(1) Fellow CS theory blogger (and, 20 years ago, member of my PhD thesis committee) Luca Trevisan interviews me about Shtetl-Optimized, for the Bulletin of the European Association for Theoretical Computer Science. Questions include: what motivates me to blog, who my main inspirations are, my favorite posts, whether blogging has influenced my actual research, and my thoughts on the role of public intellectuals in the age of social-media outrage.
(3) The Microsoft team has finally released its promised paper about the detection of Majorana zero modes (“this time for real”), a major step along the way to creating topological qubits. See also this live YouTube peer review—is that a thing now?—by Vincent Mourik and Sergey Frolov, the latter having been instrumental in the retraction of Microsoft’s previous claim along these lines. I’ll leave further discussion to people who actually understand the experiments.
(4) I’m looking forward to the 2022 Conference on Computational Complexity less than two weeks from now, in my … safe? clean? beautiful? awe-inspiring? … birth-city of Philadelphia. There I’ll listen to a great lineup of talks, including one by my PhD student William Kretschmer on his joint work with me and DeVon Ingram on The Acrobatics of BQP, and to co-receive the CCC Best Paper Award (wow! thanks!) for that work. I look forward to meeting some old and new Shtetl-Optimized readers there.
Thanks so much to everyone who sent messages of support following my last post! I vowed there that I’m going to stop letting online trolls and sneerers occupy so much space in my mental world. Truthfully, though, while there are many trolls and sneerers who terrify me, there are also some who merely amuse me. A good example of the latter came a few weeks ago, when an anonymous commenter calling themselves “String Theorist” submitted the following:
It’s honestly funny to me when you [Scott] call yourself a “nerd” or a “prodigy” or whatever [I don’t recall ever calling myself a “prodigy,” which would indeed be cringe, though “nerd” certainly —SA], as if studying quantum computing, which is essentially nothing more than glorified linear algebra, is such an advanced intellectual achievement. For what it’s worth I’m a theoretical physicist, I’m in a completely different field, and I was still able to learn Shor’s algorithm in about half an hour, that’s how easy this stuff is. I took a look at some of your papers on arXiv and the math really doesn’t get any more advanced than linear algebra. To understand quantum circuits about the most advanced concept is a tensor product which is routinely covered in undergraduate linear algebra. Wheras in my field of string theory grasping, for instance, holographic dualities relating confirmal field theories and gravity requires vastly more expertise (years of advanced study). I actually find it pretty entertaining that you’ve said yourself you’re still struggling to understand QFT, which most people I’m working with in my research group were first exposed to in undergrad 😉 The truth is we’re in entirely different leagues of intelligence (“nerdiness”) and any of your qcomputing papers could easily be picked up by a first or second year math major. It’s just a joke that this is even a field (quantum complexity theory) with journals and faculty when the results in your papers that I’ve seen are pretty much trivial and don’t require anything more than undergraduate level maths.
Why does this sort of trash-talk, reminiscent of Luboš Motl, no longer ruffle me? Mostly because the boundaries between quantum computing theory, condensed matter physics, and quantum gravity, which were never clear in the first place, have steadily gotten fuzzier. Even in the 1990s, the field of quantum computing attracted amazing physicists—folks who definitely do know quantum field theory—such as Ed Farhi, John Preskill, and Ray Laflamme. Decades later, it would be fair to say that the physicists have banged their heads against many of the same questions that we computer scientists have banged our heads against, oftentimes in collaboration with us. And yes, there were cases where actual knowledge of particle physics gave physicists an advantage—with some famous examples being the algorithms of Farhi and collaborators (the adiabatic algorithm, the quantum walk on conjoined trees, the NAND-tree algorithm). There were other cases where computer scientists’ knowledge gave them an advantage: I wouldn’t know many details about that, but conceivably shadow tomography, BosonSampling, PostBQP=PP? Overall, it’s been what you wish every indisciplinary collaboration could be.
What’s new, in the last decade, is that the scientific conversation centered around quantum information and computation has dramatically “metastasized,” to encompass not only a good fraction of all the experimentalists doing quantum optics and sensing and metrology and so forth, and not only a good fraction of all the condensed-matter theorists, but even many leading string theorists and quantum gravity theorists, including Susskind, Maldacena, Bousso, Hubeny, Harlow, and yes, Witten. And I don’t think it’s just that they’re too professional to trash-talk quantum information people the way commenter “String Theorist” does. Rather it’s that, because of the intellectual success of “It from Qubit,” we’re increasingly participating in the same conversations and working on the same technical questions. One particularly exciting such question, which I’ll have more to say about in a future post, is the truth or falsehood of the Quantum Extended Church-Turing Thesis for observers who jump into black holes.
Not to psychoanalyze, but I’ve noticed a pattern wherein, the more secure a scientist is about their position within their own field, the readier they are to admit ignorance about the neighboring fields, to learn about those fields, and to reach out to the experts in them, to ask simple or (as it usually turns out) not-so-simple questions.
I can’t imagine any better illustration of these tendencies better than the 28th Solvay Conference on the Physics of Quantum Information, which I attended two weeks ago in Brussels on my 41st birthday.
As others pointed out, the proportion of women is not as high as we all wish, but it’s higher than in 1911, when there was exactly one: Madame Curie herself.
It was my first trip out of the US since before COVID—indeed, I’m so out of practice that I nearly missed my flights in both directions, in part because of my lack of familiarity with the COVID protocols for transatlantic travel, as well as the immense lines caused by those protocols. My former adviser Umesh Vazirani, who was also at the Solvay Conference, was proud.
The Solvay Conference is the venue where, legendarily, the fundamentals of quantum mechanics got hashed out between 1911 and 1927, by the likes of Einstein, Bohr, Planck, and Curie. (Einstein complained, in a letter, about being called away from his work on general relativity to attend a “witches’ sabbath.”) Remarkably, it’s still being held in Brussels every few years, and still funded by the same Solvay family that started it. The once-every-few-years schedule has, we were constantly reminded, been interrupted only three times in its 110-year history: once for WWI, once for WWII, and now once for COVID (this year’s conference was supposed to be in 2020).
This was the first ever Solvay conference organized around the theme of quantum information, and apparently, the first ever that counted computer scientists among its participants (me, Umesh Vazirani, Dorit Aharonov, Urmila Mahadev, and Thomas Vidick). There were four topics: (1) many-body physics, (2) quantum gravity, (3) quantum computing hardware, and (4) quantum algorithms. The structure, apparently unchanged since the conference’s founding, is this: everyone attends every session, without exception. They sit around facing each other the whole time; no one ever stands to lecture. For each topic, two “rapporteurs” introduce the topic with half-hour prepared talks; then there are short prepared response talks as well as an hour or more of unstructured discussion. Everything everyone says is recorded in order to be published later.
Daniel Gottesman and I were the two rapporteurs for quantum algorithms: Daniel spoke about quantum error-correction and fault-tolerance, and I spoke about “How Much Structure Is Needed for Huge Quantum Speedups?” The link goes to my PowerPoint slides, if you’d like to check them out. I tried to survey 30 years of history of that question, from Simon’s and Shor’s algorithms, to huge speedups in quantum query complexity (e.g., glued trees and Forrelation), to the recent quantum supremacy experiments based on BosonSampling and Random Circuit Sampling, all the way to the breakthrough by Yamakawa and Zhandry a couple months ago. The last slide hypothesizes a “Law of Conservation of Weirdness,” which after all these decades still remains to be undermined: “For every problem that admits an exponential quantum speedup, there must be some weirdness in its detailed statement, which the quantum algorithm exploits to focus amplitude on the rare right answers.” My title slide also shows DALL-E2‘s impressionistic take on the title question, “how much structure is needed for huge quantum speedups?”:
The discussion following my talk was largely a debate between me and Ed Farhi, reprising many debates he and I have had over the past 20 years: Farhi urged optimism about the prospect for large, practical quantum speedups via algorithms like QAOA, pointing out his group’s past successes and explaining how they wouldn’t have been possible without an optimistic attitude. For my part, I praised the past successes and said that optimism is well and good, but at the same time, companies, venture capitalists, and government agencies are right now pouring billions into quantum computing, in many cases—as I know from talking to them—because of a mistaken impression that QCs are already known to be able to revolutionize machine learning, finance, supply-chain optimization, or whatever other application domains they care about, and to do so soon. They’re genuinely surprised to learn that the consensus of QC experts is in a totally different place. And to be clear: among quantum computing theorists, I’m not at all unusually pessimistic or skeptical, just unusually willing to say in public what others say in private.
Afterwards, one of the string theorists said that Farhi’s arguments with me had been a highlight … and I agreed. What’s the point of a friggin’ Solvay Conference if everyone’s just going to agree with each other?
Besides quantum algorithms, there was naturally lots of animated discussion about the practical prospects for building scalable quantum computers. While I’d hoped that this discussion might change the impressions I’d come with, it mostly confirmed them. Yes, the problem is staggeringly hard. Recent ideas for fault-tolerance, including the use of LDPC codes and bosonic codes, might help. Gottesman’s talk gave me the insight that, at its core, quantum fault-tolerance is all about testing, isolation, and contact-tracing, just for bit-flip and phase-flip errors rather than viruses. Alas, we don’t yet have the quantum fault-tolerance analogue of a vaccine!
At one point, I asked the trapped-ion experts in open session if they’d comment on the startup company IonQ, whose stock price recently fell precipitously in the wake of a scathing analyst report. Alas, none of them took the bait.
On a different note, I was tremendously excited by the quantum gravity session. Netta Engelhardt spoke about her and others’ celebrated recent work explaining the Page curve of an evaporating black hole using Euclidean path integrals—and by questioning her and others during coffee breaks, I finally got a handwavy intuition for how it works. There was also lots of debate, again at coffee breaks, about Susskind’s recent speculations on observers jumping into black holes and the quantum Extended Church-Turing Thesis. One of my main takeaways from the conference was a dramatically better understanding of the issues involved there—but that’s a big enough topic that it will need its own post.
Toward the end of the quantum gravity session, the experimentalist John Martinis innocently asked what actual experiments, or at least thought experiments, had been at issue for the past several hours. I got a laugh by explaining to him that, while the gravity experts considered this too obvious to point out, the thought experiments in question all involve forming a black hole in a known quantum pure state, with total control over all the Planck-scale degrees of freedom; then waiting outside the black hole for ~1070 years; collecting every last photon of Hawking radiation that comes out and routing them all into a quantum computer; doing a quantum computation that might actually require exponential time; and then jumping into the black hole, whereupon you might either die immediately at the event horizon, or else learn something in your last seconds before hitting the singularity, which you could then never communicate to anyone outside the black hole. Martinis thanked me for clarifying.
Anyway, I had a total blast. Here I am amusing some of the world’s great physicists by letting them mess around with GPT-3.
Back: Ahmed Almheiri, Juan Maldacena, John Martinis, Aron Wall. Front: Geoff Penington, me, Daniel Harlow. Thanks to Michelle Simmons for the photo.
I also had the following exchange at my birthday dinner:
Physicist: So I don’t get this, Scott. Are you a physicist who studied computer science, or a computer scientist who studied physics?
Me: I’m a computer scientist who studied computer science.
Physicist: But then you…
Me: Yeah, at some point I learned what a boson was, in order to invent BosonSampling.
Physicist: And your courses in physics…
Me: They ended at thermodynamics. I couldn’t handle PDEs.
Physicist: What are the units of h-bar?
Me: Uhh, well, it’s a conversion factor between energy and time. (*)
Physicist: Good. What’s the radius of the hydrogen atom?
Me: Uhh … not sure … maybe something like 10-15 meters?
Physicist: OK fine, he’s not one of us.
(The answer, it turns out, is more like 10-10 meters. I’d stupidly substituted the radius of the nucleus—or, y’know, a positively-charged hydrogen ion, i.e. proton. In my partial defense, I was massively jetlagged and at most 10% conscious.)
(*) Actually h-bar is a conversion factor between energy and 1/time, i.e. frequency, but the physicist accepted this answer.
Anyway, I look forward to attending more workshops this summer, seeing more colleagues who I hadn’t seen since before COVID, and talking more science … including branching out in some new directions that I’ll blog about soon. It does beat worrying about online trolls.
Thanks to everyone who asked whether I’m OK! Yeah, I’ve been living, loving, learning, teaching, worrying, procrastinating, just not blogging.
Last week, Takashi Yamakawa and Mark Zhandry posted a preprint to the arXiv, “Verifiable Quantum Advantage without Structure,” that represents some of the most exciting progress in quantum complexity theory in years. I wish I’d thought of it. tl;dr they show that relative to a random oracle (!), there’s an NP search problem that quantum computers can solve exponentially faster than classical ones. And yet this is 100% consistent with the Aaronson-Ambainis Conjecture!
A student brought my attention to Quantle, a variant of Wordle where you need to guess a true equation involving 1-qubit quantum states and unitary transformations. It’s really well-done! Possibly the best quantum game I’ve seen.
Last month, Microsoft announced on the web that it had achieved an experimental breakthrough in topological quantum computing: not quite the creation of a topological qubit, but some of the underlying physics required for that. This followed their needing to retract their previous claim of such a breakthrough, due to the criticisms of Sergey Frolov and others. One imagines that they would’ve taken far greater care this time around. Unfortunately, a research paper doesn’t seem to be available yet. Anyone with further details is welcome to chime in.
Woohoo! Maximum flow, maximum bipartite matching, matrix scaling, and isotonic regression on posets (among many others)—all algorithmic problems that I was familiar with way back in the 1990s—are now solvable in nearly-linear time, thanks to a breakthrough by Chen et al.! Many undergraduate algorithms courses will need to be updated.
For those interested, Steve Hsu recorded a podcast with me where I talk about quantum complexity theory.
A talk to UT Austin’s undergraduate math club (handwritten PDF notes) about Hao Huang’s proof of the Sensitivity Conjecture, and its implications for quantum query complexity and more. I’m still not satisfied that I’ve presented Huang’s beautiful proof as clearly and self-containedly as I possibly can, which probably just means I need to lecture on it a few more times.
A Zoom talk at the QPQIS conference in Beijing (PowerPoint slides), setting out my most recent thoughts about Google’s and USTC’s quantum supremacy experiments and the continuing efforts to spoof them classically.
Just in case anyone is depressed this afternoon and needs something to cheer them up, students William Kretschmer, DeVon Ingram, and I have finally put out a new paper:
Abstract: We show that, in the black-box setting, the behavior of quantum polynomial-time (BQP) can be remarkably decoupled from that of classical complexity classes like NP. Specifically:
– There exists an oracle relative to which NPBQP⊄BQPPH, resolving a 2005 problem of Fortnow. Interpreted another way, we show that AC0 circuits cannot perform useful homomorphic encryption on instances of the Forrelation problem. As a corollary, there exists an oracle relative to which P=NP but BQP≠QCMA.
– Conversely, there exists an oracle relative to which BQPNP⊄PHBQP.
– Relative to a random oracle, PP=PostBQP is not contained in the “QMA hierarchy” QMAQMA^QMA^…, and more generally PP⊄(MIP*)(MIP*)^(MIP*)^… (!), despite the fact that MIP*=RE in the unrelativized world. This result shows that there is no black-box quantum analogue of Stockmeyer’s approximate counting algorithm.
– Relative to a random oracle, Σk+1⊄BQPΣ_k for every k.
– There exists an oracle relative to which BQP=P#P and yet PH is infinite. (By contrast, if NP⊆BPP, then PH collapses relative to all oracles.)
– There exists an oracle relative to which P=NP≠BQP=P#P.
To achieve these results, we build on the 2018 achievement by Raz and Tal of an oracle relative to which BQP⊄PH, and associated results about the Forrelation problem. We also introduce new tools that might be of independent interest. These include a “quantum-aware” version of the random restriction method, a concentration theorem for the block sensitivity of AC0 circuits, and a (provable) analogue of the Aaronson-Ambainis Conjecture for sparse oracles.
Incidentally, particularly when I’ve worked on a project with students, I’m often tremendously excited and want to shout about it from the rooftops for the students’ sake … but then I also don’t want to use this blog to privilege my own papers “unfairly.” Can anyone suggest a principle that I should follow going forward?
About IBM’s new 127-qubit superconducting chip: As I told New Scientist, I look forward to seeing the actual details! As far as I could see, the marketing materials that IBM released yesterday take a lot of words to say absolutely nothing about what, to experts, is the single most important piece of information: namely, what are the gate fidelities? How deep of a quantum circuit can they apply? How have they benchmarked the chip? Right now, all I have to go on is a stats page for the new chip, which reports its average CNOT error as 0.9388—in other words, close to 1, or terrible! (But see also a tweet by James Wootton, which explains that such numbers are often highly misleading when a new chip is first rolled out.) Does anyone here have more information?Update (11/17): As of this morning, the average CNOT error has been updated to 2%. Thanks to multiple commenters for letting me know!
About the new simulation of Google’s 53-qubit Sycamore chip in 5 minutes on a Sunway supercomputer (see also here): This is an exciting step forward on the classical validation of quantum supremacy experiments, and—ironically, what currently amounts to almost the same thing—on the classical spoofing of those experiments. Congratulations to the team in China that achieved this! But there are two crucial things to understand. First, “5 minutes” refers to the time needed to calculate a single amplitude (or perhaps, several correlated amplitudes) using tensor network contraction. It doesn’t refer to the time needed to generate millions of independent noisy samples, which is what Google’s Sycamore chip does in 3 minutes. For the latter task, more like a week still seems to be needed on the supercomputer. (I’m grateful to Chu Guo, a coauthor of the new work who spoke in UT Austin’s weekly quantum Zoom meeting, for clarifying this point.) Second, the Sunway supercomputer has parallel processing power equivalent to approximately ten million of your laptop. Thus, even if we agreed that Google no longer had quantum supremacy as measured by time, it would still have quantum supremacy as measured by carbon footprint! (And this despite the fact that the quantum computer itself requires a noisy, closet-sized dilution fridge.) Even so, for me the new work underscores the point that quantum supremacy is not yet a done deal. Over the next few years, I hope that Google and USTC, as well as any new entrants to this race (IBM? IonQ? Harvard? Rigetti?), will push forward with more qubits and, even more importantly, better gate fidelities leading to higher Linear Cross-Entropy scores. Meanwhile, we theorists should try to do our part by inventing new and better protocols with which to demonstrate near-term quantum supremacy—especially protocols for which the classical verification is easier.
About the new anti-woke University of Austin (UATX): In general, I’m extremely happy for people to experiment with new and different institutions, and of course I’m happy for more intellectual activity in my adopted city of Austin. And, as Shtetl-Optimized readers will know, I’m probably more sympathetic than most to the reality of the problem that UATX is trying to solve—living, as we do, in an era when one academic after another has been cancelled for ideas that a mere decade ago would’ve been considered unexceptional, moderate, center-left. Having said all that, I wish I could feel more optimistic about UATX’s prospects. I found its website heavy on free-speech rhetoric but frustratingly light on what the new university is actually going to do: what courses it will offer, who will teach them, where the campus will be, etc. etc. Arguably this is all excusable for a university still in ramp-up mode, but had I been in their shoes, I might have held off on the public launch until I had at least some sample content to offer. Certainly, the fact that Steven Pinker has quit UATX’s advisory board is a discouraging sign. If UATX asks me to get involved—to lecture there, to give them advice about their CS program, etc.—I’ll consider it as I would any other request. So far, though, they haven’t.
About the Association for Mathematical Research: Last month, some colleagues invited me to join a brand-new society called the Association for Mathematical Research. Many of the other founders (Joel Hass, Abigail Thompson, Colin Adams, Richard Borcherds, Jeff Cheeger, Pavel Etingof, Tom Hales, Jeff Lagarias, Mark Lackenby, Cliff Taubes, …) were brilliant mathematicians who I admired, they seemed like they could use a bit of theoretical computer science representation, there was no time commitment, maybe they’d eventually do something good, so I figured why not? Alas, to say that AMR has proved unpopular on Twitter would be an understatement: it’s received the same contemptuous reception that UATX has. The argument seems to be: starting a new mathematical society, even an avowedly diverse and apolitical one, is really just an implicit claim that the existing societies, like the Mathematical Association of America (MAA) and the American Mathematical Society (AMS), have been co-opted by woke true-believers. But that’s paranoid and insane! I mean, it’s not as if an AMS blog has called for the mass resignation of white male mathematicians to make room for the marginalized, or the boycott of Israeli universities, or the abolition of the criminal justice system (what to do about Kyle Rittenhouse though?). Still, even though claims of that sort of co-option are obviously far-out, rabid fantasies, yeah, I did decide to give a new organization the benefit of the doubt. AMR might well fail or languish in obscurity, just like UATX might. On the other hand, the barriers to making a positive difference for the intellectual world, the world I love, the world under constant threat from the self-certain ideologues of every side, do strike me as orders of magnitude smaller for a new professional society than they do for a new university.
In my last post, I wrote (among other things) about an ongoing scientific debate between the group of Chaoyang Lu at USTC in China, which over the past year has been doing experiments that seek to demonstrate quantum supremacy via Gaussian BosonSampling; and the group of Sergio Boixo at Google, which had a recent paper on a polynomial-time classical algorithm to sample approximately from the same distributions. I reported the facts as I understood them at the time. Since then, though, a long call with the Google team gave me a new and different understanding, and I feel duty-bound to share that here.
A week ago, I considered it obvious that if, using a classical spoofer, you could beat the USTC experiment on a metric like total variation distance from the ideal distribution, then you would’ve completely destroyed USTC’s claim of quantum supremacy. The reason I believed that, in turn, is a proposition that I hadn’t given a name but needs one, so let me call it Hypothesis H:
The only way a classical algorithm to spoof BosonSampling can possibly do well in total variation distance, is by correctly reproducing the high-order correlations (correlations among the occupation numbers of large numbers of modes) — because that’s where the complexity of BosonSampling lies (if it lies anywhere).
Hypothesis H had important downstream consequences. Google’s algorithm, by the Google team’s own admission, does not reproduce the high-order correlations. Furthermore, because of limitations on both samples and classical computation time, Google’s paper calculates the total variation distance from the ideal distribution only on the marginal distribution on roughly 14 out of 144 modes. On that marginal distribution, Google’s algorithm does do better than the experiment in total variation distance. Google presents a claimed extrapolation to the full 144 modes, but eyeballing the graphs, it was far from clear to me what would happen: like, maybe the spoofing algorithm would continue to win, but maybe the experiment would turn around and win; who knows?
Chaoyang, meanwhile, made a clear prediction that the experiment would turn around and win, because of
the experiment’s success in reproducing the high-order correlations,
the admitted failure of Google’s algorithm in reproducing the high-order correlations, and
the seeming impossibility of doing well on BosonSampling without reproducing the high-order correlations (Hypothesis H).
Given everything my experience told me about the central importance of high-order correlations for BosonSampling, I was inclined to agree with Chaoyang.
Now for the kicker: it seems that Hypothesis H is false. A classical spoofer could beat a BosonSampling experiment on total variation distance from the ideal distribution, without even bothering to reproduce the high-order correlations correctly.
This is true because of a combination of two facts about the existing noisy BosonSampling experiments. The first fact is that the contribution from the order-k correlations falls off like 1/exp(k). The second fact is that, due to calibration errors and the like, the experiments already show significant deviations from the ideal distribution on the order-1 and order-2 correlations.
Put these facts together and what do you find? Well, suppose your classical spoofing algorithm takes care to get the low-order contributions to the distribution exactly right. Just for that reason alone, it could already win over a noisy BosonSampling experiment, as judged by benchmarks like total variation distance from the ideal distribution, or for that matter linear cross-entropy. Yes, the experiment will beat the classical simulation on the higher-order correlations. But because those higher-order correlations are exponentially attenuated anyway, they won’t be enough to make up the difference. The experiment’s lack of perfection on the low-order correlations will swamp everything else.
Granted, I still don’t know for sure that this is what happens — that depends on whether I believe Sergio or Chaoyang about the extrapolation of the variation distance to the full 144 modes (my own eyeballs having failed to render a verdict!). But I now see that it’s logically possible, maybe even plausible.
So, let’s imagine for the sake of argument that Google’s simulation wins on variation distance, even though the experiment wins on the high-order correlations. In that case, what would be our verdict: would USTC have achieved quantum supremacy via BosonSampling, or not?
It’s clear what each side could say.
Google could say: by a metric that Scott Aaronson, the coinventor of BosonSampling, thought was perfectly adequate as late as last week — namely, total variation distance from the ideal distribution — we won. We achieved lower variation distance than USTC’s experiment, and we did it using a fast classical algorithm. End of discussion. No moving the goalposts after the fact.
Google could even add: BosonSampling is a sampling task; it’s right there in the name! The only purpose of any benchmark — whether Linear XEB or high-order correlation — is to give evidence about whether you are or aren’t sampling from a distribution close to the ideal one. But that means that, if you accept that we are doing the latter better than the experiment, then there’s nothing more to argue about.
USTC could respond: even if Scott Aaronson is the coinventor of BosonSampling, he’s extremely far from an infallible oracle. In the case at hand, his lack of appreciation for the sources of error in realistic experiments caused him to fixate inappropriately on variation distance as the success criterion. If you want to see the quantum advantage in our system, you have to deliberately subtract off the low-order correlations and look at the high-order correlations.
USTC could add: from the very beginning, the whole point of quantum supremacy experiments was to demonstrate a clear speedup on some benchmark — we never particularly cared which one! That horse is out of the barn as soon as we’re talking about quantum supremacy at all — something the Google group, which itself reported the first quantum supremacy experiment in Fall 2019, again for a completely artificial benchmark — knows as well as anyone else. (The Google team even has experience with adjusting benchmarks: when, for example, Pan and Zhang pointed out that Linear XEB as originally specified is pretty easy to spoof for random 2D circuits, the most cogent rejoinder was: OK, fine then, add an extra check that the returned samples are sufficiently different from one another, which kills Pan and Zhang’s spoofing strategy.) In that case, then, why isn’t a benchmark tailored to the high-order correlations as good as variation distance or linear cross-entropy or any other benchmark?
Both positions are reasonable and have merit — though I confess to somewhat greater sympathy for the one that appeals to my doofosity rather than my supposed infallibility!
OK, but suppose, again for the sake of argument, that we accepted the second position, and we said that USTC gets to declare quantum supremacy as long as its experiment does better than any known classical simulation at reproducing the high-order correlations. We’d still face the question: does the USTC experiment, in fact, do better on that metric? It would be awkward if, having won the right to change the rules in its favor, USTC still lost even under the new rules.
Sergio tells me that USTC directly reported experimental data only for up to order-7 correlations, and at least individually, the order-7 correlations are easy to reproduce on a laptop (although sampling in a way that reproduces the order-7 correlations might still be hard—a point that Chaoyang confirms, and where further research would be great). OK, but USTC also reported that their experiment seems to reproduce up to order-19 correlations. And order-19 correlations, the Google team agrees, are hard to sample consistently with on a classical computer by any currently known algorithm.
So then, why don’t we have direct data for the order-19 correlations? The trouble is simply that it would’ve taken USTC an astronomical amount of computation time. So instead, they relied on a statistical extrapolation from the observed strength of the lower-order correlations — there we go again with the extrapolations! Of course, if we’re going to let Google rest its case on an extrapolation, then maybe it’s only sporting to let USTC do the same.
You might wonder: why didn’t we have to worry about any of this stuff with the other path to quantum supremacy, the one via random circuit sampling with superconducting qubits? The reason is that, with random circuit sampling, all the correlations except the highest-order ones are completely trivial — or, to say it another way, the reduced state of any small number of output qubits is exponentially close to the maximally mixed state. This is a real difference between BosonSampling and random circuit sampling—and even 5-6 years ago, we knew that this represented an advantage for random circuit sampling, although I now have a deeper appreciation for just how great of an advantage it is. For it means that, with random circuit sampling, it’s easier to place a “sword in the stone”: to say, for example, here is the Linear XEB score achieved by the trivial classical algorithm that outputs random bits, and lo, our experiment achieves a higher score, and lo, we challenge anyone to invent a fast classical spoofing method that achieves a similarly high score.
With BosonSampling, by contrast, we have various metrics with which to judge performance, but so far, for none of those metrics do we have a plausible hypothesis that says “here’s the best that any polynomial-time classical algorithm can possibly hope to do, and it’s completely plausible that even a noisy current or planned BosonSampling experiment can do better than that.”
In the end, then, I come back to the exact same three goals I would’ve recommended a week ago for the future of quantum supremacy experiments, but with all of them now even more acutely important than before:
Experimentally, to increase the fidelity of the devices (with BosonSampling, for example, to observe a larger contribution from the high-order correlations) — a much more urgent goal, from the standpoint of evading classical spoofing algorithms, than further increasing the dimensionality of the Hilbert space.
Theoretically, to design better ways to verify the results of sampling-based quantum supremacy experiments classically — ideally, even ways that could be applied via polynomial-time tests.
For Gaussian BosonSampling in particular, to get a better understanding of the plausible limits of classical spoofing algorithms, and exactly how good a noisy device needs to be before it exceeds those limits.
Thanks so much to Sergio Boixo and Ben Villalonga for the conversation, and to Chaoyang Lu and Jelmer Renema for comments on this post. Needless to say, any remaining errors are my own.
1. Huge congratulations to the winners of this year’s Nobel Prize in Physics: Syukuro Manabe and Klaus Hasselmann for climate modelling, and separately, Giorgio Parisi for statistical physics. While I don’t know the others, I had the great honor to get to know Parisi three years ago, when he was chair of the committee that awarded me the Tomassoni-Chisesi Prize in Physics, and when I visited Parisi’s department at Sapienza University of Rome to give the prize lecture and collect the award. I remember Parisi’s kindness, a lot of good food, and a lot of discussion of the interplay between theoretical computer science and physics. Note that, while much of Parisi’s work is beyond my competence to comment on, in computer science he’s very well-known for applying statistical physics methods to the analysis of survey propagation—an algorithm that revolutionized the study of random 3SAT when it was introduced two decades ago.
2. Two weeks ago, a group at Google put out a paper with a new efficient classical algorithm to simulate the recent Gaussian BosonSampling experiments from USTC in China. They argued that this algorithm called into question USTC’s claim of BosonSampling-based quantum supremacy. Since then, I’ve been in contact with Sergio Boixo from Google, Chaoyang Lu from USTC, and Jelmer Renema, a Dutch BosonSampling expert and friend of the blog, to try to get to the bottom of this. Very briefly, the situation seems to be that Google’s new algorithm outperforms the USTC experiment on one particular metric: namely, total variation distance from the ideal marginal distribution, if (crucially) you look at only a subset of the optical modes, say 14 modes out of 144 total. Meanwhile, though, if you look at the kth-order correlations for large values of k, then the USTC experiment continues to win. With the experiment, the correlations fall off exponentially with k but still have a meaningful, detectable signal even for (say) k=19, whereas with Google’s spoofing algorithm, you choose the k that you want to spoof (say, 2 or 3), and then the correlations become nonsense for larger k.
Now, given that you were only ever supposed to see a quantum advantage from BosonSampling if you looked at the kth-order correlations for large values of k, and given that we already knew, from the work of Leonid Gurvits, that very small marginals in BosonSampling experiments would be easy to reproduce on a classical computer, my inclination is to say that USTC’s claim of BosonSampling-based quantum supremacy still stands. On the other hand, it’s true that, with BosonSampling especially, more so than with qubit-based random circuit sampling, we currently lack an adequate theoretical understanding of what the target should be. That is, which numerical metric should an experiment aim to maximize, and how well does it have to score on that metric before it’s plausibly outperforming any fast classical algorithm? One thing I feel confident about is that, whichever metric is chosen—Linear Cross-Entropy or whatever else—it needs to capture the kth-order correlations for large values of k. No metric that’s insensitive to those correlations is good enough.
3. Like many others, I was outraged and depressed that MIT uninvited Dorian Abbot (see also here), a geophysicist at the University of Chicago, who was slated to give the Carlson Lecture in the Department of Earth, Atmospheric, and Planetary Sciences about the atmospheres of extrasolar planets. The reason for the cancellation was that, totally unrelatedly to his scheduled lecture, Abbot had argued in Newsweek and elsewhere that Diversity, Equity, and Inclusion initiatives should aim for equality for opportunity rather than equality of outcomes, a Twitter-mob decided to go after him in retaliation, and they succeeded. It should go without saying that it’s perfectly reasonable to disagree with Abbot’s stance, to counterargue—if those very concepts haven’t gone the way of floppy disks. It should also go without saying that the MIT EAPS department chair is free to bow to social-media pressure, as he did, rather than standing on principle … just like I’m free to criticize him for it. To my mind, though, cancelling a scientific talk because of the speaker’s centrist (!) political views completely, 100% validates the right’s narrative about academia, that it’s become a fanatically intolerant echo chamber. To my fellow progressive academics, I beseech thee in the bowels of Bertrand Russell: why would you commit such an unforced error?
Yes, one can imagine views (e.g., open Nazism) so hateful that they might justify the cancellation of unrelated scientific lectures by people who hold those views, as many physicists after WWII refused to speak to Werner Heisenberg. But it seems obvious to me—as it would’ve been obvious to everyone else not long ago—that no matter where a reasonable person draws the line, Abbot’s views as he expressed them in Newsweek don’t come within a hundred miles of it. To be more explicit still: if Abbot’s views justify deplatforming him as a planetary scientist, then all my quantum computing and theoretical computer science lectures deserve to be cancelled too, for the many attempts I’ve made on this blog over the past 16 years to share my honest thoughts and life experiences, to write like a vulnerable human being rather than like a university press office. While I’m sure some sneerers gleefully embrace that implication, I ask everyone else to consider how deeply they believe in the idea of academic freedom at all—keeping in mind that such a commitment only ever gets tested when there’s a chance someone might denounce you for it.
Update: Princeton’s James Madison Program has volunteered to host Abbot’s Zoom talk in place of MIT. The talk is entitled “Climate and the Potential for Life on Other Planets.” Like probably hundreds of others who heard about this only because of the attempted cancellation, I plan to attend!
Unrelated Bonus Update:Here’s a neat YouTube video put together by the ACM about me as well as David Silver of AlphaGo and AlphaZero, on the occasion of our ACM Prizes in Computing.
This Erev Yom Kippur, I wish to repent for not putting enough quantum computing content on this blog. Of course, repentance is meaningless unless accompanied by genuine reform. That being the case, please enjoy the YouTube video of my ACM TechTalk from last week about quantum supremacy—although, as you’ll see if you watch the thing, I oscillate between quantum supremacy and other terms like “quantum advantage” and even “quantum supremadvantage.” This represents the first time ever that I got pushback about a talk before I’d delivered it for political reasons—the social-justice people, it turns out, are actually serious about wanting to ban the term “quantum supremacy”—but my desire to point out all the difficulties with their proposal competed with my desire not to let that issue overshadow my talk.
And there’s plenty to talk about! While regular Shtetl-Optimized readers will have already heard (or read) most of what I say, I make some new comments, including about the new paper from last week, the night before my talk (!), by the USTC group in China, where they report a quantum supremacy experiment based on random circuit sampling with a superconducting chip, this time with a record-setting 60 qubits and 24 layers of gates. On the other hand, I also stress how increasing the circuit fidelity has become a much more urgent issue than further increasing the number of qubits (or in the case of BosonSampling, the number of photons), if our goal is for these experiments to remain a couple steps ahead of classical spoofing algorithms.
Anyway, I hope you enjoy my lovingly handcrafted visuals. Over the course of this pandemic, I’ve become a full convert to writing out my talks with a stylus pen rather than PowerPointing them—not only is it faster for me, not only does it allow for continuous scrolling rather than arbitrary divisions into slides, but it enforces simplicity and concision in ways they should be enforced.
While there was only time for me to field a few questions at the end of the talk, I later supplied written answers to 52 questions (!!) that I hadn’t gotten to. If you have a question, please check to see if it’s already there, and otherwise ask away in the comments!
Thanks so much to Yan Timanovsky for inviting and organizing this talk, and to whurley for hosting it.
Way back in 2005, I posed Ten Semi-Grand Challenges for Quantum Computing Theory, on at least half of which I’d say there’s been dramatic progress in the 16 years since (most of the challenges were open-ended, so that it’s unclear when to count them as “solved”). I posed more open quantum complexity problems in 2010, and some classical complexity problems in 2011. In the latter cases, I’d say there’s been dramatic progress on about a third of the problems. I won’t go through the problems one by one, but feel free to ask in the comments about any that interest you.
Shall I push my luck as a problem-poser? Shall or shall not, I have.
My impetus, this time around, was a kind invitation by Travis Humble, the editor-in-chief of the new ACM Transactions on Quantum Computing, to contribute a perspective piece to that journal on the occasion of my ACM Prize. I agreed—but only on the condition that, rather than ponderously pontificate about the direction of the field, I could simply discuss a bunch of open problems that I wanted to see solved. The result is below. It’s coming soon to an arXiv near you, but Shtetl-Optimized readers get it first.
Abstract: I offer a case that quantum query complexity still has loads of enticing and fundamental open problems—from relativized QMA versus QCMA and BQP versus IP, to time/space tradeoffs for collision and element distinctness, to polynomial degree versus quantum query complexity for partial functions, to the Unitary Synthesis Problem and more.
Some of the problems on my new hit-list are ones that I and others have flogged for years or even decades, but others, as far as I know, appear here for the first time. If your favorite quantum query complexity open problem, or a problem I’ve discussed in the past, is missing, that doesn’t mean that it’s been solved or is no longer interesting—it might mean I simply ran out of time or energy before I got to it.
Enjoy! And tell me what I missed or got wrong or has a trivial solution that I overlooked.
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