# 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}

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.

• thanks for your answer! Do algorithms designed to run on (hypothetical) quantum computers for complete combinatorial sweeps or Monte Carlo simulations already exist? – Andrew Sep 5 '11 at 13:08
• @Andrew Nope, and there is poor chance of having them soon. Most work in the field goes on cryptography, thus those practically insolvable problems from number theory. And those are, well, accelerators (i.e. magical hardware boxes that do certain thing) more than CPUs -- even Turing machine is out of reach. – user88 Sep 5 '11 at 14:18
• @Andrew BTW you could learn more by asking similar question on Physics.SE. – user88 Sep 5 '11 at 14:26
• If I post this there, will I fall foul of people being upset with cross posting? – Andrew Sep 7 '11 at 10:31
• @Andrew I wasn't thinking of cross-posting the exact Q, rather something like "Can a quantum computer do a complete combinatorial sweep? Is it worth it?" and a quick mention how such algorithm could look classically (to avoid "Yes it can solve quantum problem X directly!"-like answers). – user88 Sep 7 '11 at 11:38

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.

• Thanks! Are you able to give any thoughts on what sort of computationally statistics problems may be addressed? – Andrew Sep 6 '11 at 16:41
• I wouldn't say I'm at the cutting edge of statistical theory or the like, but one that's pretty easy to envision is the use of multiple imputation for missing/incomplete information problems, or MCMC based Bayesian models for many variables in very large datasets. In Epidemiology, data like the entire Medicare/Medicade database, or other national claims databases in countries with national healthcare systems. This can all be done now, but it's slow and requires things like clusters, which aren't accessible to some and...intimidating to others. – Fomite Sep 6 '11 at 20:18