Will quantum computing allow new statistical techniques? I just read that you can now buy a quantum computer (albeit that there has only been one sold so far!).  
Will quantum computing have any applications in statistics? 
{edit - for the purposes of the question let's assume that eventually quantum computers (in some form) will work} 
 A: Frankly I doubt this would ever work -- IMO every more complex structure will just melt from decoherence.
Nevertheless probably the most obvious use is doing complete combinatorical sweeps for larger number of variables or huge Monte Carlo simulations.
Yet those are things achievable by molecular computers -- imagine $10^{23}$ combinations evaluated at once (-; And such stuff is more realistic, similar setup has been already used for travelling salesman. Of course there are problems, like that the assembling step is still longer than than solving step and those are one-time devices, but we are on the very beginning of this path.
A: If it actually worked, and was something you could implement statistical code on in one way or another? Absolutely. There are undoubtedly new techniques that could emerge from throwing yet more computational firepower at something. Or, as importantly, making currently bleeding edge, computationally intensive techniques accessible. Just think about current computers - Bayesian estimation isn't exactly new. But being able to run MCMC-based analysis on massively complex data sets where that's not the focus of the paper, but just something that happened along the way, is profoundly powerful thing.
So even if they don't bring about new techniques (which they will) being able to go "yeah, sure we can do that" to computationally intensive techniques on huge data sets is a big deal.
