Shtetl-Optimized

Update (May 17): Daniel Lidar emailed me to clarify his views about error-correction and the viability of D-Wave’s approach.  He invited me to share his clarification with others—something that I’m delighted to do, since I agree with him wholeheartedly.  Without further ado, here’s what Lidar says:

I don’t believe D-Wave’s approach is scalable without error correction.  I believe that the incorporation of error correction is a necessary condition in order to ever achieve a speedup with D-Wave’s machines, and I don’t believe D-Wave’s machines are any different from other types of quantum information processing in this regard.  I have repeatedly made this point to D-Wave over several years, and I hope that in the future their designs will allow more flexibility in the incorporation of error correction.

Lidar also clarified that he not only doesn’t dispute what Matthias Troyer told me about the lack of speedup of the D-Wave device compared to classical simulated annealing in their experiments, but “fully agrees, endorses, and approves” of it—and indeed, that he himself was part of the team that did the comparison.

In other news, this Hacker News thread, which features clear, comprehending discussions of this blog post and the backstory that led up to it, has helped to restore my faith in humanity.

Two years ago almost to the day, I announced my retirement as Chief D-Wave Skeptic.  But—as many readers predicted at the time—recent events (and the contents of my inbox!) have given me no choice except to resume my post.  In an all-too-familiar pattern, multiple rounds of D-Wave-related hype have made it all over the world before the truth has had time to put its pants on and drop its daughter off in daycare.  And the current hype is particularly a shame, because once one slices through all the layers of ugh—the rigged comparisons, the “dramatic announcements” that mean nothing, the lazy journalists cherry-picking what they want to hear and ignoring the inconvenient bits—there really has been a huge scientific advance this past month in characterizing the D-Wave devices.  I’m speaking about the experiments on the D-Wave One installed at USC, the main results of which finally appeared in April.  Two of the coauthors of this new work—Matthias Troyer and Daniel Lidar—were at MIT recently to speak about their results, Troyer last week and Lidar this Tuesday.  Intriguingly, despite being coauthors on the same paper, Troyer and Lidar have very different interpretations of what their results mean, but we’ll get to that later.  For now, let me summarize what I think their work has established.

Evidence for Quantum Annealing Behavior

For the first time, we have evidence that the D-Wave One is doing what should be described as “quantum annealing” rather than “classical annealing” on more than 100 qubits.  (Note that D-Wave itself now speaks about “quantum annealing” rather than “quantum adiabatic optimization.”  The difference between the two is that the adiabatic algorithm runs coherently, at zero temperature, while quantum annealing is a “messier” version in which the qubits are strongly coupled to their environment throughout, but still maintain some quantum coherence.)  The evidence for quantum annealing behavior is still extremely indirect, but despite my “Chief Skeptic” role, I’m ready to accept what the evidence indicates with essentially no hesitation.

So what is the evidence?  Basically, the USC group ran the D-Wave One on a large number of randomly generated instances of what I’ll call the “D-Wave problem”: namely, the problem of finding the lowest-energy configuration of an Ising spin glass, with nearest-neighbor interactions that correspond to the D-Wave chip’s particular topology.  Of course, restricting attention to this “D-Wave problem” tilts the tables heavily in D-Wave’s favor, but no matter: scientifically, it makes a lot more sense than trying to encode Sudoku puzzles or something like that.  Anyway, the group then looked at the distribution of success probabilities when each instance was repeatedly fed to the D-Wave machine.  For example, would the randomly-generated instances fall into one giant clump, with a few outlying instances that were especially easy or especially hard for the machine?  Surprisingly, they found that the answer was no: the pattern was strongly bimodal, with most instances either extremely easy or extremely hard, and few instances in between.  Next, the group fed the same instances to Quantum Monte Carlo: a standard classical algorithm that uses Wick rotation to find the ground states of “stoquastic Hamiltonians,” the particular type of quantum evolution that the D-Wave machine is claimed to implement.  When they did that, they found exactly the same bimodal pattern that they found with the D-Wave machine.  Finally they fed the instances to a classical simulated annealing program—but there they found a “unimodal” distribution, not a bimodal one.  So, their conclusion is that whatever the D-Wave machine is doing, it’s more similar to Quantum Monte Carlo than it is to classical simulated annealing.

Curiously, we don’t yet have any hint of a theoretical explanation for why Quantum Monte Carlo should give rise to a bimodal distribution, while classical simulating annealing should give rise to a unimodal one.  The USC group simply observed the pattern empirically (as far as I know, they’re the first to do so), then took advantage of it to characterize the D-Wave machine.  I regard explaining this pattern as an outstanding open problem raised by their work.

In any case, if we accept that the D-Wave One is doing “quantum annealing,” then despite the absence of a Bell-inequality violation or other direct evidence, it’s reasonably safe to infer that there should be large-scale entanglement in the device.  I.e., the true quantum state is no doubt extremely mixed, but there’s no particular reason to believe we could decompose that state into a mixture of product states.  For years, I tirelessly repeated that D-Wave hadn’t even provided evidence that its qubits were entangled—and that, while you can have entanglement with no quantum speedup, you can’t possibly have a quantum speedup without at least the capacity to generate entanglement.  Now, I’d say, D-Wave finally has cleared the evidence-for-entanglement bar—and, while they’re not the first to do so with superconducting qubits, they’re certainly the first to do so with so many superconducting qubits.  So I congratulate D-Wave on this accomplishment.  If this had been advertised from the start as a scientific research project—”of course we’re a long way from QC being practical; no one would ever claim otherwise; but as a first step, we’ve shown experimentally that we can entangle 100 superconducting qubits with controllable couplings”—my reaction would’ve been, “cool!”  (Similar to my reaction to any number of other steps toward scalable QC being reported by research groups all over the world.)

No Speedup Compared to Classical Simulated Annealing

But of course, D-Wave’s claims—and the claims being made on its behalf by the Hype-Industrial Complex—are far more aggressive than that.  And so we come to the part of this post that has not been pre-approved by the International D-Wave Hype Repeaters Association.  Namely, the same USC paper that reported the quantum annealing behavior of the D-Wave One, also showed no speed advantage whatsoever for quantum annealing over classical simulated annealing.  In more detail, Matthias Troyer’s group spent a few months carefully studying the D-Wave problem—after which, they were able to write optimized simulated annealing code that solves the D-Wave problem on a normal, off-the-shelf classical computer, about 15 times faster than the D-Wave machine itself solves the D-Wave problem!  Of course, if you wanted even more classical speedup than that, then you could simply add more processors to your classical computer, for only a tiny fraction of the ~$10 million that a D-Wave One would set you back.

Some people might claim it’s “unfair” to optimize the classical simulated annealing code to take advantage of the quirks of the D-Wave problem.  But think about it this way: D-Wave has spent ~$100 million, and hundreds of person-years, optimizing the hell out of a special-purpose annealing device, with the sole aim of solving this one problem that D-Wave itself defined.  So if we’re serious about comparing the results to a classical computer, isn’t it reasonable to have one professor and a few postdocs spend a few months optimizing the classical code as well?

As I said, besides simulated annealing, the USC group also compared the D-Wave One’s performance against a classical implementation of Quantum Monte Carlo.  And maybe not surprisingly, the D-Wave machine was faster than a “direct classical simulation of itself” (I can’t remember how many times faster, and couldn’t find that information in the paper).  But even here, there’s a delicious irony.  The only reason the USC group was able to compare the D-Wave one against QMC at all, is that QMC is efficiently implementable on a classical computer!  (Albeit probably with a large constant overhead compared to running the D-Wave annealer itself—hence the superior performance of classical simulated annealing over QMC.)  This means that, if the D-Wave machine can be understood as reaching essentially the same results as QMC (technically, “QMC with no sign problem”), then there’s no real hope for using the D-Wave machine to get an asymptotic speedup over a classical computer.  The race between the D-Wave machine and classical simulations of the machine would then necessarily be a cat-and-mouse game, a battle of constant factors with no clear asymptotic victor.  (Some people might conjecture that it will also be a “Tom & Jerry game,” the kind where the classical mouse always gets the better of the quantum cat.)

At this point, it’s important to give a hearing to three possible counterarguments to what I’ve written above.

The first counterargument is that, if you plot both the runtime of simulated annealing and the runtime of the D-Wave machine as functions of the instance size n, you find that, while simulated annealing is faster in absolute terms, it can look like the curve for the D-Wave machine is less steep.  Over on the blog “nextbigfuture”, an apparent trend of this kind has been fearlessly extrapolated to predict that with 512 qubits, the D-Wave machine will be 10 billion times faster than a classical computer.  But there’s a tiny fly in the ointment.  As Troyer carefully explained to me last week, the “slow growth rate” of the D-Wave machine’s runtime is, ironically, basically an artifact of the machine being run too slowly on small values of n.  Run the D-Wave machine as fast as it can run for small n, and the difference in the slopes disappears, with only the constant-factor advantage for simulated annealing remaining.  In short, there seems to be no evidence, at present, that the D-Wave machine is going to overtake simulated annealing for any instance size.

The second counterargument is that the correlation between the two “bimodal distributions”—that for the D-Wave machine and that for the Quantum Monte Carlo simulation—is not perfect.  In other words, there are a few instances (not many) that QMC solves faster than the D-Wave machine, and likewise a few instances that the D-Wave machine solves faster than QMC.  Not surprisingly, the latter fact has been eagerly seized on by the D-Wave boosters (“hey, sometimes the machine does better!”).  But Troyer has a simple and hilarious response to that.  Namely, he found that his group’s QMC code did a better job of correlating with the D-Wave machine, than the D-Wave machine did of correlating with itself!  In other words, calibration errors seem entirely sufficient to explain the variation in performance, with no need to posit any special class of instances (however small) on which the D-Wave machine dramatically outperforms QMC.

The third counterargument is just the banal one: the USC experiment was only one experiment with one set of instances (albeit, a set one might have thought would be heavily biased toward D-Wave).  There’s no proof that, in the future, it won’t be discovered that the D-Wave machine does something more than QMC, and that there’s some (perhaps specially-designed) set of instances on which the D-Wave machine asymptotically outperforms both QMC and Troyer’s simulated annealing code.  (Indeed, I gather that folks at D-Wave are now assiduously looking for such instances.)  Well, I concede that almost anything is possible in the future—but “these experiments, while not supporting D-Wave’s claims about the usefulness of its devices, also don’t conclusively disprove those claims” is a very different message than what’s currently making it into the press.

Comparison to CPLEX is Rigged

Unfortunately, the USC paper is not the one that’s gotten the most press attention—perhaps because half of it inconveniently told the hypesters something they didn’t want to hear (“no speedup”).  Instead, journalists have preferred a paper released this week by Catherine McGeoch and Cong Wang, which reports that the D-Wave machine outperformed the classical CPLEX optimization package by a factor of ~3600, on Ising spin problems involving 439 bits.  Wow!  That sounds awesome!  But before rushing to press, let’s pause to ask ourselves: how can we reconcile this with the USC group’s result of no speedup?

The answer turns out to be painfully simple.  CPLEX is a general-purpose, off-the-shelf exact optimization package.  Of course an exact solver can’t compete against quantum annealing—or for that matter, against classical annealing or other classical heuristics!  Noticing this problem, McGeoch and Wang do also compare the D-Wave machine against tabu search, a classical heuristic algorithm.  When they do so, they find that an advantage for the D-Wave machine persists, but it becomes much, much smaller (they didn’t report the exact time comparison).  Amusingly, they write in their “Conclusions and Future Work” section:

It would of course be interesting to see if highly tuned implementations of, say, tabu search or simulated annealing could compete with Blackbox or even QA [i.e., the D-Wave machines] on QUBO [quadratic binary optimization] problems; some preliminary work on this question is underway.

As I said above, at the time McGeoch and Wang’s paper was released to the media (though maybe not at the time it was written?), the “highly tuned implementation” of simulated annealing that they ask for had already been written and tested, and the result was that it outperformed the D-Wave machine on all instance sizes tested.  In other words, their comparison to CPLEX had already been superseded by a much more informative comparison—one that gave the “opposite” result—before it ever became public.  For obvious reasons, most press reports have simply ignored this fact.

Troyer, Lidar, and Stone Soup

Much of what I’ve written in this post, I learned by talking to Matthias Troyer—the man who carefully experimented with the D-Wave machine and figured out how to beat it using simulated annealing, and who I regard as probably the world’s #1 expert right now on what exactly the machine does.  Troyer wasn’t shy about sharing his opinions, and while couched with qualifications, they tended toward extremely skeptical.  For example, Troyer conjectured that, if D-Wave ultimately succeeds in getting a speedup over classical computers in a fair comparison, then it will probably be by improving coherence and calibration, incorporating error-correction, and doing other things that “traditional,” “academic” quantum computing researchers had said all along would need to be done.

As I said, Danny Lidar is another coauthor on the USC paper, and also recently visited MIT to speak.  Lidar and Troyer agree on the basic facts—yet Lidar noticeably differed from Troyer, in trying to give each fact the most “pro-D-Wave spin” it could possibly support.  Lidar spoke at our quantum group meeting, not about the D-Wave vs. simulated annealing performance comparison (which he agrees with), but about a proposal of his for incorporating quantum error-correction into the D-Wave device, together with some experimental results.  He presented his proposal, not as a reductio ad absurdum of D-Wave’s entire philosophy, but rather as a positive opportunity to get a quantum speedup using D-Wave’s approach.

So, to summarize my current assessment of the situation: yes, absolutely, D-Wave might someday succeed—ironically, by adapting the very ideas from “the gate model” that its entire business plan has been based on avoiding, and that D-Wave founder Geordie Rose has loudly denigrated for D-Wave’s entire history!  If that’s what happens, then I predict that science writers, and blogs like “nextbigfuture,” will announce from megaphones that D-Wave has been vindicated at last, while its narrow-minded, theorem-obsessed, ivory-tower academic naysayers now have egg all over their faces.  No one will care that the path to success—through quantum error-correction and so on—actually proved the academic critics right, and that D-Wave’s “vindication” was precisely like that of the deliciousness of stone soup in the old folktale.  As for myself, I’ll probably bang my head on my desk until I sustain so much brain damage that I no longer care either.  But at least I’ll still have tenure, and the world will have quantum computers.

The Messiah’s Quantum Annealer

Over the past few days, I’ve explained the above to at least six different journalists who asked.  And I’ve repeatedly gotten a striking response: “What you say makes sense—but then why are all these prestigious people and companies investing in D-Wave?  Why did Bo Ewald, a prominent Silicon Valley insider, recently join D-Wave as president of its US operations?  Why the deal with Lockheed Martin?  Why the huge deal with NASA and Google, just announced today?  What’s your reaction to all this news?”

My reaction, I confess, is simple.  I don’t care—I actually told them this—if the former Pope Benedict has ended his retirement to become D-Wave’s new marketing director.  I don’t care if the Messiah has come to Earth on a flaming chariot, not to usher in an age of peace but simply to spend $10 million on D-Wave’s new Vesuvius chip.  And if you imagine that I’ll ever care about such things, then you obviously don’t know much about me.  I’ll tell you what: if peer pressure is where it’s at, then come to me with the news that Umesh Vazirani, or Greg Kuperberg, or Matthias Troyer is now convinced, based on the latest evidence, that D-Wave’s chip asymptotically outperforms simulated annealing in a fair comparison, and does so because of quantum effects.  Any one such scientist’s considered opinion would mean more to me than 500,000 business deals.

The Argument from Consequences

Let me end this post with an argument that several of my friends in physics have explicitly made to me—not in the exact words below but in similar ones.

“Look, Scott, let the investors, government bureaucrats, and gullible laypeople believe whatever they want—and let D-Wave keep telling them whatever’s necessary to stay in business.  It’s unsportsmanlike and uncollegial of you to hold D-Wave’s scientists accountable for whatever wild claims their company’s PR department might make.  After all, we’re in this game too!  Our universities put out all sorts of overhyped press releases, but we don’t complain because we know that it’s done for our benefit.  Besides, you’d doubtless be trumpeting the same misleading claims, if you were in D-Wave’s shoes and needed the cash infusions to survive.  Anyway, who really cares whether there’s a quantum speedup yet or no quantum speedup?  At least D-Wave is out there trying to build a scalable quantum computer, and getting millions of dollars from Jeff Bezos, Lockheed, Google, the CIA, etc. etc. to do so—resources more of which would be directed our way if we showed a more cooperative attitude!  If we care about scalable QCs ever getting built, then the wise course is to celebrate what D-Wave has done—they just demonstrated quantum annealing on 100 qubits, for crying out loud!  So let’s all be grownups here, focus on the science, and ignore the marketing buzz as so much meaningless noise—just like a tennis player might ignore his opponent’s trash-talking (‘your mother is a whore,’ etc.) and focus on the game.”

I get this argument: really, I do.  I even concede that there’s something to be said for it.  But let me now offer a contrary argument for the reader’s consideration.

Suppose that, unlike in the “stone soup” scenario I outlined above, it eventually becomes clear that quantum annealing can be made to work on thousands of qubits, but that it’s a dead end as far as getting a quantum speedup is concerned.  Suppose the evidence piles up that simulated annealing on a conventional computer will continue to beat quantum annealing, if even the slightest effort is put into optimizing the classical annealing code.  If that happens, then I predict that the very same people now hyping D-Wave will turn around and—without the slightest acknowledgment of error on their part—declare that the entire field of quantum computing has now been unmasked as a mirage, a scam, and a chimera.  The same pointy-haired bosses who now flock toward quantum computing, will flock away from it just as quickly and as uncomprehendingly.  Academic QC programs will be decimated, despite the slow but genuine progress that they’d been making the entire time in a “parallel universe” from D-Wave.  People’s contempt for academia is such that, while a D-Wave success would be trumpeted as its alone, a D-Wave failure would be blamed on the entire QC community.

When it comes down to it, that’s the reason why I care about this matter enough to have served as “Chief D-Wave Skeptic” from 2007 to 2011, and enough to resume my post today.  As I’ve said many times, I really, genuinely hope that D-Wave succeeds at building a QC that achieves an unambiguous speedup!  I even hope the academic QC community will contribute to D-Wave’s success, by doing careful independent studies like the USC group did, and by coming up with proposals like Lidar’s for how D-Wave could move forward.  On the other hand, in the strange, unlikely event that D-Wave doesn’t succeed, I’d like people to know that many of us in the QC community were doing what academics are supposed to do, which is to be skeptical and not leave obvious questions unasked.  I’d like them to know that some of us simply tried to understand and describe what we saw in front of us—changing our opinions repeatedly as new evidence came in, but disregarding “meta-arguments” like my physicist friends’ above.  The reason I can joke about how easy it is to bribe me is that it’s actually kind of hard.

Two years ago, when I attended the FQXi conference on a ship from Norway to Denmark, I (along with many other conference participants) was interviewed by Robert Lawrence Kuhn, who produces a late-night TV program called “Closer to Truth.”  I’m pleased to announce (hat tip: Sean Carroll) that four videos from my interview are finally available online:

• Is the Universe a Computer?

(like a politician, I steer the question toward “what kind of computer is the universe?,” then start talking about P vs. NP, quantum computing, and the holographic principle)

• What Does Quantum Theory Mean?

(here I mostly talk about the idea of computational intractability as a principle of physics)

• Quantum Computing Mysteries

(basics of quantum mechanics and quantum computing)

• Setting Time Aright (about the differences between time and space, the P vs. PSPACE problem, and computing with closed timelike curves)

(No, I didn’t choose the titles!)

For regular readers of this blog, there’s probably nothing new in these videos, but for those who are “just tuning in,” they provide an extremely simple and concise introduction to what I care about and why.  I’m pretty happy with how they came out.

Once you’re finished with me (or maybe even before then…), click here for the full list of interviewees, which includes David Albert, Raphael Bousso, Sean Carroll, David Deutsch, Rebecca Goldstein, Seth Lloyd, Marvin Minsky, Roger Penrose, Lenny Susskind, Steven Weinberg, and many, many others who might be of interest to Shtetl-Optimized readers.

Back in February, I gave a talk with the above title at the Annual MIT Latke-Hamentaschen Debate.  I’m pleased to announce that streaming video of my talk is now available!  (My segment starts about 10 minutes into the video, and lasts for 10 minutes.)  You can also download my PowerPoint slides here.

Out of hundreds of talks I’ve given in my life, on five continents, this is the single talk of which I’m the proudest.

Of course, before you form an opinion about the issue at hand, you should also check out the contributions of my fellow debaters.  On the sadly-mistaken hamentasch side, my favorite presentation was that of mathematician Arthur Mattuck, which starts in at 56 minutes and lasts for a full half hour (!! – the allotted time was only 8 minutes).  Mattuck relates the shapes of latkes and hamentaschen to the famous Kakeya problem in measure theory—though strangely, his final conclusions seem to provide no support whatsoever for the hamentaschen, even on Mattuck’s own terms.

Finally, what if you’re a reader for whom the very words “latke” and “hamentaschen” are just as incomprehensible as the title of this blog?  OK, here are some Cliff Notes:

• Latkes are fried potato pancakes, traditionally eaten by Jews on Hannukah.
• Hamentaschen are triangular fruit-filled cookies, traditionally eaten by Jews on Purim.
• Beginning at the University of Chicago in 1946, many universities around the world have held farcical annual “debates” between faculty members (both Jewish and non-Jewish) about which of those two foods is better.  (The reason I say “farcical” is simply that, as I explain in my talk, the truth has always been overwhelmingly on one side.)  The debaters have invoked everything from feminist theory to particle physics to bolster their case.

Thanks very much to Dean of Admissions Stu Schmill for moderating, and to MIT Hillel for organizing the debate.

Update: Luboš has a new blog post announcing that he finally found a chapter in Quantum Computing Since Democritus that he likes!  Woohoo!  Whether coincidentally or not, the chapter he likes makes exactly the same points about quantum mechanics that I also make in my pro-latke presentation.

Friend-of-the-blog Dorit Aharonov asked me to advertise the QStart Conference, which will be held at Hebrew University of Jerusalem June 24-27 of this year, to celebrate the opening of Hebrew University’s new Quantum Information Science Center.  Speakers include Yakir Aharonov, Jacob Bekenstein, Hans Briegel, Ed Farhi, Patrick Hayden, Ray Laflamme, Elon Lindenstrauss, Alex Lubotzky, John Martinis, Barbara Terhal, Umesh Vazirani, Stephanie Wehner, Andrew Yao … and me, your humble blogger (who will actually be there with Lily, on her first trip abroad—or for that matter, beyond the Boston metropolitan area).  Dorit tells me that the conference should be of interest to mathematicians, physicists, chemists, philosophers, and computer scientists; that registration is open now; and that student travel support is available.  Oh, and if you’re one of the people who think quantum computing is bunk?  As displayed on the poster above, leading QC skeptic Gil Kalai is a co-organizer of the conference.

On Wednesday, I gave a fun talk with that title down the street at Microsoft Research New England.  Disappointingly, no one in the audience did seem to think quantum computing was bunk (or if they did, they didn’t speak up): I was basically preaching to the choir.  My PowerPoint slides are here.  There’s also a streaming video here, but watch it at your own risk—my stuttering and other nerdy mannerisms seemed particularly bad, at least in the short initial segment that I listened to.  I really need media training.  Anyway, thanks very much to Boaz Barak for inviting me.

Update (March 22): The Kindle edition of Quantum Computing Since Democritus is now available, for the low price of $15.40!  (Not factorial.)  Click here to get it from amazon.com, or here to get it from amazon.co.uk.  And let me know how it looks (I haven’t seen it yet).  Another Update: Just saw the Kindle edition, and the figures and formulas came out great!  It’s a product I stand behind with pride.

In the meantime, I regret to say that the marketing for this book is getting crasser and more exploitative by the day.

It seems like wherever I go these days, all anyone wants to talk about is Quantum Computing Since Democritus—the sprawling new book by Scott Aaronson, published by Cambridge University Press and available for order now.  Among leading figures in quantum information science—many of them well-known to Shtetl-Optimized readers—the book is garnering the sort of hyperbolic praise that would make Shakespeare or Tolstoy blush:

“I laughed, I cried, I fell off my chair – and that was just reading the chapter on Computational Complexity.  Aaronson is a tornado of intellectual activity: he rips our brains from their intellectual foundations; twists them through a tour of physics, mathematics, computer science, and philosophy; stuffs them full of facts and theorems; tickles them until they cry ‘Uncle’; and then drops them, quivering, back into our skulls.  Aaronson raises deep questions of how the physical universe is put together and why it is put together the way it is.  While we read his lucid explanations we can believe – at least while we hold the book in our hands – that we understand the answers, too.” –Seth Lloyd

“Scott Aaronson has written a beautiful and highly original synthesis of what we know about some of the most fundamental questions in science: What is information? What does it mean to compute? What is the nature of mind and of free will?” –Michael Nielsen

“Not since Richard Feynman’s Lectures on Physics has there been a set of lecture notes as brilliant and as entertaining.  Aaronson leads the reader on a wild romp through the most important intellectual achievements in computing and physics, weaving these seemingly disparate fields into a captivating narrative for our modern age of information.  Aaronson wildly runs through the fields of physics and computers, showing us how they are connected, how to understand our computational universe, and what questions exist on the borders of these fields that we still don’t understand.   This book is a poem disguised as a set of lecture notes.  The lectures are on computing and physics, complexity theory and mathematical logic and quantum physics.  The poem is made up of proofs, jokes, stories, and revelations, synthesizing the two towering fields of computer science and physics into a coherent tapestry of sheer intellectual awesomeness.” –Dave Bacon

After months of overhearing people saying things like the above—in the halls of MIT, the checkout line at Trader Joe’s, the bathroom, anywhere—I finally had to ask in annoyance: “is all this buzz justified?  I mean, I’m sure the book is as deep, hilarious, and worldview-changing as everyone says it is.  But, after all, it’s based off lecture notes that have long been available for free on the web.  And Aaronson, being the magnanimous, open-access-loving saint that he is, has no plans to remove the online notes, even though he could really use the royalties from book sales to feed his growing family.  Nor does Cambridge University Press object to his principled decision.”

“No, you don’t understand,” they told me.  “Word on the street has it that the book is extensively updated for 2013—that it’s packed with new discussions of things like algebrization, lattice-based cryptography, the QIP=PSPACE theorem, the ‘quantum time travel controversy,’ BosonSampling, black-hole firewalls, and even the Australian models episode.  They say it took years of painstaking work, by Aaronson and his student Alex Arkhipov, to get the notes into book form: fixing mistakes, clarifying difficult points, smoothing out rough edges, all while leaving intact the original’s inimitable humor.  I even heard Aaronson reveals he’s changed his mind about certain things since 2006.  How could you not want such a labor of love on your bookshelf?”

Exasperated, I finally exclaimed: “But the book isn’t even out yet in North America!  Amazon.com says it won’t ship until April 30.”

“Sure,” one gas-station attendant replied to me, “but the secret is, it’s available now from Amazon.co.uk.  Personally, I couldn’t wait a month, so I ordered it shipped to me from across the pond.  But if you’re a less hardcore quantum complexity theory fan, and you live in North America, you can also preorder the book from Amazon.com, and they’ll send it to you when it arrives.”

Much as the hype still grated, I had to admit that I’d run out of counterarguments, so I looked into ordering a copy for myself.

I got back a couple days ago from John Preskill‘s 60th birthday symposium at Caltech.  To the general public, Preskill is probably best known for winning two bets against Stephen Hawking.  To readers of Shtetl-Optimized, he might be known for his leadership in quantum information science, his pioneering work in quantum error-correction, his beautiful lecture notes, or even his occasional comments here (though these days he has his own group blog and Twitter feed to keep him busy).  I know John as a friend, colleague, and mentor who’s done more for me than I can say.

The symposium was a blast—a chance to hear phenomenal talks, enjoy the California sun, and catch up with old friends like Dave Bacon (who stepped down as Pontiff before stepping down as Pontiff was cool).  The only bad part was that I inadvertently insulted John in my talk, by calling him my “lodestar of sanity.”  What I meant was that, for 13 years, I’ve known plenty of physicists who can be arbitrarily off-base when they talk about computer science and vice versa, but I’ve only ever known John to be on-base about either.  If you asked him a question involving, say, both Barrington’s Theorem and Majorana fermions, he’s one of the few people on earth who would know both, seem totally unfazed by your juxtaposing them, and probably have an answer that he’d carefully tailor to your level of knowledge and interest.  In a polyglot field like quantum information, that alone makes him invaluable.  But along with his penetrating insight comes enviable judgment and felicity of expression: unlike some of us (me), John always manages to tell the truth without offending his listeners.  If I were somehow entrusted with choosing a President of the United States, he’d be one of my first choices, certainly ahead of myself.

Anyway, it turned out that John didn’t like my use of the word “sane” to summarize the above: for him (understandably, in retrospect), it had connotations of being humorless and boring, two qualities I’ve never seen in him.  (Also, as I pointed out later, the amount of time John has spent helping me and patiently explaining stuff to me does weigh heavily against his sanity.)  So I hereby rename John my Lodestar of Awesomeness.

In case anyone cares, my talk was entitled “Hidden Variables as Fruitful Dead Ends”; the PowerPoint slides are here.  I spoke about a new preprint by Adam Bouland, Lynn Chua, George Lowther, and myself, on possibility and impossibility results for “ψ-epistemic theories” (a class of hidden-variable theories that was also the subject of the recent PBR Theorem, discussed previously on this blog).  My talk also included material from my old paper Quantum Computing and Hidden Variables.

The complete program is here.  A few highlights (feel free to mention others in the comments):

• Patrick Hayden spoke about a beautiful result of himself and Alex May, on “where and when a qubit can be.”  After the talk, I commented that it’s lucky for the sake of Hayden and May’s induction proof that 3 happens to be the next integer after 2.  If you get that joke, then I think you’ll understand their result and vice versa.
• Lenny Susskind—whose bestselling The Theoretical Minimum is on my to-read list—spoke about his views on the AMPS firewall argument.  As you know if you’ve been reading physics blogs, the firewall argument has been burning up (har, har) the world of quantum gravity for months, putting up for grabs aspects of black hole physics long considered settled (or not, depending on who you ask).  Lenny gave a typically-masterful summary, which for the first time enabled me to understand the role played in the AMPS argument by “the Zone” (a region near the black hole but outside its event horizon, in which the Hawking radiation behaves a little differently than it does when it’s further away).  I was particularly struck by Lenny’s comment that whether an observer falling into a black hole encounters a firewall might be “physics’ Axiom of Choice”: that is, we can only follow the logical consequences of theories we formulate outside black-hole event horizons, and maybe those theories simply don’t decide the firewall question one way or the other.  (Then again, maybe they do.)  Lenny also briefly mentioned a striking recent paper by Harlow and Hayden, which argues that the true resolution of the AMPS paradox might involve … wait for it … computational complexity, and specifically, the difficulty of solving QSZK (Quantum Statistical Zero Knowledge) problems in BQP.  And what’s a main piece evidence that QSZK⊄BQP?  Why, the collision lower bound, which I proved 12 years ago while a summer student at Caltech and an awestruck attendee of Preskill’s weekly group meetings.  Good thing no one told me back then that black holes were involved.
• Charlie Bennett talked about things that I’ve never had the courage to give a talk about, like the Doomsday Argument and the Fermi Paradox.  But his disarming, avuncular manner made it all seem less crazy than it was.
• Paul Ginsparg, founder of the arXiv, presented the results of a stylometric analysis of John Preskill’s and Alexei Kitaev’s research papers.  The main results were as follows: (1) John and Alexei are easily distinguishable from each other, due in part to the more latter’s “Russian” use of function words (“the,” “which,” “that,” etc.).   (2) Alexei, despite having lived in the US for more than a decade, is if anything becoming more “Russian” in his function word use over time. (3) Even more interestingly, John is also becoming more “Russian” in his function word use—a possible result of his long interaction with Alexei. (4) A joint paper by Kitaev and Preskill was indeed written by both of them.  (Update: While detained at the airport, Paul decided to post an online video of his talk.)

Speaking of which, the great Alexei Kitaev himself—the $3 million man—spoke about Berry curvature for many-body systems, but unfortunately I had to fly back early (y’know, 2-month-old baby) and missed his talk.  Maybe someone else can provide a summary.

Happy 60th birthday, John!

Two unrelated announcements.

1. Everyone who reads this blog should buy Sean Carroll’s two recent books: From Eternity to Here (about the arrow of time) and The Particle at the End of the Universe (about the Higgs boson and quantum field theory more generally).  They’re two of the best popular physics books I’ve ever read—in their honesty, humor, clarity, and total lack of pretense, they exemplify what every book in this genre should be but very few are.  If you need even more inducement, go watch Sean hit it out of the park on the Colbert Report (and then do it again).  I can’t watch those videos without seething with jealousy: given how many “OK”s and “y’know”s lard my every spoken utterance, I’ll probably never get invited to hawk a book on Colbert.  Which is a shame, because as it happens, my Quantum Computing Since Democritus book will finally be released in the US by Cambridge University Press on April 30th!  (It’s already available in the UK, but apparently needs to be shipped to the US by boat.)  And it’s loaded with new material, not contained in the online lecture notes.  And you can preorder it now.  And my hawking of Sean’s books is in no way whatsoever related to any hope that Sean might return the favor with my book.

2. Recent Turing Award winner Silvio Micali asks me to advertise the Second Cambridge Area Economics and Computation Day (CAEC’13), which will be held on Friday April 26 at MIT.  Anything for you, Silvio!  (At least for the next week or two.)

At least eight people—journalists, colleagues, blog readers—have now asked my opinion of a recent paper by Ross Anderson and Robert Brady, entitled “Why quantum computing is hard and quantum cryptography is not provably secure.”  Where to begin?

1. Based on a “soliton” model—which seems to be almost a local-hidden-variable model, though not quite—the paper advances the prediction that quantum computation will never be possible with more than 3 or 4 qubits.  (Where “3 or 4″ are not just convenient small numbers, but actually arise from the geometry of spacetime.)  I wonder: before uploading their paper, did the authors check whether their prediction was, y’know, already falsified?  How do they reconcile their proposal with (for example) the 8-qubit entanglement observed by Haffner et al. with trapped ions—not to mention the famous experiments with superconducting Josephson junctions, buckyballs, and so forth that have demonstrated the reality of entanglement among many thousands of particles (albeit not yet in a “controllable” form)?
2. The paper also predicts that, even with 3 qubits, general entanglement will only be possible if the qubits are not collinear; with 4 qubits, general entanglement will only be possible if the qubits are not coplanar.  Are the authors aware that, in ion-trap experiments (like those of David Wineland that recently won the Nobel Prize), the qubits generally are arranged in a line?  See for example this paper, whose abstract reads in part: “Here we experimentally demonstrate quantum error correction using three beryllium atomic-ion qubits confined to a linear, multi-zone trap.”
3. Finally, the paper argues that, because entanglement might not be a real phenomenon, the security of quantum key distribution remains an open question.  Again: are the authors aware that the most practical QKD schemes, like BB84, never use entanglement at all?  And that therefore, even if the paper’s quasi-local-hidden-variable model were viable (which it’s not), it still wouldn’t justify the claim in the title that “…quantum cryptography is not provably secure”?

Yeah, this paper is pretty uninformed even by the usual standards of attempted quantum-mechanics-overthrowings.  Let me now offer three more general thoughts.

First thought: it’s ironic that I’m increasingly seeing eye-to-eye with Lubos Motl—who once called me “the most corrupt piece of moral trash”—in his rantings against the world’s “anti-quantum-mechanical crackpots.”  Let me put it this way: David Deutsch, Chris Fuchs, Sheldon Goldstein, and Roger Penrose hold views about quantum mechanics that are diametrically opposed to one another’s.  Yet each of these very different physicists has earned my admiration, because each, in his own way, is trying to listen to whatever quantum mechanics is saying about how the world works.  However, there are also people all of whose “thoughts” about quantum mechanics are motivated by the urge to plug their ears and shut out whatever quantum mechanics is saying—to show how whatever naïve ideas they had before learning QM might still be right, and how all the experiments of the last century that seem to indicate otherwise might still be wiggled around.  Like monarchists or segregationists, these people have been consistently on the losing side of history for generations—so it’s surprising, to someone like me, that they continue to show up totally unfazed and itching for battle, like the knight from Monty Python and the Holy Grail with his arms and legs hacked off.  (“Bell’s Theorem?  Just a flesh wound!”)

Like any physical theory, of course quantum mechanics might someday be superseded by an even deeper theory.  If and when that happens, it will rank alongside Newton’s apple, Einstein’s elevator, and the discovery of QM itself among the great turning points in the history of physics.  But it’s crucial to understand that that’s not what we’re discussing here.  Here we’re discussing the possibility that quantum mechanics is wrong, not for some deep reason, but for a trivial reason that was somehow overlooked since the 1920s—that there’s some simple classical model that would make everyone exclaim,  “oh!  well, I guess that whole framework of exponentially-large Hilbert space was completely superfluous, then.  why did anyone ever imagine it was needed?”  And the probability of that is comparable to the probability that the Moon is made of Gruyère.  If you’re a Bayesian with a sane prior, stuff like this shouldn’t even register.

Second thought: this paper illustrates, better than any other I’ve seen, how despite appearances, the “quantum computing will clearly be practical in a few years!” camp and the “quantum computing is clearly impossible!” camp aren’t actually opposed to each other.  Instead, they’re simply two sides of the same coin.  Anderson and Brady start from the “puzzling” fact that, despite what they call “the investment of tremendous funding resources worldwide” over the last decade, quantum computing still hasn’t progressed beyond a few qubits, and propose to overthrow quantum mechanics as a way to resolve the puzzle.  To me, this is like arguing in 1835 that, since Charles Babbage still hasn’t succeeded in building a scalable classical computer, we need to rewrite the laws of physics in order to explain why classical computing is impossible.  I.e., it’s a form of argument that only makes sense if you’ve adopted what one might call the “Hype Axiom”: the axiom that any technology that’s possible sometime in the future, must in fact be possible within the next few years.

Third thought: it’s worth noting that, if (for example) you found Michel Dyakonov’s arguments against QC (discussed on this blog a month ago) persuasive, then you shouldn’t find Anderson’s and Brady’s persuasive, and vice versa.  Dyakonov agrees that scalable QC will never work, but he ridicules the idea that we’d need to modify quantum mechanics itself to explain why.  Anderson and Brady, by contrast, are so eager to modify QM that they don’t mind contradicting a mountain of existing experiments.  Indeed, the question occurs to me of whether there’s any pair of quantum computing skeptics whose arguments for why QC can’t work are compatible with one another’s.  (Maybe Alicki and Dyakonov?)

But enough of this.  The truth is that, at this point in my life, I find it infinitely more interesting to watch my two-week-old daughter Lily, as she discovers the wonderful world of shapes, colors, sounds, and smells, than to watch Anderson and Brady, as they fail to discover the wonderful world of many-particle quantum mechanics.  So I’m issuing an appeal to the quantum computing and information community.  Please, in the comments section of this post, explain what you thought of the Anderson-Brady paper.  Don’t leave me alone to respond to this stuff; I don’t have the time or the energy.  If you get quantum probability, then stand up and be measured!

A month and a half ago, I gave a 45-minute lecture / attempted standup act with the intentionally-nutty title above, for my invited talk at the wonderful NIPS (Neural Information Processing Systems) conference at Lake Tahoe.  Video of the talk is now available at VideoLectures net.  That site also did a short written interview with me, where they asked about the “message” of my talk (which is unfortunately hard to summarize, though I tried!), as well as the Aaron Swartz case and various other things.  If you just want the PowerPoint slides from my talk, you can get those here.

Now, I could’ve just given my usual talk on quantum computing and complexity.  But besides increasing boredom with that talk, one reason for my unusual topic was that, when I sent in the abstract, I was under the mistaken impression that NIPS was at least half a “neuroscience” conference.  So, I felt a responsibility to address how quantum information science might intersect the study of the brain, even if the intersection ultimately turned out to be the empty set!  (As I say in the talk, the fact that people have speculated about connections between the two, and have sometimes been wrong but for interesting reasons, could easily give me 45 minutes’ worth of material.)

Anyway, it turned out that, while NIPS was founded by people interested in modeling the brain, these days it’s more of a straight machine learning conference.  Still, I hope the audience there at least found my talk an amusing appetizer to their hearty meal of kernels, sparsity, and Bayesian nonparametric regression.  I certainly learned a lot from them; while this was my first machine learning conference, I’ll try to make sure it isn’t my last.

(Incidentally, the full set of NIPS videos is here; it includes great talks by Terry Sejnowski, Stanislas Dehaene, Geoffrey Hinton, and many others.  It was a weird honor to be in such distinguished company — I wouldn’t have invited myself!)

If you have opinions about quantum computing, and haven’t yet read through the discussion following my “response to Dyakonov” post, you’re missing out.  The comments—by QC researchers (Preskill, Kuperberg, Gottesman, Fitzsimons…), skeptics (Dyakonov, Kalai, …), and interested outsiders alike—are some of the most interesting I’ve seen in this two-decade-old debate.

At the risk of crass immodesty, I just posted a comment whose ending amused me so much, I had to promote it to its own post.  My starting point was an idea that several skeptics, including Dyakonov, have articulated in this debate, and which I’ll paraphrase as follows:

Sure, quantum computing might be “possible in principle.”  But only in the same sense that teaching a donkey how to read, transmuting large amounts of lead into gold, or doing a classical computation in the center of the Sun are “possible in principle.”  In other words, the task is at the same time phenomenally difficult, and fundamentally arbitrary and quixotic even if you did somehow achieve it.

Since I considered this argument an important one, I wrote a response, which stressed how quantum computing is different both because it strives to solve problems that flat-out can’t feasibly be solved any other way if standard complexity conjectures are correct, and because the goal—namely, expanding the human race’s computational powers beyond classical polynomial time—is not at all an arbitrary one.  However, I then felt the need to expand on the last point, since it occurred to me that it’s both central to this debate and almost never discussed explicitly.

How do I know that the desire for computational power isn’t just an arbitrary human quirk?

Well, the reason I know is that math isn’t arbitrary, and computation is nothing more or less than the mechanizable part of solving math problems.

Let me put it this way: if we ever make contact with an advanced extraterrestrial civilization, they might have three sexes and five heads. But they, too, will have encountered the problem of factoring integers into primes. Indeed, because they’ll inhabit the same physical universe as we do, they’ll even have encountered the problem of simulating quantum physics. And therefore, putting the two together, they’ll almost certainly have discovered something like Shor’s algorithm — though they’ll call it “Zork’s bloogorithm” or whatever.