my life, has focused around innovation and the environment. So I feel tuned in to the issues and the potential solutions.
We need an abundant energy source: something that can provide more energy than we currently use - to allow for growth but also to deliver better quality lives for those in the developing world, and everyone wherever they are.
Some people miss the obvious. We don't need to discover a new type of physics or a new type of energy. We already have much more energy around us than we can use: Sun, oceans (waves, tidal, thermal gradient), wind, geothermal, etc.
The secret is to use innovation to grab these huge quantities of energy in a much more effective and efficient way. Innovative thinking will find the solutions. And, when we need even more energy (in the next century) we'll start to harness much more of the Sun's energy in space.
The energy sources are all known, and they provide much more energy than we need.
Centuries from now when the Sun has been fully utilised [if we still exist] then we'll probably progress to collecting energy near a black-hole - but that's way in the future.
The key point is that we have vast amounts of energy available - we just need an innovative way to grab it.
Data and calculations
Petrol energy density
1 Gallons (US) into Kilograms: 2.79 For substance with density: 737.22 kg/m3 Calculator
Gallon of gasoline: 1.3x10^8 J Washington Uni
Joules/kg: 1.3x10^8 / 2.79 = 46594982 J/kg = 46,594 kJ/kg
=> 12 kWh/kg comparable to Wikipedia value