A quantum computer is a device that could exploit the weirdness of the quantum world to solve certain specific problems much faster than we know how to solve them using a conventional computer. Alas, although scientists have been working toward the goal for 20 years, we don’t yet have useful quantum computers. While the theory is now well-developed, and there’s also been spectacular progress on the experimental side, we don’t have any computers that uncontroversially use quantum mechanics to solve a problem faster than we know how to solve the same problem using a conventional computer.It is funny how he can claim "spectacular progress" and yet no speedup whatsoever. It is as if the Wright brothers claims spectacular progress in heavier-than-air flight, but had never left the ground. Or progress in perpetual motion machines.
But is there anything that could support such a hope? Well, quantum gravity might force us to reckon with breakdowns of causality itself, if closed timelike curves (i.e., time machines to the past) are possible. A time machine is definitely the sort of thing that might let us tackle problems too hard even for a quantum computer, as David Deutsch, John Watrous and I have pointed out. To see why, consider the “Shakespeare paradox,” in which you go back in time and dictate Shakespeare’s plays to him, to save Shakespeare the trouble of writing them. Unlike with the better-known “grandfather paradox,” in which you go back in time and kill your grandfather, here there’s no logical contradiction. The only “paradox,” if you like, is one of “computational effort”: somehow Shakespeare’s plays pop into existence without anyone going to the trouble to write them!Now this is science fiction.
But cooling takes energy. So, is there some fundamental limit here? It turns out that there is. Suppose you wanted to cool your computer so completely that it could perform about 1043 operations per second — that is, one about operation per Planck time (where a Planck time, ~10-43 seconds, is the smallest measurable unit of time in quantum gravity). To run your computer that fast, you’d need so much energy concentrated in so small a space that, according to general relativity, your computer would collapse into a black hole!Okay, if my computer ever runs that fast, I'll worry about being sucked into a black hole.
He also claims that if they can ever make true qubits, then they could simulate some dumbed-down models of quantum mechanics. And maybe the qubits could help with quantum gravity, if anyone can figure out what that is.
I guess this is why quantum computing is usually hyped with dubious claims about breaking internet security systems.