>Check the publications page for the encouraging part. They might be wrong but they're doing real science. I've personally spoken to a fusion scientist who thought they might be on to something.
I checked the publications page and so far I'm not seeing any real theory here. That doesn't mean it's wrong, but it certainly feels weird. The most in-depth equation I saw in any of their linked papers is the definition of the electromagnetic field tensor.
I'm not saying you couldn't develop a fusion reactor by doing purely experimental work with bleeding-edge laser technology. But I'd feel a lot more confident if they were to produce, for example, some kind of prediction of their net power, or a relation between e.g. laser power and fusion yield, or some other quantitative prediction about something.
For example, I'm not sure what prediction they exceeded by a factor of a billion in TFA. Shouldn't you mention that somewhere?
Another poster mention's Todd Rider's thesis, a famous barrier to creative fusion. In this particular case I think the way they evade Rider is by using higher laser powers and shorter reaction times than Rider considered to be possible. One of the important exceptions Rider acknowledges (and that I remember) is ultradense fusion; ultrafast fusion seems to be at least similar in principle.