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Cracking the Top Fifty!

2025-05-09 05:26:34

I’ve now been blogging for nearly twenty years—through five presidential administrations, my own moves from Waterloo to MIT to UT Austin, my work on algebrization and BosonSampling and BQP vs. PH and quantum money and shadow tomography, the publication of Quantum Computing Since Democritus, my courtship and marriage and the birth of my two kids, a global pandemic, the rise of super-powerful AI and the terrifying downfall of the liberal world order.

Yet all that time, through more than a thousand blog posts on quantum computing, complexity theory, philosophy, the state of the world, and everything else, I chased a form of recognition for my blogging that remained elusive.

Until now.

This week I received the following email:

I emailed regarding your blog Shtetl-Optimized Blog which was selected by FeedSpot as one of the Top 50 Quantum Computing Blogs on the web.

https://bloggers.feedspot.com/quantum_computing_blogs

We recommend adding your website link and other social media handles to get more visibility in our list, get better ranking and get discovered by brands for collaboration.

We’ve also created a badge for you to highlight this recognition. You can proudly display it on your website or share it with your followers on social media.

We’d be thankful if you can help us spread the word by briefly mentioning Top 50 Quantum Computing Blogs in any of your upcoming posts.

Please let me know if you can do the needful.

You read that correctly: Shtetl-Optimized is now officially one of the top 50 quantum computing blogs on the web. You can click the link to find the other 49.


Maybe it’s not unrelated to this new notoriety that, over the past few months, I’ve gotten a massively higher-than-usual volume of emailed solutions to the P vs. NP problem, as well as the other Clay Millennium Problems (sometimes all seven problems at once), as well as quantum gravity and life, the universe, and everything. I now get at least six or seven confident such emails per day.

While I don’t spend much time on this flood of scientific breakthroughs (how could I?), I’d like to note one detail that’s new. Many of the emails now include transcripts where ChatGPT fills in the details of the emailer’s theories for them—unironically, as though that ought to clinch the case. Who said generative AI wasn’t poised to change the world? Indeed, I’ll probably need to start relying on LLMs myself to keep up with the flood of fan mail, hate mail, crank mail, and advice-seeking mail.

Anyway, thanks for reading everyone! I look forward to another twenty years of Shtetl-Optimized, if my own health and the health of the world cooperate.

Opposing SB37

2025-05-07 02:21:56

Yesterday, the Texas State Legislature heard public comments about SB37, a bill that would give a state board direct oversight over course content and faculty hiring at public universities, perhaps inspired by Trump’s national crackdown on higher education. (See here or here for coverage.) So, encouraged by a friend in the history department, I submitted the following public comment, whatever good it will do.


I’m a computer science professor at UT, although I’m writing in my personal capacity. For 20 years, on my blog and elsewhere, I’ve been outspoken in opposing woke radicalism on campus and (especially) obsessive hatred of Israel that often veers into antisemitism, even when that’s caused me to get attacked from my left. Nevertheless, I write to strongly oppose SB37 in its current form, because of my certainty that no world-class research university can survive ceding control over its curriculum and faculty hiring to the state. If this bill passes, for example, it will severely impact my ability to recruit the most talented computer scientists to UT Austin, if they have competing options that will safeguard their academic freedom as traditionally conceived. Even if our candidates are approved, the new layer of bureaucracy will make it difficult and slow for us to do anything. For those concerned about intellectual diversity in academia, a much better solution would include safeguarding tenure and other protections for faculty with heterodox views, and actually enforcing content-neutral time, place, and manner rules for protests and disruptions. UT has actually done a better job on these things than many other universities in the US, and could serve as a national model for how viewpoint diversity can work — but not under an intolerably stifling regime like the one proposed by this bill.

Quantum! AI! Everything but Trump!

2025-05-01 11:16:57

  • Grant Sanderson, of 3blue1brown, has put up a phenomenal YouTube video explaining Grover’s algorithm, and dispelling the fundamental misconception about quantum computing, that QC works simply by “trying all the possibilities in parallel.” Let me not futz around: this video explains, in 36 minutes, what I’ve tried to explain over and over on this blog for 20 years … and it does it better. It’s a masterpiece. Yes, I consulted with Grant for this video (he wanted my intuitions for “why is the answer √N?”), and I even have a cameo at the end of it, but I wish I had made the video. Damn you, Grant!
  • The incomparably great, and absurdly prolific, blogger Zvi Mowshowitz and yours truly spend 1 hour and 40 minutes discussing AI existential risk, education, blogging, and more. I end up “interviewing” Zvi, who does the majority of the talking, which is fine by me, as he has many important things to say! (Among them: his searing critique of those K-12 educators who see it as their life’s mission to prevent kids from learning too much too fast—I’ve linked his best piece on this from the header of this blog.) Thanks so much to Rick Coyle for arranging this conversation.
  • Progress in quantum complexity theory! In 2000, John Watrous showed that the Group Non-Membership problem is in the complexity class QMA (Quantum Merlin-Arthur). In other words, if some element g is not contained in a given subgroup H of an exponentially large finite group G, which is specified via a black box, then there’s a short quantum proof that g∉H, with only ~log|G| qubits, which can be verified on a quantum computer in time polynomial in log|G|. This soon raised the question of whether Group Non-Membership could be used to separate QMA from QCMA by oracles, where QCMA (Quantum Classical Merlin Arthur), defined by Aharonov and Naveh in 2002, is the subclass of QMA where the proof needs to be classical, but the verification procedure can still be quantum. In other words, could Group Non-Membership be the first non-quantum example where quantum proofs actually help?

    In 2006, alas, Greg Kuperberg and I showed that the answer was probably “no”: Group Non-Membership has “polynomial QCMA query complexity.” This means that there’s a QCMA protocol for the problem where Arthur makes only polylog|G| quantum queries to the group oracle—albeit, possibly an exponential in log|G| number of quantum computation steps besides that! To prove our result, Greg and I needed to make mild use of the Classification of Finite Simple Groups, one of the crowning achievements of 20th-century mathematics (its proof is about 15,000 pages long). We conjectured (but couldn’t prove) that someone else, who knew more about the Classification than we did, could show that Group Non-Membership was simply in QCMA outright.

    Now, after almost 20 years, François Le Gall, Harumichi Nishimura, and Dhara Thakkar have finally proven our conjecture—showing that Group Order, and therefore also Group Non-Membership, are indeed in QCMA. They did indeed need to use the Classification, doing one thing for almost all finite groups covered by the Classification, but a different thing for groups of “Ree type” (whatever those are).

    Interestingly, the Group Membership problem had also been a candidate for separating BQP/qpoly, or quantum polynomial time with polynomial-size quantum advice—my personal favorite complexity class—from BQP/poly, or the same thing with polynomial-size classical advice. And it might conceivably still be! The authors explain to me that their protocol doesn’t put Group Membership (with group G and subgroup H depending only on the input length n) into BQP/poly, the reason being that their short classical witnesses for g∉H depend on both g and H, in contrast to Watrous’s quantum witnesses which depended only on H. So there’s still plenty that’s open here! Actually, for that matter, I don’t know of good evidence that the entire Group Membership problem isn’t in BQP—i.e., that quantum computers can’t just solve the whole thing outright, with no Merlins or witnesses in sight!

    Anyway, huge congratulations to Le Gall, Nishimura, and Thakkar for peeling back our ignorance of these matters a bit further! Reeeeeeeee!
  • Potential big progress in quantum algorithms! Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone (GLM) have given what they present as a quantum algorithm to estimate the determinant of an n×n matrix A, exponentially faster in some contexts than we know how to do it classically.

    [Update (May 5): In the comments, Alessandro Luongo shares a paper where he and Changpeng Shao describe what appears to be essentially the same algorithm back in 2020.]

    The algorithm is closely related to the 2008 HHL (Harrow-Hassidim-Lloyd) quantum algorithm for solving systems of linear equations. Which means that anyone who knows the history of this class of quantum algorithms knows to ask immediately: what’s the fine print? A couple weeks ago, when I visited Harvard and MIT, I had a chance to catch up with Seth Lloyd, so I asked him, and he kindly told me. Firstly, we assume the matrix A is Hermitian and positive semidefinite. Next, we assume A is sparse, and not only that, but there’s a QRAM data structure that points to its nonzero entries, so you don’t need to do Grover search or the like to find them, and can query them in coherent superposition. Finally, we assume that all the eigenvalues of A are at least some constant λ>0. The algorithm then estimates det(A), to multiplicative error ε, in time that scales linearly with log(n), and polynomially with 1/λ and 1/ε.

    Now for the challenge I leave for ambitious readers: is there a classical randomized algorithm to estimate the determinant under the same assumptions and with comparable running time? In other words, can the GLM algorithm be “Ewinized”? Seth didn’t know, and I think it’s a wonderful crisp open question! On the one hand, if Ewinization is possible, it wouldn’t be the first time that publicity on this blog had led to the brutal murder of a tantalizing quantum speedup. On the other hand … well, maybe not! I also consider it possible that the problem solved by GLM—for exponentially-large, implicitly-specified matrices A—is BQP-complete, as for example was the general problem solved by HHL. This would mean, for example, that one could embed Shor’s factoring algorithm into GLM, and that there’s no hope of dequantizing it unless P=BQP. (Even then, though, just like with the HHL algorithm, we’d still face the question of whether the GLM algorithm was “independently useful,” or whether it merely reproduced quantum speedups that were already known.)

    Anyway, quantum algorithms research lives! So does dequantization research! If basic science in the US is able to continue at all—the thing I promised not to talk about in this post—we’ll have plenty to keep us busy over the next few years.

Fight Fiercely

2025-04-24 19:48:25

Last week I visited Harvard and MIT, and as advertised in my last post, gave the Yip Lecture at Harvard on the subject “How Much Math Is Knowable?” The visit was hosted by Harvard’s wonderful Center of Mathematical Sciences and Applications (CMSA), directed by my former UT Austin colleague Dan Freed. Thanks so much to everyone at CMSA for the visit.

And good news! You can now watch my lecture on YouTube here:

I’m told it was one of my better performances. As always, I strongly recommend watching at 2x speed.

I opened the lecture by saying that, while obviously it would always be an honor to give the Yip Lecture at Harvard, it’s especially an honor right now, as the rest of American academia looks to Harvard to defend the value of our entire enterprise. I urged Harvard to “fight fiercely,” in the words of the Tom Lehrer song.

I wasn’t just fishing for applause; I meant it. It’s crucial for people to understand that, in its total war against universities, MAGA has now lost, not merely the anti-Israel leftists, but also most conservatives, classical liberals, Zionists, etc. with any intellectual scruples whatsoever. To my mind, this opens up the possibility for a broad, nonpartisan response, highlighting everything universities (yes, even Harvard 😂) do for our civilization that’s worth defending.

For three days in my old hometown of Cambridge, MA, I met back-to-back with friends and colleagues old and new. Almost to a person, they were terrified about whether they’ll be able to keep doing science as their funding gets decimated, but especially terrified for anyone who they cared about on visas and green cards. International scholars can now be handcuffed, deported, and even placed in indefinite confinement for pretty much any reason—including long-ago speeding tickets—or no reason at all. The resulting fear has paralyzed, in a matter of months, an American scientific juggernaut that took a century to build.

A few of my colleagues personally knew Rümeysa Öztürk, the Turkish student at Tufts who currently sits in prison for coauthoring an editorial for her student newspaper advocating the boycott of Israel. I of course disagree with what Öztürk wrote … and that is completely irrelevant to my moral demand that she go free. Even supposing the government had much more on her than this one editorial, still the proper response would seem to be a deportation notice—“either contest our evidence in court, or else get on the next flight back to Turkey”—rather than grabbing Öztürk off the street and sending her to indefinite detention in Louisiana. It’s impossible to imagine any university worth attending where the students live in constant fear of imprisonment for the civil expression of opinions.

To help calibrate where things stand right now, here’s the individual you might expect to be most on board with a crackdown on antisemitism at Harvard:

Jason Rubenstein, the executive director of Harvard Hillel, said that the school is in the midst of a long — and long-overdue — reckoning with antisemitism, and that [President] Garber has taken important steps to address the problem. Methodical federal civil rights oversight could play a constructive role in that reform, he said. “But the government’s current, fast-paced assault against Harvard – shuttering apolitical, life-saving research; targeting the university’s tax-exempt status; and threatening all student visas … is neither deliberate nor methodical, and its disregard for the necessities of negotiation and due process threatens the bulwarks of institutional independence and the rule of law that undergird our shared freedoms.”

Meanwhile, as the storm clouds over American academia continue to darken, I’ll just continue to write what I think about everything, because what else can I do?

Last night, alas, I lost yet another left-wing academic friend, the fourth or fifth I’ve lost since October 7. For while I was ready to take a ferocious public stand against the current US government, for the survival and independence of our universities, and for free speech and due process for foreign students, this friend regarded all that as insufficient. He demanded that I also clear the tentifada movement of any charge of antisemitism. For, as he patiently explained to me (while worrying that I wouldn’t grasp the point), while the protesters may have technically violated university rules, disrupted education, created a hostile environment in the sense of Title VI antidiscrimination law in ways that would be obvious were we discussing any other targeted minority, etc. etc., still, the only thing that matters morally is that the protesters represent “the powerless,” whereas Zionist Jews like me represent “the powerful.” So, I told this former friend to go fuck himself. Too harsh? Maybe if he hadn’t been Jewish himself, I could’ve forgiven him for letting the world’s oldest conspiracy theory colonize his brain.

For me, the deep significance of in-person visits, including my recent trip to Harvard, is that they reassure me of the preponderance of sanity within my little world—and thereby of my own sanity. Online, every single day I feel isolated and embattled: pressed in on one side by MAGA forces who claim to care about antisemitism, but then turn out to want the destruction of science, universities, free speech, international exchange, due process of law, and everything else that’s made the modern world less than fully horrible; and on the other side, by leftists who say they stand with me for science and academic freedom and civil rights and everything else that’s good, but then add that the struggle needs to continue until the downfall of the scheming, moneyed Zionists and the liberation of Palestine from river to sea.

When I travel to universities to give talks, though, I meet one sane, reasonable human being after another. Almost to a person, they acknowledge the reality of antisemitism, ideological monoculture, bureaucracy, spiraling costs, and many other problems at universities—and they care about universities enough to want to fix those problems, rather than gleefully nuking the universities from orbit as MAGA is doing. Mostly, though, people just want me to sign Quantum Computing Since Democritus, or tell me how much they like this blog, or ask questions about quantum algorithms or the Busy Beaver function. Which is fine too, and which you can do in the comments.

I speak at Harvard as it faces its biggest crisis since 1636

2025-04-16 01:22:35

Every week, I tell myself I won’t do yet another post about the asteroid striking American academia, and then every week events force my hand otherwise.

No one on earth—certainly no one who reads this blog—could call me blasé about the issue of antisemitism at US universities. I’ve blasted the takeover of entire departments and unrelated student clubs and campus common areas by the dogmatic belief that the State of Israel (and only Israel, among all nations on earth) should be eradicated, by the use of that belief as a litmus test for entry. Since October 7, I’ve dealt with comments and emails pretty much every day calling me a genocidal Judeofascist Zionist.

So I hope it means something when I say: today I salute Harvard for standing up to the Trump administration. And I’ll say so in person, when I visit Harvard’s math department later this week to give the Fifth Annual Yip Lecture, on “How Much Math Is Knowable?” The more depressing the news, I find, the more my thoughts turn to the same questions that bothered Euclid and Archimedes and Leibniz and Russell and Turing. Actually, what the hell, why don’t I share the abstract for this talk?

Theoretical computer science has over the years sought more and more refined answers to the question of which mathematical truths are knowable by finite beings like ourselves, bounded in time and space and subject to physical laws.  I’ll tell a story that starts with Gödel’s Incompleteness Theorem and Turing’s discovery of uncomputability.  I’ll then introduce the spectacular Busy Beaver function, which grows faster than any computable function.  Work by me and Yedidia, along with recent improvements by O’Rear and Riebel, has shown that the value of BB(745) is independent of the axioms of set theory; on the other end, an international collaboration proved last year that BB(5) = 47,176,870.  I’ll speculate on whether BB(6) will ever be known, by us or our AI successors.  I’ll next discuss the P≠NP conjecture and what it does and doesn’t mean for the limits of machine intelligence.  As my own specialty is quantum computing, I’ll summarize what we know about how scalable quantum computers, assuming we get them, will expand the boundary of what’s mathematically knowable.  I’ll end by talking about hypothetical models even beyond quantum computers, which might expand the boundary of knowability still further, if one is able (for example) to jump into a black hole, create a closed timelike curve, or project oneself onto the holographic boundary of the universe.

Now back to the depressing news. What makes me take Harvard’s side is the experience of Columbia. Columbia had already been moving in the right direction on fighting antisemitism, and on enforcing its rules against disruption, before the government even got involved. Then, once the government did take away funding and present its ultimatum—completely outside the process specified in Title VI law—Columbia’s administration quickly agreed to everything asked, to howls of outrage from the left-leaning faculty. Yet despite its total capitulation, the government has continued to hold Columbia’s medical research and other science funding hostage, while inventing a never-ending list of additional demands, whose apparent endpoint is that Columbia submit to state ideological control like a university in Russia or Iran.

By taking this scorched-earth route, the government has effectively telegraphed to all the other universities, as clearly as possible: “actually, we don’t care what you do or don’t do on antisemitism. We just want to destroy you, and antisemitism was our best available pretext, the place where you’d most obviously fallen short of your ideals. But we’re not really trying to cure a sick patient, or force the patient to adopt better health habits: we’re trying to shoot, disembowel, and dismember the patient. That being the case, you might as well fight us and go down with dignity!”

No wonder that my distinguished Harvard friends (and past Shtetl-Optimized guest bloggers) Steven Pinker and Boaz Barak—not exactly known as anti-Zionist woke radicals—have come out in favor of Harvard fighting this in court. So has Harvard’s past president Larry Summers, who’s welcome to guest-blog here as well. They all understand that events have given us no choice but to fight Trump as if there were no antisemitism, even while we continue to fight antisemitism as if there were no Trump.


Update (April 16): Commenter Greg argues that, in the title of this post, I probably ought to revise “Harvard’s biggest crisis since 1636” to “its biggest crisis since 1640.” Why 1640? Because that’s when the new college was shut down, over allegations that its head teacher was beating the students and that the head teacher’s wife (who was also the cook) was serving the students food adulterated with dung. By 1642, Harvard was back on track and had graduated its first class.

My most rage-inducing beliefs

2025-04-14 23:42:43

A friend and I were discussing whether there’s anything I could possibly say, on this blog, in 2025, that wouldn’t provoke an outraged reaction from my commenters. So I started jotting down ideas. Let’s see how I did.

  1. Pancakes are a delicious breakfast, especially with blueberries and maple syrup.
  2. Since it’s now Passover, and no pancakes for me this week, let me add: I think matzoh has been somewhat unfairly maligned. Of course it tastes like cardboard if you eat it plain, but it’s pretty tasty with butter, fruit preserves, tuna salad, egg salad, or chopped liver.
  3. Central Texas is actually really nice in the springtime, with lush foliage and good weather for being outside.
  4. Kittens are cute. So are puppies, although I’d go for kittens given the choice.
  5. Hamilton is a great musical—so much so that it’s become hard to think about the American Founding except as Lin-Manuel Miranda reimagined it, with rap battles in Washington’s cabinet and so forth. I’m glad I got to take my kids to see it last week, when it was in Austin (I hadn’t seen it since it its pre-Broadway previews a decade ago). Two-hundred fifty years on, I hope America remembers its founding promise, and that Hamilton doesn’t turn out to be America’s eulogy.
  6. The Simpsons and Futurama are hilarious.
  7. Young Sheldon and The Big Bang Theory are unjustly maligned. They were about as good as any sitcoms can possibly be.
  8. For the most part, people should be free to live lives of their choosing, as long as they’re not harming others.
  9. The rapid progress of AI might be the most important thing that’s happened in my lifetime. There’s a huge range of plausible outcomes, from “merely another technological transformation like computing or the Internet” to “biggest thing since the appearance of multicellular life,” but in any case, we ought to proceed with caution and with the wider interests of humanity foremost in our minds.
  10. Research into curing cancer is great and should continue to be supported.
  11. The discoveries of NP-completeness, public-key encryption, zero-knowledge and probabilistically checkable proofs, and quantum computational speedups were milestones in the history of theoretical computer science, worthy of celebration.
  12. Katalin Karikó, who pioneered mRNA vaccines, is a heroine of humanity. We should figure out how to create more Katalin Karikós.
  13. Scientists spend too much of their time writing grant proposals, and not enough doing actual science. We should experiment with new institutions to fix this.
  14. I wish California could build high-speed rail from LA to San Francisco. If California’s Democrats could show they could do this, it would be an electoral boon to Democrats nationally.
  15. I wish the US could build clean energy, including wind, solar, and nuclear. Actually, more generally, we should do everything recommended in Derek Thompson and Ezra Klein’s phenomenal new book Abundance, which I just finished.
  16. The great questions of philosophy—why does the universe exist? how does consciousness relate to the physical world? what grounds morality?—are worthy of respect, as primary drivers of human curiosity for millennia. Scientists and engineers should never sneer at these questions. All the same, I personally couldn’t spend my life on such questions: I also need small problems, ones where I can make definite progress.
  17. Quantum physics, which turns 100 this year, is arguably the most metaphysical of all empirical discoveries. It’s worthy of returning to again and again in life, asking: but how could the world be that way? Is there a different angle that we missed?
  18. If I knew for sure that I could achieve Enlightenment, but only by meditating on a mountaintop for a decade, a further question would arise: is it worth it? Or would I rather spend that decade engaged with the world, with scientific problems and with other people?
  19. I, too, vote for political parties, and have sectarian allegiances. But I’m most moved by human creative effort, in science or literature or anything else, that transcends time and place and circumstance and speaks to the eternal.
  20. As I was writing this post, a bird died by flying straight into the window of my home office. As little sense as it might make from a utilitarian standpoint, I am sad for that bird.