Hopefully my last D-Wave post ever

Several people asked me to comment on an entry by Hartmut Neven in the Google Research Blog, about using D-Wave’s “quantum” computers for image recognition.

I said nothing: what is there to say?  Didn’t I already spend enough time on this subject for 10400 lifetimes?  I want to create, explore, discover things that no one expected—not be some talking-head playing his assigned role in a script, a blogger-pundit who journalists know they can rely on to say “f(X)” whenever X happens.  Even if f(X) is true.  Why can’t I just tell the world what f is and be done with it?

Then more people asked me to comment.

I set the matter aside.  I worked on the complexity problem that’s currently obsessing me.  I met with students, sent recommendation letters, answered emails, went ice-skating with my girlfriend.

Then more people asked me to comment.

And I thought: yes, I believe it’s vital for scientists to communicate with the broader public, not just a few colleagues.  And yes, it’s important for scientists to offer a skeptical perspective on the news—since otherwise, they implicitly cede the field to those making dubious and unsubstantiated claims.  And yes, blogging is a wonderful tool for scientists to connect directly with anyone in the world who’s curious about their work.  But isn’t there some statute of limitations on a given story?  When does it end?  And why me?

Then more people asked me to comment—so I wrote the following only-slightly-fictionalized exchange.

Skeptic: Let me see if I understand correctly.  After three years, you still haven’t demonstrated two-qubit entanglement in a superconducting device (as the group at Yale appears to have done recently)?  You still haven’t explained how your “quantum computer” demos actually exploit any quantum effects?  While some of your employees are authoring or coauthoring perfectly-reasonable papers on various QC topics, those papers still bear essentially zero relation to your marketing hype?  The academic physicists working on superconducting QC—who have no interest in being scooped—still pay almost no attention to you?  So, what exactly has changed since the last ten iterations?  Why are we still talking?

D-Wave: Then you must not have read our latest press release!  Your questions are all obsolete, because now we’re recruiting thousands of volunteers over the Internet to study the power of adiabatic quantum computing!

Onlooker: Hmm, an interesting counterargument!  D-Wave might not be using quantum mechanics, but they are using the Internet!  And their new project even has a cool code-name: “AQUA@home”!  So, skeptic, how do you respond to that?

Skeptic (distractedly): You know, when I was eight years old, and dreamed of building starships and artificial intelligences in my basement, my first order of business was always to invent code-names—not just for the projects themselves, but for every little subcomponent of them.  The second order of business was to think through the marketing aspects.  What should the robot look like?  What recreational facilities should be available on the starship, and what color should it be painted?  It really, genuinely felt like I was making concrete progress toward realizing my plans.  Sure, the engine and control system still needed to be built, but at least I had code-names and “design specs”!  How many others had even gotten that far?

D-Wave: Who cares?  This isn’t some children’s game.  Keep in mind that we’re delivering a product—serving our customers, by solving the 4-by-4 Sudoku puzzles they rely on to keep their businesses running.

Skeptic: We’ve been through this how many times?  A pigeon can probably be trained to solve 4-by-4 Sudokus.  So the only relevant questions concern the details of how you solve them.  For example, how do you encode a problem instance?  How much of the work is done in the encoding procedure itself?  What evidence do you have for quantum coherence at intermediate points of the computation?  Can you measure an entanglement witness, to give people confidence that you’re doing something other than classical simulated annealing?

Onlooker: Hmm, those do seem like important questions…

D-Wave: But they’re based on outdated premises!  Today, we’re pleased to announce that, using what might be a quantum computer, and might also be a noisy, probabilistic classical computer, we can solve 5-by-5 Sudoku puzzles!

Onlooker: Whoa, awesome!  So we’re back to square one then.  As long as D-Wave’s demos only involved 4-by-4 Sudokus, the skeptic’s arguments almost had me persuaded.  But 5-by-5?  I don’t know what to think anymore.  Skeptic, where are you?  What’s your reaction to this latest development?


D-Wave: That silence you hear is the sound of the skeptic’s worldview crashing all around him!  But we haven’t even played our top card yet.  Today, we’re positively ecstatic to announce that we’ve entered into an official-sounding partnership with GOOGLE, Inc. (or anyway, with someone who works at Google Research).  Together, we’re harnessing the power of quantum adiabatic optimization to create the next generation of car-recognition systems!

Onlooker: WOW!  This debate is over, then.  I confess: D-Wave on its own did seem a bit flaky to me.  But Google is the company born without sin.  Everything they do, have done, and will ever do is perfect by definition—from building the search engine that changed the world, to running mail servers that only fail for an insignificant 0.001% of users, to keeping the Chinese people safe from lies.  And, as Google is infallible, so too its 20,000 diverse employees—who are encouraged to spend 20% of their time on high-risk, exploratory projects—have nevertheless failed to come up with a single idea that didn’t pan out.  Skeptic, show your face!  Will you admit that, through grit, moxie, old-fashioned Canadian inventiveness, and the transformative power of the Internet, D-Wave has finally achieved what the naysayers said was impossible—namely, getting someone from Google Research to coauthor a paper with them?

Skeptic: Yes.  I concede!  D-Wave wins, and I hereby retire as skeptic.  In particular, the next time D-Wave announces something, there’s no need to ask me for my reaction.  I’ll be busy tending to my own project, codenamed ARGHH@home, which consists of banging my head against a brick wall.

53 Responses to “Hopefully my last D-Wave post ever”

  1. wolfgang Says:


    can you please at least use the famous crayon colors when you write GOOGLE, otherwise your skeptical arguments are hardly convincing.

  2. Scott Says:

    Wolfgang: I thought about it, and decided it would be too over-the-top. But, as the post itself hopefully illustrates, I’m nothing if not obliging.

  3. John Preskill Says:

    You went ice skating?

  4. Ray Dupree Says:

    The problem with this post Scott is that you offer nothing in the way of substantive criticism. What this sounds like is that you are annoyed that D-Wave is actually producing something someone in the real world can actually use without asking you for permission. Which is very puzzling and counterintuitive for an outsider like me (coming from a machine learning background). It seems like you also didn’t read the Neven/Macready/Dentchev/Rose paper you are criticizing or if you did you didn’t understand it. The resource requirements are laid out explicitly and in fact I reproduced something like what they did with a conventional solver in about a day. Why don’t you code it up and then post something about it? There may be some hole in it but it looks solid to me.

    Also this whole “marketing hype” thing–where is that coming from? D-Wave has had several things that a normal company would have PR’ed to hell, like the fact that the ex-CTO of Goldman Sachs/founder of Egenera is running the company. The Google announcement was a third-party endorsement that the D-Wave tech worked for them. Shouldn’t the QC community be celebrating this? Machine learning is way more valuable than factoring.

  5. Stas Says:

    As Scott is busy/annoyed, could someone else with expert knowledge in QC provide here an unbiased review of the Google/D-Wave’s NIPS paper? I stay skeptical, but I do believe D-Wave has done enough to start paying close attention to what they are doing…

  6. Someone from D-Wave Says:

    Ok, the 5 by 5 Sudoku might sound useless, but why are you so irritated by the new generation car-recognition systems? Isn’t it already great that we have beaten their solvers? This fact alone is an achievement. Just wait for a little bit, and you will get your answers about quantumness – don’t think convincing you is on top of our list and you are the first to get the most valuable information – we value our customers, they get the priority.

  7. Josh Says:

    Shouldn’t ARGHH@home not just be you banging your head against a wall, but an invitation to everyone on the internet to bang their heads against a wall, and report their results? That way you could have the following explanation:

    ARGHH@home is a research project whose goal is to predict the performance of banging-heads-against-the-wall computers on a variety of hard problems arising in fields ranging from debunking myths to proving impossible results (or is that impossibility results?). ARGHH@home uses Internet-connected people to help design and analyze head-against-the-wall algorithms, using brick wall Monte Carlo techniques. You can participate by running a free program on your very own brick wall.

  8. Scott Says:

    The problem with this post Scott is that you offer nothing in the way of substantive criticism.

    I—and others like Greg Kuperberg, Barbara Terhal, Wim van Dam, and Umesh Vazirani—offered lots of substantive criticism starting three years ago (see here for my dozen or so previous D-Wave posts). The point of this admittedly-low-content post was simply that the previous criticisms stand—none of the “new initiatives” D-Wave is talking about appear to do anything to address them. Why should D-Wave get the privilege of pushing “reset” on the whole debate with every public announcement?

  9. Dave Bacon Says:

    Sorry Scott I couldn’t help myself: http://scienceblogs.com/pontiff/2009/12/in_defense_of_d-wave.php

    And see now everyone will bug you even more about D-wave 🙁

  10. Warren Says:

    Hopefully my last D-Wave post ever

    And I hope we’ll see world piece this decade.

  11. Scott Says:

    As Scott is busy/annoyed, could someone else with expert knowledge in QC provide here an unbiased review of the Google/D-Wave’s NIPS paper?

    I’d be delighted too if someone did so!

    At least in my experience, though, when experts tried to give D-Wave the benefit of the doubt, and focus only on the technical issues that D-Wave wanted to raise, people got the mistaken impression that the disagreements between D-Wave and the QC community were only over abstruse technical matters. They lost sight of the elephant in the room—or rather the elephant that’s missing from the room, namely the evidence for coherence and multi-qubit entanglement. Without that, the car never leaves the garage. So, yes, write an unbiased review of the leather seats, but don’t pass over in silence the fact that nobody’s seen the engine.

  12. Freud Says:

    Scott…why do you let it bother you? You know a pathological liar when you see one…right?

    They are a VC motivated by greed. That’s it.

    They probably get off on trying to fool academics to sustain their narcasistic delusions.

  13. _|_ Says:

    Scott or anyone else:
    What experiment could D-Wave do that would convince you that their system is non-classical enough to be computationally useful?

  14. Pete R Says:

    Speaking of quantum misunderstandings, why is superluminal communication such a closed issue? Say you set up an apparatus in the middle of the moon and earth that emits a pair of quantum entangled particles (position entangled, like the ones in the quantum eraser experiment). On earth, you have a detector that can detect position. On the moon, you have a double slit apparatus set up. The emission apparatus can emit pairs very rapidly (say a million pairs/second), so in .1 seconds an interference pattern can be seen if the waveform has not yet collapsed. However, if for that .1 seconds the detector on earth is turned on, no interference will be seen on the moon, because the waveform has already collapsed via entanglement. So, if earth chooses to detect for .1 seconds, the moon will not see interference, and can interpret this as a “1”. If the earth does not detect for that .1 seconds, the moon will see interference, and can interpret this as a “0”. This transfer of 1 bit will be accomplished in .1 seconds, faster than the speed of light (1.3 seconds). What’s the flaw in this logic, other than practical considerations?

  15. Yatima Says:

    >>What’s the flaw in this logic, other than practical considerations?

    You need to start with introductory courses in QM.

  16. Jim L. Says:

    I don’t have a problem with the latest D-Wave announcements. Well, I only read the Google research blog entry. But it did not claim to have a quantum computer, or even to be using inherently quantum effects. It just said that they have some chip, a sort of analog device, that improved performance for some weird task. Good for them. Since the blog entry did not repeat any of D-Wave’s old, unbelievable claims, I found it entirely unobjectionable.

  17. Peter Morgan Says:

    This is still at the level of toy models, so it may be as irritating as D-wave, but focusing on whether D-wave computing is classical or quantum is old. In particular, a complex Klein-Gordon quantum field is empirically equivalent to a Hilbert space presentation of a real Klein-Gordon random field (EPL 87 (2009) 31002, http://www.iop.org/EJ/abstract/0295-5075/87/3/31002/, which is Open Access), and a similar construction is possible for the quantized electromagnetic field (http://arxiv.org/abs/0908.2439v1).
    A random field that is presented using measure theoretic methods instead of using differential equations introduces additional resources into classical modeling. Because we work with a Hilbert space of states over a commuting algebra of observables, an algebra of non-commuting observables emerges (a vacuum projection operator allows us to construct bounded non-local operators that are the same as can be constructed for the corresponding free quantum field theory), but the non-commutation of observables is comprehensible in terms that are moderately familiar in classical signal analysis. Everything is similar enough to quantum field theory that there is such a thing as an entangled random field state, however, so the question of whether D-wave can construct entangled states remains pertinent.
    I guess this amounts to a code-name, random fields, and design specs for the free field case, but it’s enough that care would be well-advised when in the pulpit.

  18. Stephan Says:

    Pete — you’re not properly ignoring (tracing out) the Earth particle when you consider the particle on the moon. If you do that, you’ll notice that the moon particle is in a classical mixed state (not a superposition), so it can’t interfere with itself.

    See Wikipedia: http://en.wikipedia.org/wiki/Quantum_entanglement#Reduced_density_matrices

  19. Scott Says:

    You went ice skating?

    Yes, and it was great (though suffice it to say, I won’t be participating in next year’s Winter Olympics).

    However, a consistent problem I have when ice-skating is quantization error: the size-8 skates feel (I assume) like traditional Chinese foot-binding, while the size-9 ones feel like unattached skis.

  20. Pierre Says:

    Google themselves admitted that what they did with D-WAVE does not in any prove that the D-WAVE hardware is really a quantum computer. So I’m guessing their joint work on image recognition is all theory and simulations. Which is fine and will surely be useful, but it’s got nothing to do with the ‘quantumness’ of their adiabatic system.

  21. Jack in Danville Says:

    _|_ Says,

    It can be computationally useful and not a quantum computer. It’s conceivable to build a hardware engine that very efficiently computes a particular class of problem.

  22. Jack in Danville Says:

    Peter R,

    take a look at this http://www.bottomlayer.com/bottom/kim-scully/kim-scully-web.htm

  23. Job Says:

    How do we measure a speedup between a classical and a quantum computer? Do we just compare the overall execution time for the same algorithm on the same instances? How do we ensure that we have N units of classical computing versus N units of quantum computing?

  24. Job Says:

    In particular when talking about the possibility of a Quantum Computer providing only a small speedup over conventional computers for certain difficult problems. I’ve always expected QC performance to be that much better that one wouldn’t even have to ask this type of question.

    Wouldn’t an implementation of a Factoring algorithm, rather than an one providing only a small gain on NP-Complete problems, be a much better indicator of the “Quantum Advantage”?

  25. Job Says:

    I don’t understand that how can it be such a problem to convince people that you have a working QC. It sounds like it should be the easiest thing in the world, like proving that you can bend steel.

  26. Scott Says:

    Job: It’s a good question!

    As a first observation, proving that you can bend steel isn’t completely straightforward either! For example, you’d have to prove that the substance you’re bending was indeed steel, and not some other alloy that was easier to bend.

    (In the QC context, this is roughly analogous to proving that the problem you’re solving is indeed hard for classical computers.)

    Having said that, if you had a QC that could factor 10,000-digit numbers, then proving that would be more-or-less like proving you can bend steel. You’d just challenge anyone to give you a huge composite number, and give them back the factors. That would prove that either you had a QC, or else you had some other factoring method that was also amazing.

    The problem is that the only QCs anyone even claims to have right now are ones that solve tiny toy problems—problems that we can also easily solve on a classical computer. Furthermore, to load even those toy problems onto the QCs, a classical computer has to encode them somehow as (say) a sequence of laser pulses (in the ion-trap setting). So people argue about whether the classical encoding procedure is doing all the real work, and whether the QC is “pulling its weight.” Finally, the toy QCs people have now are extremely noisy—if you like, they’re part-classical and part-quantum. And proving that the “quantum part” actually contributed to solving the toy problem can be extremely subtle. This is especially true for the adiabatic algorithm (what D-Wave uses exclusively), since it appears to “degrade gracefully” into classical simulated annealing.

  27. Joe Fitzsimons Says:

    _|_: If they could implement blind quantum computation, that would convince me (indeed that was part of the motivation). Perhaps the pontiff’s recent work could be used translate the protocol to adiabatic systems.

  28. Scott Says:

    One other remark: I agree that Neven’s blog entry itself was surprisingly responsible—notice how it pointedly declines to take any position on the core issue of whether D-Wave’s device actually exploits any quantum speedup. Neven, and Google, deserve credit for that.

    The trouble is that, WHATEVER they say, experience shows it will quickly get distorted to: “Google vouches for D-Wave’s scientific claims! Therefore the claims must be true!” Indeed that’s already happening, and is what set me off.

  29. Pete R Says:


    John Cramer (http://en.wikipedia.org/wiki/John_G._Cramer) experimental physicist from UW, seems to think I have a point. Check out his latest experiment – it’s basically the same idea.

    Thanks to all who posted thoughtful responses.

  30. Scott Says:

    Pete R.: Superluminal signalling isn’t possible in conventional QM. That’s not a statement of belief, it’s a theorem — please look it up!

    What that means is that, if an experiment such as you propose showed that superluminal signalling was possible, that experiment would also overthrow QM.

  31. Greg Kuperberg Says:

    What this sounds like is that you are annoyed that D-Wave is actually producing something someone in the real world can actually use without asking you for permission.

    It’s fine if they produce something that someone in the real world can actually use. The only thing that’s annoying is that they claim that it’s quantum. Their arguments that their work is quantum are really bad. They could conceivably have some proprietary evidence that helps make the case, but if part of the argument is too confidential to state, that counts as a bad argument.

    Aren’t you annoyed when people pretend to succeed in your field? It isn’t enough to try at A and succeed at B. Isaac Asimov was a biochemist and a great writer, but he didn’t argue that that proved that he was a great biochemist.

    Anyway, people in QC aren’t all that annoyed any more about D-Wave. D-Wave and the QC research community have largely just parted ways. At QIP in 2009, the only mention of D-Wave that I heard was after drinks at a dinner — an informal dinner, not scheduled by the conference. Scott mostly doesn’t care either. As he says, he only posted this because people pestered him for an opinion.

  32. John Sidles Says:

    In Richard Gordon’s The Alarming History of Medicine we find this aphorism: “Great breakthroughs are often accomplished without the slightest idea of what is being broken through.”

    Perhaps folks should reflect on the possibility—which is very real IMHO—that the question Scott’s skeptic asked, namely “How do you encode a problem instance?” is the right question, and that D-Wave has demonstrated that this question has an unanticipated answer.

    That answer being, that a pretty good state-space for optimization is not the binary state-space of classical bits, nor the Hilbert space of quibits, but the Kählerian space of … uhhh … I guess these computational entities don’t presently have a name … so let’s call them … käbitz! 🙂

    The point being, that the dynamics of D-Wave’s (noisy) qubits can plausibly be well-represented on a concentration-and-pullback käbitz manifold having Schmidt rank (say) thirty … which is far more dimensions than classical binary bits … yet far fewer dimensions than Hilbert space qubits.

    How well do annealing-type optimization methods work on state-spaces that have been “Kählerized”?

    AFAIK, no-one knows the answer to this question. But it is a perfectly feasible question to investigate, not only by D-Wave’s experimental methods, but also by numerical methods—systems of 500 käbitz having Schmidt rank 100 being feasible even on laptop computers—or alternatively by the purely mathematical methods of concentration theory.

    After all, from a purely mathematical point of view, isn’t the following statement statement true? All of the problems in computational complexity theory (both classical and quantum) can be systematically “Kählerized”—via well-posed concentration and pullback methods—for the purpose of increasing the too-small dimensionality of classical computation, or conversely, for the purpose of decreasing the too-large dimensionality of Hilbert space computation.

    Perhaps someday we will all look back and say (as David Hilbert once said): “No-one shall expel us from the paradise of käbitz that Geordie/D-Wave/Google has demonstrated for us!”

    That would be plenty of fun, IMHO! On which note, happy holidays to all! 🙂

  33. John Sidles Says:

    By the way, the above post was conceived in a light-hearted vein … hence the insertion of a “metal umlaut“, aka “rock dots” in the portmanteau word “käbitz”.

    But it often happens when try to write funny, it somehow comes out serious (and vice versa), and so I want to say that the technical aspects of the above post were written with (reasonably) serious intent.

    And therefore, my sincere appreciation and congratulations are extended to Geordie Rose, and to D-Wave/Google, for this very interesting work.

  34. lifeofpi Says:

    Am I the only one who doesn’t understand at all John Sidles’ posts about everything being related to Kähler manifolds? John Sidles, is there a reasonable exposition of this “Kählerian” model of computing?

  35. John Sidles Says:

    Hmmm … the way we think about it within our QSE group, there are two natural ways to “Kählerize” a dynamical system: (1) by pushforward of classical dynamics onto a larger-dimension space, and (2) by pullback of Hilbert-space dynamics onto a smaller-dimension space.

    These two ways are naturally dual—once you learn one of them, it’s pretty easy to learn the other.

    Needless to say, both of these methods have a long history in quantum research. The folks who use pushforward methods have fully embraced the language of geometers, and there are excellent reviews by Ashtekar and Schilling, and by Tyurin (see the appended BibTeX references).

    On the dual side, there are plenty of folks who are using pullback methods—pretty much everyone who calculates with matrix product states, for example—but the pullback community has not (so far) widely adopted the language of the geometers.

    We just finished a seminar that systematically pulled-back (” Kählerized”) the Hilbert-space formalism of Nielsen and Chuang, and expressed the result in the language of symplectic and metric geometry. As expected, the resulting pullback framework is naturally dual to existing pushforward frameworks; a short syllabus, reading-list, and hyperlinked vocabulary is here.

    It turns out that “Kählerizing” the quantum framework of Nielsen and Chuang requires learning (about) 82 geometric mathematical terms, over-and-above the terminology that Nielsen and Chuang themselves introduce.

    The good news is, all 82 vocabulary terms are standard elements of modern geometry, and so they are well worth learning on their own.

    It is interesting—as the vocabulary notes point out—that Bjarne Stroustrup’s C++ vocabulary introduces 558 new terms … does this mean that C++ is 7X harder to learn than geometric quantum mechanics?

    Well … no … but learning the elements of geometric quantum mechanics is reasonably natural and feasible.


    Summary: anyone who already knows some Hilbert space quantum mechanics, and learns some symplectic and metric geometry, and thinks about pushforward and pullback, pretty much can’t help learning the fundamental principles of geometric quantum mechanics.


    @incollection{***, Title = {Geometric quantization and algebraic {L}agrangian geometry}, Author = {Tyurin, Nikolai A.}, Address = {Cambridge}, Booktitle = {Surveys in {G}eometry and {N}umber {T}heory: {R}eports on {C}ontemporary {R}ussian {M}athematics}, Pages = {279–318}, Publisher = {Cambridge University Press}, Series = {London Math. Soc. Lecture Note Series}, Volume = {338}, Year = {2007}}

    @incollection{***, Title = {Geometrical formulation of quantum mechanics}, Author = {Abhay Ashtekar and Troy A. Schilling}, Booktitle = {On Einstein’s Path}, Editor = {A. Harvey}, Pages = {23–65}, Publisher = {Springer}, Year = 1999, Address = {New York}}

  36. Greg Kuperberg Says:

    Am I the only one who doesn’t understand at all John Sidles’ posts about everything being related to Kähler manifolds?

    I have seen these comments for several years, and I also know what a Kähler manifold is. (It is a curved version of a complex vector space, just as a Riemannian manifold is a curved version of a real vector space.) I have never understood what he’s talking about.

  37. Raoul Ohio Says:

    Googling on Ashtekar and Schilling leads to a brief and simple discussion of why Kähler manifolds are a good way to think about QM over at “Quantum mechanics and geometry”,


    Check it out.

  38. Greg Kuperberg Says:

    Googling on Ashtekar and Schilling leads to a brief and simple discussion of why Kähler manifolds are a good way to think about QM over at “Quantum mechanics and geometry”,

    Except for the words “brief”, “simple”, and “good”, I agree with you. That week I gave the colloquium at Berkeley on quantum probability. I was really happy that Scott Morrison, who kicked off the blog discussion that you linked to, understood my point.

  39. Raoul Ohio Says:

    Good point Greg.

    Brief? I think it was only a couple pages long.

    Simple? I guess it reminded me of problems I had worked a few decades ago and thought I understood at that time.

    Good? It seemed like Scott M. thought it was good. I am only a spectator on QM issues, but think there is a reasonable chance that someday a new framework will clarify things, eliminate the mystery and spookiness, and we will all be saying “darn, why didn’t I think of that?”.

  40. John Sidles Says:

    For me, some of the most impressive work in geometric quantum mechanics has been done by Lane Hughston, Dorje Brody, and collaborators at Imperial College, London (the arxiv server has plenty of articles by this group). I particularly want to commend recent work by Anna Gustavsson relating to symplectic structures in multi-qubit Bloch equations, which is directly relevant to our QSE Group’s interests in quantum spin imaging.

    The way that the Hughston/Brody/et al. articles treat quantum probability closely resembles the way that financial mathematicians treat probability. And this is unsurprising, since (if memory serves) Lane Hughston is one of Roger Penrose’ students on the one hand, and Chair in Financial Mathematics at Imperial College on the other hand.

    Is this trans-disciplinary dovetailing of formalisms good, bad, or irrelevant? That depends (in my experience) largely upon how interested one is in geometric descriptions of dynamical and stochastic processes. And this helps us understand why there is a rather broad spread of opinion regarding how useful people think these Kählerian geometric methods will prove to be in quantum physics.

    This diversity of both formalisms and opinions is good IMHO … it being neither necessary nor desirable that everyone think alike (in any sphere of human endeavor). Where would algebraic geometry be, if there were a rigid distinction between algebra and geometry?

    That is why John Godfrey Saxe’s 19th century poem The Blindmen and the Elephant is IMHO among the best (short) accounts of quantum mathematics, physics, and engineering, as we presently understand it. 🙂

  41. Greg Kuperberg Says:

    It seemed like Scott M. thought it was good.

    I don’t want to speak too much for him, but I can say this. My position in that thread was that the construction could be interesting, but the motivation is silly. I gave a colloquium at Berkeley that week with a more orthodox interpretation of quantum probability. Scott told me after the talk that he was starting to see my point.

  42. Gil Kalai Says:

    The aspect of Scott’s skepticism concerning D-wave which I disagree with is that his skepticism turned into an all-out crusade.

    Certainly the Suduku demo and rhetoric surrounding it required some response, and, of course, the overall target of the company is very ambitous which makes it a long shot, and, yes, a success may depend on breakthroughs regarding fault torerant adiabatic computation that nobody can guarantee.

    Maybe something D-wave did harmed their credibility beyond repair in your eyes, but, in general, I do not see why scientists and engineers working in a commercial company to promote QC technology (and do some basic research along the way) is necessarily a worse idea compared to scientists and engineers who do it in a university.

    A company like D-wave need not compete with the academia, it can take advantage of advances in academia. (So progress by the excellent Yale’s scientists in a direction of interest to the company is a good sign and not a bad sign for their endeavor.)

  43. rrtucci Says:

    Gil, in defense of Scott, MIT has a really aggressive publicity machine, worse than that of Merck or BlueCross Blue Shield or Intel, and I suspect they’ve been prodding him to no end to make a “juicy” statement. Driving the poor guy crazy

  44. John Sidles Says:

    Perhaps what some folks (students especially) find disquieting about D-Wave/Google is not the math, not the theory, and not the technology … but rather, the D-Wave/Google narrative.

    The point is, it’s not clear that D-Wave’s device is most naturally described in terms of qubits. It seems plausible (to me) that the D-Wave device can more usefully be viewed as an analog computer, which (possibly?) achieves its speedup by operating in a state-space that is larger-than-classical, but smaller-than-Hilbert.

    Everyone is familiar with the derivation of high-accuracy asymptotic expansions by deforming integral paths into the complex plain. Integral approximations that work poorly on the real axis, can work exceedingly well when they are extended in the complex plane.

    By analogy, perhaps D-Wave/Google have shown that analog annealing methods can work better when they too are extended into complex state-spaces?

    That is why it seems plausible (to me) that there is plenty of good math, science, and engineering to be found in this new quantum territory that D-Wave/Google are exploring.

    It is clear that exploring this new quantum territory requires rather different tools (in terms of math, science, and engineering) from what the QIT/QIP community are accustomed to … and in the long run, perhaps this novelty will prove to be a good thing.

  45. Gil Says:

    rr, if I will ever need defence, you will certainly be the first person I will ask.

  46. Greg Kuperberg Says:

    I do not see why scientists and engineers working in a commercial company to promote QC technology is necessarily a worse idea compared to scientists and engineers who do it in a university.

    I have no objection to that at all. Unfortunately, the feeling is that they are promoting themselves at the expense of QC technology.

  47. John Sidles Says:

    Greg Kuperberg Says: I have no objection to [D-Wave corporate promotion] at all. Unfortunately, the feeling is that they are promoting themselves at the expense of QC technology.

    IMHO, it would be interesting (and a service to the community too) if these often-voiced sentiments were fleshed-out with specific instances.

    For example, when we say “the feeling is”, whose feelings are we talking about? The feelings of algebraists? The feelings of geometers? The feelings of complexity theorists? The point is that quantum theory is so protean (in its mathematical, physical *and* engineering aspects), that there is plenty of room for very different perspectives regarding the D-Wave/Google enterprise.

    My own perspective on the uneasy relation between the engineering-style research of D-Wave/Google, and the logician-style research of academic QIT/QIP, is very much summed-up by one of the classic Great Truths: “It is one of the chief merits of proofs, that they instill a certain skepticism about the result proved” (Russell).

    Or as von Neumann said it (at greater length), in his 1947 essay “The Mathematician”: “There is a quite peculiar duplicity in the nature of mathematics … much of the best mathematical inspiration comes from experience … [this requires] the re-injection of more or less directly empirical ideas.”

    Thus, it might perhaps be rigorously proved that (under some definitions) the D-Wave device is not a “quantum computer.” And yet it would show no disrespect for complexity theory, if this led us to wonder whether we might broaden our conception of what quantum computing is, and therefore, what quantum computers are, in response to the D-Wave/Google’s stimulating “re-injection of more or less directly empirical ideas.”

    Conversely, it is evident nowadays that rigorous QIT/QIP theorems are serving equally to narrow and broaden the domain of discourse … both of which are good.

    In summary, it seems (to me) that the D-Wave/Google work is broadening the domain of QIT/QIP discourse, in a way that (eventually) will benefit the most rigorous logicians, the most skilled hardware-builders, *and* the most ambitious entrepreneurs.

    *ALL* of which is good! On which note, best wishes for a a Happy New Year are extended to everyone! 🙂

  48. Hopefully Anonymous Says:

    If you (the specific you, Professor Aaronson, not the general you, reader) intuit that an argument is wasting your time, it probably is.

    Very, very funny post and follow up comments.

    Professor Sidles, I’m glad to see you linking to your “what’s new” department page, but I still recommend a blog that more like your comments here.

  49. John SIdles Says:

    Like many people, I am often tempted — *very* tempted — to start a blog, but IMHO the world is not crying out for more math/science/engineering blogs, but rather, for better posts on the (many) such blogs that already exist.

    Hence my admiration and appreciation for bloggers like Scott Aaronson, Dave Bacon, Terry Tao, Dick Lipton, the Fortnow/Gasarch team, Michael Nielsen, Igor Carron, Gil Kalai, the Secret Blogging Seminar, and the (many) financial engineers at Wilmott … to name just some of the hard-working bloggers who (IMHO) deserve everyone’s thanks.

  50. r4 Says:

    I have my blog but it is pretend one I want to start my new blog now but at first time when i want to start my blog then it is much hard work for me I am very happy to see this one it is really a very nice one.

  51. anon Says:

    You know, I liked this post. 🙂

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