Shtetl-Optimized

I’ve put up a new paper.  Unusually for me these days, it’s a very short and simple one (8 pages)—I should do more like this!  Here’s the abstract:

We show that combining two different hypothetical enhancements to quantum computation—namely, quantum advice and non-collapsing measurements—would let a quantum computer solve any decision problem whatsoever in polynomial time, even though neither enhancement yields extravagant power by itself. This complements a related result due to Raz. The proof uses locally decodable codes.

I welcome discussion in the comments.  The real purpose of this post is simply to fulfill a request by James Gallagher, in the comments of my Robin Hanson post:

The probably last chance for humanity involves science progressing, can you apply your efforts to quantum computers, which is your expertise, and stop wasting many hours of you [sic] time with this [expletive deleted]

Indeed, I just returned to Tel Aviv, for the very tail end of my sabbatical, from a weeklong visit to Google’s quantum computing group in LA.  While we mourned tragedies—multiple members of the quantum computing community lost loved ones in recent weeks—it was great to be among so many friends, and great to talk and think for once about actual progress that’s happening in the world, as opposed to people saying mean things on Twitter.  Skipping over its plans to build a 49-qubit chip, Google is now going straight for 72 qubits.  And we now have some viable things that one can do, or try to do, with such a chip, beyond simply proving quantum supremacy—I’ll say more about that in subsequent posts.

Anyway, besides discussing this progress, the other highlight of my trip was going from LA to Santa Barbara on the back of Google physicist Sergio Boixo’s motorcycle—weaving in and out of rush-hour traffic, the tightness of my grip the only thing preventing me from flying out onto the freeway.  I’m glad to have tried it once, and probably won’t be repeating it.

Update: I posted a new version of the PDQP/qpoly=ALL paper, which includes an observation about communication complexity, and which—inspired by the comments section—clarifies that when I say “all languages,” I really do mean “all languages” (even the halting problem).

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Various people pointed me to a Washington Post piece by Vivek Wadhwa, entitled “Quantum computers may be more of an immiment threat than AI.”  I know I’m late to the party, but in the spirit of Pete Wells’ famous New York Times “review” of Guy Fieri’s now-closed Times Square restaurant, I have a few questions that have been gnawing at me:

Mr. Wadhwa, when you decided to use the Traveling Salesman Problem as your go-to example of a problem that quantum computers can solve quickly, did the thought ever cross your mind that maybe you should look this stuff up first—let’s say, on Wikipedia?  Or that you should email one person—just one, anywhere on the planet—who works in quantum algorithms?

When you wrote of the Traveling Salesman Problem that “[i]t would take a laptop computer 1,000 years to compute the most efficient route between 22 cities”—how confident are you about that?  Willing to bet your house?  Your car?  How much would it blow your mind if I told you that a standard laptop, running a halfway decent algorithm, could handle 22 cities in a fraction of a second?

When you explained that quantum computing is “equivalent to opening a combination lock by trying every possible number and sequence simultaneously,” where did this knowledge come from?  Did it come from the same source you consulted before you pronounced the death of Bitcoin … in January 2016?

Had you wanted to consult someone who knew the first thing about quantum computing, the subject of your column, would you have been able to use a search engine to find one?  Or would you have simply found another “expert,” in the consulting or think-tank worlds, who “knew” the same things about quantum computing that you do?

Incidentally, when you wrote that quantum computing “could pose a greater burden on businesses than the Y2K computer bug did toward the end of the ’90s,” were you trying to communicate how large the burden might be?

And when you wrote that

[T]here is substantial progress in the development of algorithms that are “quantum safe.” One promising field is matrix multiplication, which takes advantage of the techniques that allow quantum computers to be able to analyze so much information.

—were you generating random text using one of those Markov chain programs?  If not, then what were you referring to?

Would you agree that the Washington Post has been a leader in investigative journalism exposing Trump’s malfeasance?  Do you, like me, consider them one of the most important venues on earth for people to be able to trust right now?  How does it happen that the Washington Post publishes a quantum computing piece filled with errors that would embarrass a high-school student doing a term project (and we won’t even count the reference to Stephen “Hawkings”—that’s a freebie)?

Were the fact-checkers home with the flu?  Did they give your column a pass simply because it was “perspective” rather than news?  Or did they trust you as a widely-published technology expert?  How does one become such an expert, anyway?

Thanks!

Update (Feb. 21): For casual readers, Vivek Wadhwa quickly came into the comments section to try to defend himself—before leaving in a huff as a chorus of commenters tried to explain why he was wrong. As far as I know, he has not posted any corrections to his Washington Post piece. Wadhwa’s central defense was that he was simply repeating what Michelle Simmons, a noted quantum computing experimentalist in Australia, said in various talks in YouTube—which turns out to be largely true (though Wadhwa said explicitly that quantum computers could efficiently solve TSP, while Simmons mostly left this as an unstated implication). As a result, while Wadhwa should obviously have followed the journalistic practice of checking incredible-sounding claims—on Wikipedia if nowhere else!—before repeating them in the Washington Post, I now feel that Simmons shares in the responsibility for this. As John Preskill tweeted, an excellent lesson to draw from this affair is that everyone in our field needs to be careful to say things that are true when speaking to the public.

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1. I was extremely sorry to learn about the loss of Joe Polchinski, a few days ago, to brain cancer.  Joe was a leading string theorist, one of the four co-discoverers of the AMPS firewall paradox, and one of the major figures in the Simons It from Qubit collaboration that I’ve been happy to be part of since its inception.  I regret that I didn’t get to know Joe as well as I should have, but he was kind to me in all of our interactions.  He’ll be missed by all who knew him.
2. Edge has posted what will apparently be its final Annual Edge Question: “What is the last question?”  They asked people to submit just a single, one sentence question “for which they’ll be remembered,” with no further explanation or elaboration.  You can read mine, which not surprisingly is alphabetically the first.  I tried to devise a single question that gestured toward the P vs. NP problem, and the ultimate physical limits of computation, and the prospects for superintelligent AI, and the enormity of what could be Platonically lying in wait for us within finite but exponentially search spaces, and the eternal nerd’s conundrum, of the ability to get the right answers to clearly-stated questions being so ineffectual in the actual world.  I’m not thrilled with the result, but reading through the other questions makes it clear just how challenging it is to ask something that doesn’t boil down to: “When will the rest of the world recognize the importance of my research topic?”
3. I’m now reaping the fruits of my decision to take a year-long sabbatical from talking to journalists.  Ariel Bleicher, a writer for Quanta magazine, asked to interview me for an article she was writing about the difficulty of establishing quantum supremacy.  I demurred, mentioning my sabbatical, and pointed her to others she could ask instead.  Well, last week the article came out, and while much of it is quite good, it opens with an extended presentation of a forehead-bangingly wrong claim by Cristian Calude: namely, that the Deutsch-Jozsa problem (i.e. computing the parity of two bits) can be solved with one query even by a classical algorithm, so that (in effect) one of the central examples used in introductory quantum computing courses is a lie.  This claim is based on a 2006 paper wherein, with all the benefits of theft over honest toil, Calude changes the query model so that you can evaluate not just the original oracle function f, but an extension of f to the complex numbers (!).  Apparently Calude justifies this by saying that Deutsch also changed the problem, by allowing it to be solved with a quantum computer, so he gets to change the problem as well.  The difference, of course, is that the quantum query complexity model is justified by its relevance for quantum algorithms, and (ultimately) by quantum mechanics being true of our world.  Calude’s model, by contrast, is (as far as I can tell) pulled out of thin air and justified by nothing.  Anyway, I regard this incident as entirely, 100% my fault, and 0% Ariel’s.  How was she to know that, while there are hundreds of knowledgeable quantum computing experts to interview, almost all of them are nice and polite?  Anyway, this has led me to a revised policy: while I’ll still decline interviews, news organizations should feel free to run completed quantum computing pieces by me for quick fact checks.

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I’ve been way too distracted by actual research lately from my primary career as a nerd blogger—that’s what happens when you’re on sabbatical.  But now I’m sick, and in no condition to be thinking about research.  And this morning, in a thread that had turned to my views on the interpretation of quantum mechanics called “QBism,” regular commenter Atreat asked me the following pointed question:

Scott, what is your preferred interpretation of QM? I don’t think I’ve ever seen you put your cards on the table and lay out clearly what interpretation(s) you think are closest to the truth. I don’t think your ghost paper qualifies as an answer, BTW. I’ve heard you say you have deep skepticism about objective collapse theories and yet these would seemingly be right up your philosophical alley so to speak. If you had to bet on which interpretation was closest to the truth, which one would you go with?

Many people have asked me some variant of the same thing.  As it happens, I’d been toying since the summer with a huge post about my views on each major interpretation, but I never quite got it into a form I wanted.  By contrast, it took me only an hour to write out a reply to Atreat, and in the age of social media and attention spans measured in attoseconds, many readers will probably prefer that short reply to the huge post anyway.  So then I figured, why not promote it to a full post and be done with it?  So without further ado:

Dear Atreat,

It’s no coincidence that you haven’t seen me put my cards on the table with a favored interpretation of QM!

There are interpretations (like the “transactional interpretation”) that make no sense whatsoever to me.

There are “interpretations” like dynamical collapse that aren’t interpretations at all, but proposals for new physical theories.  By all means, let’s test QM on larger and larger systems, among other reasons because it could tell us that some such theory is true or—vastly more likely, I think—place new limits on it! (People are trying.)

Then there’s the deBroglie-Bohm theory, which does lay its cards on the table in a very interesting way, by proposing a specific evolution rule for hidden variables (chosen to match the predictions of QM), but which thereby opens itself up to the charge of non-uniqueness: why that rule, as opposed to a thousand other rules that someone could write down?  And if they all lead to the same predictions, then how could anyone ever know which rule was right?

And then there are dozens of interpretations that seem to differ from one of the “main” interpretations (Many-Worlds, Copenhagen, Bohm) mostly just in the verbal patter.

As for Copenhagen, I’ve described it as “shut-up and calculate except without ever shutting up about it”!  I regard Bohr’s writings on the subject as barely comprehensible, and Copenhagen as less of an interpretation than a self-conscious anti-interpretation: a studied refusal to offer any account of the actual constituents of the world, and—most of all—an insistence that if you insist on such an account, then that just proves that you cling naïvely to a classical worldview, and haven’t grasped the enormity of the quantum revolution.

But the basic split between Many-Worlds and Copenhagen (or better: between Many-Worlds and “shut-up-and-calculate” / “QM needs no interpretation” / etc.), I regard as coming from two fundamentally different conceptions of what a scientific theory is supposed to do for you.  Is it supposed to posit an objective state for the universe, or be only a tool that you use to organize your experiences?

Also, are the ultimate equations that govern the universe “real,” while tables and chairs are “unreal” (in the sense of being no more than fuzzy approximate descriptions of certain solutions to the equations)?  Or are the tables and chairs “real,” while the equations are “unreal” (in the sense of being tools invented by humans to predict the behavior of tables and chairs and whatever else, while extraterrestrials might use other tools)?  Which level of reality do you care about / want to load with positive affect, and which level do you want to denigrate?

This is not like picking a race horse, in the sense that there might be no future discovery or event that will tell us who was closer to the truth.  I regard it as conceivable that superintelligent AIs will still argue about the interpretation of QM … or maybe that God and the angels argue about it now.

Indeed, about the only thing I can think of that might definitively settle the debate, would be the discovery of an even deeper level of description than QM—but such a discovery would “settle” the debate only by completely changing the terms of it.

I will say this, however, in favor of Many-Worlds: it’s clearly and unequivocally the best interpretation of QM, as long as we leave ourselves out of the picture!  I.e., as long as we say that the goal of physics is to give the simplest, cleanest possible mathematical description of the world that somewhere contains something that seems to correspond to observation, and we’re willing to shunt as much metaphysical weirdness as needed to those who worry themselves about details like “wait, so are we postulating the physical existence of a continuum of slightly different variants of me, or just an astronomically large finite number?” (Incidentally, Max Tegmark’s “mathematical multiverse” does even better than MWI by this standard.  Tegmark is the one waiting for you all the way at the bottom of the slippery slope of always preferring Occam’s Razor over trying to account for the specificity of the observed world.)  It’s no coincidence, I don’t think, that MWI is so popular among those who are also eliminativists about consciousness.

When I taught my undergrad Intro to Quantum Information course last spring—for which lecture notes are coming soon, by the way!—it was striking how often I needed to resort to an MWI-like way of speaking when students got confused about measurement and decoherence. (“So then we apply this unitary transformation U that entangles the system and environment, and we compute a partial trace over the environment qubits, and we see that it’s as if the system has been measured, though of course we could in principle reverse this by applying U^-1 … oh shoot, have I just conceded MWI?”)

On the other hand, when (at the TAs’ insistence) we put an optional ungraded question on the final exam that asked students their favorite interpretation of QM, we found that there was no correlation whatsoever between interpretation and final exam score—except that students who said they didn’t believe any interpretation at all, or that the question was meaningless or didn’t matter, scored noticeably higher than everyone else.

Anyway, as I said, MWI is the best interpretation if we leave ourselves out of the picture.  But you object: “OK, and what if we don’t leave ourselves out of the picture?  If we dig deep enough on the interpretation of QM, aren’t we ultimately also asking about the ‘hard problem of consciousness,’ much as some people try to deny that? So for example, what would it be like to be maintained in a coherent superposition of thinking two different thoughts A and B, and then to get measured in the |A⟩+|B⟩, |A⟩-|B⟩ basis?  Would it even be like anything?  Or is there something about our consciousness that depends on decoherence, irreversibility, full participation in the arrow of the time, not living in an enclosed little unitary box like AdS/CFT—something that we’d necessarily destroy if we tried to set up a large-scale interference experiment on our own brains, or any other conscious entities?  If so, then wouldn’t that point to a strange sort of reconciliation of Many-Worlds with Copenhagen—where as soon as we had a superposition involving different subjective experiences, for that very reason its being a superposition would be forevermore devoid of empirical consequences, and we could treat it as just a classical probability distribution?”

I’m not sure, but The Ghost in the Quantum Turing Machine will probably have to stand as my last word (or rather, last many words) on those questions for the time being.

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I saw today that Ryan Lackey generously praised my and Zach Weinersmith’s quantum computing SMBC comic on Twitter:

Somehow this SMBC comic is the best explanation of quantum computing for non-professionals that I’ve ever found

To which the venture capitalist Matthew Ocko replied, in another tweet:

Except Scott Aaronson is a surly little troll who has literally never built anything at all of meaning. He’s a professional critic of braver people.  So, no, this is not a good explanation – anymore than Jeremy Rifkin on CRISPR would be…

Now, I don’t mind if Ocko hates me, and also hates my and Zach’s comic.  What’s been bothering me is just the logic of his tweet.  Like: what did he have in his head when he wrote the word “So”?  Let’s suppose for the sake of argument that I’m a “surly little troll,” and an ax murderer besides.  How does it follow that my explanation of quantum computing wasn’t good?  To reach that stop in proposition-space, wouldn’t one still need to point to something wrong with the explanation?

But I’m certain that my inability to understand this is just another of my many failings.  In a world where Trump is president, bitcoin is valued at $11,000 when I last checked, and the attack-tweet has fully replaced the argument, it’s obvious that those of us who see a word like “so” or “because,” and start looking for the inferential step, are merely insufficiently brave.  For godsakes, I’m not even on Twitter!  I’m a sclerotic dinosaur who needs to get with the times.

But maybe I, too, could learn the art of the naked ad-hominem.  Let me try: from a Google search, we learn that Ocko is an enthusiastic investor in D-Wave.  Is it possible he’s simply upset that there’s so much excitement right now in experimental quantum computing—including “things of meaning” being built by brave people, at Google and IBM and Rigetti and IonQ and elsewhere—but that virtually none of this involves D-Wave, whose devices remain interesting from various physics and engineering standpoints, but still fail to achieve any clear quantum speedups, just as the professional critics predicted?  Is he upset that the brave system-builders who are racing finally to achieve quantum computational supremacy over the next year, are the ones who actually interacted with academic researchers (sorry: surly little trolls), and listened to what they said?  Who understood, for example, why scaling up to 50+ qubits only made a lot of sense once you had one or two qubits that at least behaved well enough in isolation—which, after years of heroic effort, many of these system-builders now do?

How’d I do?  Was there still too much argument there for the world of 2018?

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The purpose of this post is just to call everyone’s attention to a beautiful and accessible new article by John Preskill: Quantum Computing in the NISQ era and beyond.  The article is based on John’s keynote address at the recent “Q2B” (Quantum Computing for Business) conference, which I was unfortunately unable to attend.  Here’s the abstract:

Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today’s classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away — we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.

Did you ever wish you had something even better than a clone: namely, someone who writes exactly what you would’ve wanted to write, on a topic people keep asking you to write about, but ten times better than you would’ve written it?  To all journalists and others who ask me over the coming year about the application potential for near-term quantum computers, I can now simply respond with a link.

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(1) My TEDx talk from Dresden, entitled “What Quantum Computing Isn’t,” is finally up on YouTube.  For regular Shtetl-Optimized readers, there’s unlikely to be much that’s new here: it’s basically 15 minutes of my usual spiel, packaged for mass consumption.  But while it went over well with the live audience, right now the only comment on the video is—I quote—“uuuuuuuuuuuuuuu,” from user “imbatman8472.”  So if you feel so inclined, go over there, watch it, and try to start a more contentful discussion!  Thanks so much to Andrés Goens, and everyone else in Dresden, for inviting me there and hosting a great visit.

(2) On December 4-6, there’s going to be a new conference in Mountain View, called Q2B (Quantum Computing for Business).  There, if it interests you, you can hear about the embryonic QC industry, from some of the major players at Google, IBM, Microsoft, academia, and government, as well as some of the QC startups (like IonQ) that have blossomed over the last few years.  Oh yes, and D-Wave.  The keynote speaker will be John Preskill; Google’s John Martinis and IBM’s Jerry Chow will also be giving talks.  I regret that another commitment will prevent me from attending myself, but I hope to attend next year’s iteration.  (Full disclosure: I’m a scientific adviser to QC Ware, the firm that’s organizing the conference.)

(3) On October 24, the House Science Committee heard three hours of testimony—you can watch it all here—about the need for quantum information research and the danger of the US falling behind China.  In what I believe is my first entry in the Congressional record, I’m quoted (for something totally incidental) at 1:09.  John Preskill was mostly just delighted that the witness, Jim Kurose, referred to me as a “physicist.”

(4) For several years, people have been asking me whether Bitcoin is resistant against quantum attack.  Now there’s finally an expert analysis, by Aggarwal et al., that looks into exactly that question.  Two-sentence summary: the proof-of-work is probably fine, although Grover’s algorithm can of course be used against it, which might eventually necessitate adjusting the difficulty parameter to account for that, and/or migrating from a pure preimage search task to collision-finding, where my result with Yaoyun Shi showed that quantum computers offer “only” an n^2/3 black-box speedup over classical computers, rather than a square-root speedup.  The scheme for signing the transactions, which is currently based on elliptic curve cryptography, is the real danger point, but again one could address that by migrating to a post-quantum signature scheme.  My main comment about the matter is that, if I’d invested in Bitcoin when I first learned about it, I’d be rich now.

(5) In the first significant victory for my plan to spend a whole sabbatical year just writing up unwritten papers, I’ve got a new paper out today: Shadow Tomography of Quantum States.  Comments extremely welcome!

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I’m eagerly seeking PhD students and postdocs to join our Quantum Information Center at UT Austin, starting in Fall 2018.  We’re open to any theoretical aspects of quantum information, although if you wanted to work with me personally, then areas close to computer science would be the closest fit.  I’m also able to supervise PhD students in physics, but am not directly involved with admissions to the physics department: this is a discussion we would have after you were already admitted to UT.

I, along with my theoretical computer science colleagues at UT Austin, am also open to outstanding students and postdocs in classical complexity theory. My wife, Dana Moshkovitz, tells me that she and David Zuckerman in particular are looking for a postdoc in the areas of pseudorandomness and derandomization (and for PhD students as well).

If you want to apply to the UTCS PhD program, please visit here.  The deadline is December 15.  If you specify that you want to work on quantum computing and information, and/or with me, then I’ll be sure to see your application.  Emailing faculty at this stage doesn’t help; we won’t “estimate your chances” or even look at your qualifications until we can see all the applications together.

If you want to apply for a postdoc with me, here’s what to do:

• Email me introducing yourself (if I don’t already know you), and include your CV, your thesis (if you already have one), and up to 3 representative papers.  Do this even if you already emailed me before.
• Arrange for two recommendation letters to be emailed to me.

Let’s set a deadline for postdoc applications of, I dunno, December 15?

In addition to the above, I’m happy to announce that the UT CS department is looking to hire a new faculty member in quantum computing and information—most likely a junior person.  The UT physics department is also looking to hire quantum information faculty members, with a focus on a senior-level experimentalist right now.  If you’re interested in these opportunities, just email me; I can put you in touch with the relevant people.

All in all, this is shaping up to be the most exciting era for quantum computing and information in Austin since a group of UT students, postdocs, and faculty including David Deutsch, John Wheeler, Wojciech Zurek, Bill Wootters, and Ben Schumacher laid much of the intellectual foundation of the field in the late 1970s and early 1980s.  We hope you’ll join us.  Hook ’em Hadamards!

Unrelated Announcements: Avi Wigderson has released a remarkable 368-page book, Mathematics and Computation, for free on the web.  This document surveys pretty much the entire current scope of theoretical computer science, in a way only Avi, our field’s consummate generalist, could do.  It also sets out Avi’s vision for the future and his sociological thoughts about TCS and its interactions with neighboring fields.  I was a reviewer on the manuscript, and I recommend it to anyone looking for a panoramic view of TCS.

In other news, my UT friend and colleague Adam Klivans, and his student Surbhi Goel, have put out a preprint entitled Learning Depth-Three Neural Networks in Polynomial Time.  (Beware: what the machine learning community calls “depth three,” is what the TCS community would call “depth two.”)  This paper learns real-valued neural networks in the so-called p-concept model of Kearns and Schapire, and thereby evades a 2006 impossibility theorem of Klivans and Sherstov, which showed that efficiently learning depth-2 threshold circuits would require breaking cryptographic assumptions.  More broadly, there’s been a surge of work in the past couple years on explaining the success of deep learning methods (methods whose most recent high-profile victory was, of course, AlphaGo Zero).  I’m really hoping to learn more about this direction during my sabbatical this year—though I’ll try and take care not to become another deep learning zombie, chanting “artificial BRAINSSSS…” with outstretched arms.

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Unrelated Update (Oct. 23) I still feel bad that there was no time for public questions at my “Theoretically Speaking” talk in Berkeley, and also that the lecture hall was too small to accomodate a large fraction of the people who showed up. So, if you’re someone who came there wanting to ask me something, go ahead and ask in the comments of this post.

During my whirlwind tour of the Bay Area, questions started pouring in about a preprint from a group mostly at IBM Yorktown Heights, entitled Breaking the 49-Qubit Barrier in the Simulation of Quantum Circuits.  In particular, does this paper make a mockery of everything the upcoming quantum supremacy experiments will try to achieve, and all the theorems about them that we’ve proved?

Following my usual practice, let me paste the abstract here, so that we have the authors’ words in front of us, rather than what a friend of a friend said a popular article reported might have been in the paper.

With the current rate of progress in quantum computing technologies, 50-qubit systems will soon become a reality.  To assess, refine and advance the design and control of these devices, one needs a means to test and evaluate their fidelity. This in turn requires the capability of computing ideal quantum state amplitudes for devices of such sizes and larger.  In this study, we present a new approach for this task that significantly extends the boundaries of what can be classically computed.  We demonstrate our method by presenting results obtained from a calculation of the complete set of output amplitudes of a universal random circuit with depth 27 in a 2D lattice of 7 × 7 qubits.  We further present results obtained by calculating an arbitrarily selected slice of 2³⁷ amplitudes of a universal random circuit with depth 23 in a 2D lattice of 8×7 qubits.  Such calculations were previously thought to be impossible due to impracticable memory requirements. Using the methods presented in this paper, the above simulations required 4.5 and 3.0 TB of memory, respectively, to store calculations, which is well within the limits of existing classical computers.

This is an excellent paper, which sets a new record for the classical simulation of generic quantum circuits; I congratulate the authors for it.  Now, though, I want you to take a deep breath and repeat after me:

This paper does not undercut the rationale for quantum supremacy experiments.  The truth, ironically, is almost the opposite: it being possible to simulate 49-qubit circuits using a classical computer is a precondition for Google’s planned quantum supremacy experiment, because it’s the only way we know to check such an experiment’s results!  The goal, with sampling-based quantum supremacy, was always to target the “sweet spot,” which we estimated at around 50 qubits, where classical simulation is still possible, but it’s clearly orders of magnitude more expensive than doing the experiment itself.  If you like, the goal is to get as far as you can up the mountain of exponentiality, conditioned on people still being able to see you from the base.  Why?  Because you can.  Because it’s there.  Because it challenges those who think quantum computing will never scale: explain this, punks!  But there’s no point unless you can verify the result.

Related to that, the paper does not refute any prediction I made, by doing anything I claimed was impossible.  On the contrary (if you must know), the paper confirms something that I predicted would be possible.  People said: “40 qubits is the practical limit of what you can simulate, so there’s no point in Google or anyone else doing a supremacy experiment with 49 qubits, since they can never verify the results.”  I would shrug and say something like: “eh, if you can do 40 qubits, then I’m sure you can do 50.  It’s only a thousand times harder!”

So, how does the paper get up to 50 qubits?  A lot of computing power and a lot of clever tricks, one of which (the irony thickens…) came from a paper that I recently coauthored with Lijie Chen: Complexity-Theoretic Foundations of Quantum Supremacy Experiments.  Lijie and I were interested in the question: what’s the best way to simulate a quantum circuit with n qubits and m gates?  We noticed that there’s a time/space tradeoff here: you could just store the entire amplitude vector in memory and update, which would take exp(n) memory but also “only” about exp(n) time.  Or you could compute the amplitudes you cared about via Feynman sums (as in the proof of BQP⊆PSPACE), which takes only linear memory, but exp(m) time.  If you imagine, let’s say, n=50 and m=1000, then exp(n) might be practical if you’re IBM or Google, but exp(m) is certainly not.

So then we raised the question: could one get the best of both worlds?  That is, could one simulate such a quantum circuit using both linear memory and exp(n) time?  And we showed that this is almost possible: we gave an algorithm that uses linear memory and d^O(n) time, where d is the circuit depth.  Furthermore, the more memory it has available, the faster our algorithm will run—until, in the limit of exponential memory, it just becomes the “store the whole amplitude vector” algorithm mentioned above.  I’m not sure why this algorithm wasn’t discovered earlier, especially since it basically just amounts to Savitch’s Theorem from complexity theory.  In any case, though, the IBM group used this idea among others to take full advantage of the RAM it had available.

Let me make one final remark: this little episode perfectly illustrates why theoretical computer scientists like to talk about polynomial vs. exponential rather than specific numbers.  If you keep your eyes on the asymptotic fundamentals, rather than every factor of 10 or 1000, then you’re not constantly shocked by events, like a dog turning its head for every passing squirrel.  Before you could simulate 40 qubits, now you can simulate 50.  Maybe with more cleverness you could get to 60 or even 70.  But … dude.  The problem is still exponential time.

We saw the same “SQUIRREL!  SQUIRREL!” reaction with the people who claimed that the wonderful paper by Clifford and Clifford had undercut the rationale for BosonSampling experiments, by showing how to solve the problem in “merely” ~2ⁿ time rather than ~mⁿ, where n is the number of photons and m is the number of modes.  Of course, Arkhipov and I had never claimed more than ~2ⁿ hardness for the problem, and Clifford and Clifford’s important result had justified our conservatism on that point, but, y’know … SQUIRREL!

More broadly, it seems to me that this dynamic constantly occurs in the applied cryptography world.  OMIGOD a 128-bit hash function has been broken!  Big news!  OMIGOD a new, harder hash function has been designed!  Bigger news!  OMIGOD OMIGOD OMIGOD the new one was broken too!!  All of it fully predictable once you realize that we’re on the shores of an exponentially hard problem, and for some reason, refusing to go far enough out into the sea (i.e., pick large enough security parameters) that none of this back-and-forth would happen.

I apologize, sincerely, if I come off as too testy in this post.  No doubt it’s entirely the fault of a cognitive defect on my end, wherein ten separate people asking me about something get treated by my brain like a single person who still doesn’t get it even after I’ve explained it ten times.

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By email, by Twitter, even as the world was convulsed by tragedy, the inquiries poured in yesterday about a different topic entirely: Scott, did physicists really just prove that the universe is not a computer simulation—that we can’t be living in the Matrix?

What prompted this was a rash of popular articles like this one (“Researchers claim to have found proof we are NOT living in a simulation”).  The articles were all spurred by a recent paper in Science Advances: Quantized gravitational responses, the sign problem, and quantum complexity, by Zohar Ringel of Hebrew University and Dmitry L. Kovrizhin of Oxford.

I’ll tell you what: before I comment, why don’t I just paste the paper’s abstract here.  I invite you to read it—not the whole paper, just the abstract, but paying special attention to the sentences—and then make up your own mind about whether it supports the interpretation that all the popular articles put on it.

Ready?  Set?

Abstract: It is believed that not all quantum systems can be simulated efficiently using classical computational resources.  This notion is supported by the fact that it is not known how to express the partition function in a sign-free manner in quantum Monte Carlo (QMC) simulations for a large number of important problems.  The answer to the question—whether there is a fundamental obstruction to such a sign-free representation in generic quantum systems—remains unclear.  Focusing on systems with bosonic degrees of freedom, we show that quantized gravitational responses appear as obstructions to local sign-free QMC.  In condensed matter physics settings, these responses, such as thermal Hall conductance, are associated with fractional quantum Hall effects.  We show that similar arguments also hold in the case of spontaneously broken time-reversal (TR) symmetry such as in the chiral phase of a perturbed quantum Kagome antiferromagnet.  The connection between quantized gravitational responses and the sign problem is also manifested in certain vertex models, where TR symmetry is preserved.

For those tuning in from home, the “sign problem” is an issue that arises when, for example, you’re trying to use the clever trick known as Quantum Monte Carlo (QMC) to learn about the ground state of a quantum system using a classical computer—but where you needed probabilities, which are real numbers from 0 to 1, your procedure instead spits out numbers some of which are negative, and which you can therefore no longer use to define a sensible sampling process.  (In some sense, it’s no surprise that this would happen when you’re trying to simulate quantum mechanics, which of course is all about generalizing the rules of probability in a way that involves negative and even complex numbers!  The surprise, rather, is that QMC lets you avoid the sign problem as often as it does.)

Anyway, this is all somewhat far from my expertise, but insofar as I understand the paper, it looks like a serious contribution to our understanding of the sign problem, and why local changes of basis can fail to get rid of it when QMC is used to simulate certain bosonic systems.  It will surely interest QMC experts.

OK, but does any of this prove that the universe isn’t a computer simulation, as the popular articles claim (and as the original paper does not)?

It seems to me that, to get from here to there, you’d need to overcome four huge difficulties, any one of which would be fatal by itself, and which are logically independent of each other.

1. As a computer scientist, one thing that leapt out at me, is that Ringel and Kovrizhin’s paper is fundamentally about computational complexity—specifically, about which quantum systems can and can’t be simulated in polynomial time on a classical computer—yet it’s entirely innocent of the language and tools of complexity theory.  There’s no BQP, no QMA, no reduction-based hardness argument anywhere in sight, and no clearly-formulated request for one either.  Instead, everything is phrased in terms of the failure of one specific algorithmic framework (namely QMC)—and within that framework, only “local” transformations of the physical degrees of freedom are considered, not nonlocal ones that could still be accessible to polynomial-time algorithms.  Of course, one does whatever one needs to do to get a result.
   To their credit, the authors do seem aware that a language for discussing all possible efficient algorithms exists.  They write, for example, of a “common understanding related to computational complexity classes” that some quantum systems are hard to simulate, and specifically of the existence of systems that support universal quantum computation.  So rather than criticize the authors for this limitation of their work, I view their paper as a welcome invitation for closer collaboration between the quantum complexity theory and quantum Monte Carlo communities, which approach many of the same questions from extremely different angles.  As official ambassador between the two communities, I nominate Matt Hastings.
2. OK, but even if the paper did address computational complexity head-on, about the most it could’ve said is that computer scientists generally believe that BPP≠BQP (i.e., that quantum computers can solve more decision problems in polynomial time than classical probabilistic ones); and that such separations are provable in the query complexity and communication complexity worlds; and that at any rate, quantum computers can solve exact sampling problems that are classically hard unless the polynomial hierarchy collapses (as pointed out in the BosonSampling paper, and independently by Bremner, Jozsa, Shepherd).  Alas, until someone proves P≠PSPACE, there’s no hope for an unconditional proof that quantum computers can’t be efficiently simulated by classical ones.
   (Incidentally, the paper comments, “Establishing an obstruction to a classical simulation is a rather ill-defined task.”  I beg to differ: it’s not ill-defined; it’s just ridiculously hard!)
3. OK, but suppose it were proved that BPP≠BQP—and for good measure, suppose it were also experimentally demonstrated that scalable quantum computing is possible in our universe.  Even then, one still wouldn’t by any stretch have ruled out that the universe was a computer simulation!  For as many of the people who emailed me asked themselves (but as the popular articles did not), why not just imagine that the universe is being simulated on a quantum computer?  Like, duh?
4. Finally: even if, for some reason, we disallowed using a quantum computer to simulate the universe, that still wouldn’t rule out the simulation hypothesis.  For why couldn’t God, using Her classical computer, spend a trillion years to simulate one second as subjectively perceived by us?  After all, what is exponential time to She for whom all eternity is but an eyeblink?

Anyway, if it weren’t for all four separate points above, then sure, physicists would have now proved that we don’t live in the Matrix.

I do have a few questions of my own, for anyone who came here looking for my reaction to the ‘news’: did you really need me to tell you all this?  How much of it would you have figured out on your own, just by comparing the headlines of the popular articles to the descriptions (however garbled) of what was actually done?  How obvious does something need to be, before it no longer requires an ‘expert’ to certify it as such?  If I write 500 posts like this one, will the 501^st post basically just write itself?

Asking for a friend.

Comment Policy: I welcome discussion about the Ringel-Dovrizhin paper; what might’ve gone wrong with its popularization; QMC; the sign problem; the computational complexity of condensed-matter problems more generally; and the relevance or irrelevance of work on these topics to broader questions about the simulability of the universe.  But as a little experiment in blog moderation, I won’t allow comments that just philosophize in general about whether or not the universe is a simulation, without making further contact with the actual content of this post.  We’ve already had the latter conversation here—probably, like, every week for the last decade—and I’m ready for something new.

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