{"id":444,"date":"2012-07-16T03:12:15","date_gmt":"2012-07-16T03:12:15","guid":{"rendered":"http:\/\/www.dabacon.org\/newpontiff\/?p=116"},"modified":"2012-07-16T03:12:15","modified_gmt":"2012-07-16T03:12:15","slug":"the-viewpoint-skeptics-of-quantum-computers-dont-want-you-to-hear","status":"publish","type":"post","link":"https:\/\/dabacon.org\/caelifera\/2012\/07\/16\/the-viewpoint-skeptics-of-quantum-computers-dont-want-you-to-hear\/","title":{"rendered":"The Viewpoint Skeptics of Quantum Computers Don’t Want You To Hear"},"content":{"rendered":"

Quantum computers are fascinating devices. \u00a0Our current understanding of these devices is that they can do something that classical computers cannot: they can factor numbers in polynomial time (thank you Peter Shor<\/a>!) \u00a0Interestingly, however, we can’t prove that these devices outperform classical computers on any class of problems. \u00a0What this means is something very particularly: we can’t show that the model of a quantum Turing machine can solve problems more efficiently than the classical model of a Turing machine. \u00a0Complexity theorists say that we can’t show that BPP does not equal BQP. \u00a0Complexity theorists remind me of my son learning new letters. \u00a0Sorry I can’t help it. \u00a0S. T. O. P. spells….stop!<\/p>\n

A dark secret (okay it’s not really secret, but this is a blog) of classical computing is that we (or rather, they, since I’m as much a complexity theorist as I am handsomely good looking) also can’t say a lot along the same lines about classical computers. \u00a0The most famous example of this, currently (2012), is that classically we don’t know whether there are computations which take polynomial (in the size of the problem) space and\u00a0unlimited<\/strong> time, but can’t be done with just a polynomial (in the size of the problem)\u00a0limit in time. \u00a0In jargon this is the fact that we don’t know whether P (or BPP) equals PSPACE. \u00a0That’s a huge gap, because PSPACE includes nearly everything in the sun, including computers which use time machines<\/a>. \u00a0That’s right. \u00a0Classical complexity theory has yet to show that computers that use frickin’ time machines aren’t more powerful than the laptop I’m typing this on.<\/p>\n

A reasonable person, I would think, given this state of affairs, would admit that we just don’t know and try to figure out more about the model of quantum computation. \u00a0Interesting, however, academia attracts an interesting class of hyper smart person who try to get places in life by being contrarian. \u00a0That’s great when it leads to results, and often it does. \u00a0Being skeptical is an important part of the scientific process. \u00a0But when it doesn’t lead to results, which I think is the current state of arguments about quantum computers, it leads to senior professors acting very unprofessionally, and stifling a field. \u00a0Quantum computing is in exactly this state of existence. \u00a0I can count the number of jobs given to theorists in quantum computing over the last decade on my hands. \u00a0It’s far greater than the number of senior folks I’ve talked to who are credulously skeptical of quantum computers and show know better (i.e. they’ve at least read the relevant papers.) \u00a0The number who are skeptical but who haven’t actually read the papers? \u00a0My registers don’t count that high.<\/p>\n

For an example of this phenomenon, hop on over at to the awesome and widely read blog Godel’s Lost Letter and P=NP<\/a>\u00a0where\u00a0one of the coauthors of the blog Ken Regan has a post describing some work on trying to understanding the limits of quantum computers. \u00a0That’s great! \u00a0But in this post, Ken, who is an associate professor, can’t help but in a dig at quantum computers along the lines of “we can’t prove that it can’t do anything”:<\/p>\n

But there is no proof today\u2014let me repeat, no proof\u2014that quantum circuits in BQP\u00a0are not easy to simulate classically<\/p><\/blockquote>\n

Because I like poking tigers, and am no longer beholden to the whims of an academic community that strongly rejects quantum computing, I posted a comment (okay I’d post this even when I was a psuedo-professor) which included the last line<\/p>\n

Oh, and, p.s. there is also no proof that classical circuits can\u2019t solve NP-complete problems efficiently, but for some reason I don\u2019t see that in all of your posts on classical computers\u00a0\";)\"<\/p><\/blockquote>\n

to which Ken responded<\/p>\n

As for \u201cno proof\u201d, Dick provided some thoughts which I merged into my intro; I pondered upgrading that line to add \u201c\u2026, nor even a convincing hardness argument\u201d\u2014but thought that better left-alone in the post<\/p><\/blockquote>\n

So you can see the kind of thoughts that go through many theoretical computer scientists which confronted with quantum computing. \u00a0Instead of “lets figure this out” the response is “I want to remind you that we haven’t proved anything, even though we also haven’t proved the same thing about likely even more powerful models of computation.” \u00a0If you don’t think this isn’t a case of bias in academia, then you’re reading a different novel than I am. \u00a0And if you don’t think this has an impact on junior academics, please see the correlation evidence of past hiring in academia (Or if you don’t like that: do an experiment. \u00a0Give the damn people the jobs to hang themselves by. \u00a0Or at least don’t give them advice to avoid quantum computing because of your own biases, I’m looking at you, you know who you are. \u00a0Pffst!)<\/p>\n

Like I said, however, I think focusing on making actual progress in understanding quantum computers is the important path to take (and to the credit of Ken, who I’m picking on simply because he’s at the top of the temporal queue of a long line of guys who like to pontificate about the power of quantum computers without having any arguments that go beyond “I think…”, he has tried to answer this question. \u00a0But not without throwing in a backhand that he seems to find utterly professionally appropriate.) \u00a0And of course the previous two paragraphs are enough of the same ad slander’n reasoning, but exactly from my own completely biased perspective. \u00a0But toward being *ahem* productive, I’m completely convinced that quantum computers offer significant, proven, reasons to be built. \u00a0This is a controversial statement, because I know all complexity theorists will disagree with this point of view. \u00a0So this is aimed at the group of people with minds open enough to think not about complexity classes, but about real world experiments (we might call them, physicists.). \ud83d\ude09<\/p>\n

The argument is almost as old as quantum computing itself. \u00a0These are the so called “black-box” query complexity results in quantum computing, albeit as seen through a physicist’s measuring device. \u00a0What these models do is as follows. \u00a0They consider a set of black box functions (say functions from n bits to 1 bit, so-called binary functions) and ask one to identify something about this set of black box functions. \u00a0For example, the set of functions could be all binary functions that are either constant (on all inputs they output 0 or on all inputs they output 1) or balanced (on half of inputs they output 0 and on the other half they output 1). Then the problem would be to distinguish whether, if I give you a machine that implements one of these functions, whether the function is constant or whether it is balanced. \u00a0Then one “measures” the effectiveness of an algorithm for solving this by the number of times that you have to use the black box in order to figure out which set the function belongs to.<\/p>\n

So what is the state of query complexity differences between classical and quantum computers? \u00a0It can be proven that there are black box problems that can be solved by quantum computers using a polynomial number of queries in the size of the problem, but that\u00a0require<\/strong> an exponential number of queries classical. \u00a0That’s right. \u00a0There is a proven exponential separation. \u00a0(For those who would like to argue that the comparison is not fair because a quantum device that computes a function implements a different physics than that which gives you a classical computation, I would only note that our world is quantum mechanical, and we can compare a quantum querying of the quantum device to a classical one. \u00a0A classical query of this quantum device is exponentially less efficient.)<\/p>\n

At this point you may then wonder why all of the fuss about quantum computers not being proven to be more powerful than classical computers. \u00a0The answer is interesting and starts with the way we set up the problem. \u00a0We were given a black box that computes a classical function. \u00a0We can think about this literally as a machine that we can’t probe any deeper into how it actually works. \u00a0In this respect it is a sort of a-physical device, one that isn’t connected to the normal context of what a computation is (as modeled by, say a parallel Turing machine.) \u00a0Suppose that this were a real physical device, then you could take it apart and look at how it worked. \u00a0This means that you could get more information about the computation being performed. \u00a0And when you allow this, well, it is then not clear that you couldn’t solve the problems for which quantum computers offer speedups just as fast on a classical computer. \u00a0Thus while we know that with respect to these black box problems, quantum computers are exponentially faster than their classical\u00a0brethren, we can’t carry this over to statements about models of computation.<\/p>\n

But take a step back. \u00a0Suppose you are an experimental physicist and I give you a black box and ask you to figure out whether the box implements one or another sets of functions. \u00a0Well then, if you use this experimental device without peering into its innards, then you really really want to use a quantum computer for your experiment. \u00a0The difference between exponential graduate students and polynomial graduate students is most certainly something that will get your grant funded by the NSF. \u00a0Because the universe is quantum mechanical, damnit, and if you want to perform experiments that more quickly reveal how that universe operates, you’ve got to query it quantum mechanically to be most efficient.<\/p>\n

Okay, you may not be convinced. \u00a0You may argue that at its heart you can’t ever have a box that one can’t take apart and probe its innards (can you?) \u00a0Fine. \u00a0So I’ll modify the game a bit. \u00a0I’ll give you a quantum system that is the output of the standard way this device if queried in these computeres $sum_x |x> |f(x)>$. \u00a0Now you either get to query this using only classical measurements on this device in the computational basis, or you get to use the full power of quantum computers, querying with a measurement you can build in your quantum laboratory. \u00a0In that case, you can show that a quantum experimentalist will exponentially outperform characterizing this state, i.e. solving the given promise problem. \u00a0Think about this as a game, a game in which you can win by being quantum mechanical exponentially faster than you could being classical.<\/p>\n

Of course this won’t convince anyone, especially not classical theoretical computer scientists (who once were at the vanguard of a totally new field, but now find themselves defending their own legacy code.) Does it at least pass the test of trying to present evidence in either direction for the power of quantum computers? \u00a0Not really, for those who refuse to believe that quantum theory isn’t actually the right theory of nature. \u00a0But it does seem to tell us something is fundamentally very very different about the ability to use quantum theory in a setting where you’re trying to extract information about an unknown quantum system. \u00a0And it’s proven. \u00a0And it’s not a way of thinking that the old guys would like you to think \ud83d\ude42<\/p>\n","protected":false},"excerpt":{"rendered":"

Quantum computers are fascinating devices. \u00a0Our current understanding of these devices is that they can do something that classical computers cannot: they can factor numbers in polynomial time (thank you Peter Shor!) \u00a0Interestingly, however, we can’t prove that these devices outperform classical computers on any class of problems. \u00a0What this means is something very particularly: … <\/p>\n

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