Shtetl-Optimized

Sir Charles Antony Richard Hoare (1934-2026) won the 1980 Turing Award for numerous contributions to computer science, including foundational work on concurrency and formal verification and the invention (with Dijkstra) of the dining philosophers problem. But he’s perhaps best known, to pretty much everyone who’s ever studied CS, as the inventor of the Quicksort algorithm. I’m sorry that I never got to meet him.

Michael O. Rabin (1931-2026), of Harvard University, was one of the founders of theoretical computer science and winner of the 1976 Turing Award. In 1959, he and Dana Scott introduced the concept of a “nondeterministic machine”—that is, a machine with exponentially many possible computation paths, which accepts if and only if there exists an accepting path—which would of course later play a central role in the formulation of P vs. NP problem. He’s also known for the Miller-Rabin primality test, which helped to establish randomness as a central concept in algorithms, and for many other things. He’s survived by his daughter Tal Rabin, also a distinguished theoretical computer scientist. I was privileged to meet the elder Rabin on several visits to Harvard, where he showed me great kindness.

Sir Anthony Leggett (1938-2026), of the University of Illinois Urbana-Champaign, was one of the great quantum physicists of the late 20th century, and recipient of the 2003 Nobel Prize for his work on superfluidity. When I knew him, he was a sort of elder statesman of quantum computing and information, who helped remind the rest of us of why we got into the field in the first place—not to solve Element Distinctness moderately faster, but to learn the truth of quantum mechanics itself. Tony insisted, over and over, that the validity of quantum mechanics on the scale of everyday life is an open empirical problem, to be settled by better experiments and not by a-priori principles. I first met Tony at a Gordon Research Conference in southern California. Even though I was then a nobody and he a recent Nobel laureate, he took the time to listen to my ideas about Sure/Shor separators, and to suggest (correctly) what we now call 2D cluster states as an excellent candidate for what I wanted. In all my later interactions with Tony, at both the University of Waterloo (where he was visiting faculty for a while) and at UIUC (where my wife Dana and I considered taking jobs), he was basically the friendliest, funniest guy you could possibly meet at his level of achievement and renown. I was bummed to hear about his passing.

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For those of you who haven’t seen, there were actually two “bombshell” QC announcements this week. One, from Caltech, including friend-of-the-blog John Preskill, showed how to do quantum fault-tolerance with lower overhead than was previously known, by using high-rate codes, which could work for example in neutral-atom architectures (or possibly other architectures that allow nonlocal operations, like trapped ions). The second bombshell, from Google, gave a lower-overhead implementation of Shor’s algorithm to break 256-bit elliptic curve cryptography.

Notably, out of an abudance of caution, the Google team chose to “publish” its result via a cryptographic zero-knowledge proof that their circuit exists (so, without revealing the details to attackers). This is the first time I’ve ever seen a new mathematical result actually announced that way, although I understand that there’s precedent in the 1500’s, when mathematicians would (for example) prove their ability to solve quartic equations by challenging their rivals to duels. I’m not sure how much it will actually help, as once other groups know that a smaller circuit exists, it might be only a short time until they’re able to find it as well.

Neither of these results change the basic principles of QC that we’ve known for decades, but they do change the numbers.

When you put both of them together, Bitcoin signatures for example certainly look vulnerable to quantum attack earlier than was previously known!  In particular, the Caltech group estimates that a mere 25,000 physical qubits might suffice for this, where a year ago the best estimates were in the millions. How much time will this save — maybe a year?  Subtracting, of course, off a number of years that no one knows.

In any case, these results provide an even stronger impetus for people to upgrade now to quantum-resistant cryptography.  They—meaning you, if relevant—should really get on that!

When I got an early heads-up about these results—especially the Google team’s choice to “publish” via a zero-knowledge proof—I thought of Frisch and Peierls, calculating how much U-235 was needed for a chain reaction in 1940, but not publishing it, even though the latest results on nuclear fission had been openly published just the year prior. Will we, in quantum computing, also soon cross that threshold? But I got strong pushback on that analogy from the cryptography and cybersecurity people who I most respect. They said: we have decades of experience with this, and the answer is that you publish. And, they said, if publishing causes people still using quantum-vulnerable systems to crap their pants … well, maybe that’s what needs to happen right now.

Naturally, journalists have been hounding me for comments, though it was the worst possible week, when I needed to host like four separate visitors in Austin. I hope this post helps! Please feel free to ask questions or post further details in the comments.

And now, with no time for this blog post to leaven and rise, I need to go home for my family’s Seder. Happy Passover!

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Last summer, I was privileged to teach a two-week course on theoretical computer science to exceptional 11- and 12-year-olds at Epsilon Camp, held at Washington University in St. Louis. The course was basically a shorter version of the 6.045 course that I used to teach to undergrads at MIT.

I was at Epsilon Camp to accompany my son Daniel, who attended a different course there, for the 7- and 8-year-olds. So they got me to teach while I was there.

Teaching at Epsilon was some of the hardest work I’ve done in years: I taught two classes, held office hours, and interacted with or supervised students for 6-7 hours per day (compared to ~4 hours per week as a professor), on top of being Daniel’s sole caregiver, on top of email and all my other normal responsibilities. But it was also perhaps the most extraordinary teaching I’ve ever done: during “lecture,” the kids were throwing paper planes, talking over and interrupting me every ten seconds, and sometimes getting in physical fights with each other. In my ~20 years as a professor, this was the first time that I ever needed to worry about classroom discipline (!). It gave me newfound respect for what elementary school teachers handle every day.

But then, when I did have the kids’ attention, they would often ask questions or make observations that I would’ve been thrilled to hear from undergrads at UT Austin or MIT. Some of these kids, I felt certain, can grow up if they want to be world-leading mathematicians and physicists and computer scientists, Terry Taos and Ed Wittens of their generation. Or at least, that’ll be true if AI isn’t soon going to outperform the top human scientists at their own game, a prospect that of course casts a giant shadow not only over Epsilon Camp but over our entire enterprise. But enough about the future. For now I can say: it was a privilege of a lifetime to teach these kids, to be the one who first introduced them to theoretical computer science.

Or at least, the one who first systematically introduced them. As I soon realized, there was no topic I could mention—not the halting problem or the Busy Beaver function, not NP-completeness or Diffie-Hellman encryption—that some of these 11-year-olds hadn’t previously seen, and that they didn’t want to interrupt me to share everything they already knew about. Rather than fighting that tendency, I smiled and let them do this. While their knowledge was stunningly precocious, it was also fragmentary and disjointed and weirdly overindexed on examples rather than general principles. So fine, I still had something to teach them!

Coming to Epsilon Camp was also an emotional experience for me. When I was 15, I attended Canada/USA Mathcamp 1996, the first year that that camp operated. I might not have gone into research otherwise. Coming from a public high school—from the world of English teachers who mainly cared whether you adhered to the Five Paragraph Format, and chemistry teachers who’d give 0 on right answers if you didn’t write “1 mol / 1 mol” and then cross off both of the moles—I was suddenly thrust, sink or swim, into a course on elliptic curves taught by Ken Ribet, who’d played a major role in the proof of Fermat’s Last Theorem that had just been completed, and a talk on algorithms and complexity by Richard Karp himself, and lectures on number theory by Richard Guy, who had stories from when he knew G. H. Hardy.

Back when I was 15, I got to know George Rubin Thomas, the founding director of Mathcamp … and then, after 29 years, there he was again at Epsilon Camp—the patriarch of a whole ecosystem of math camps—and not only there, but sitting in on my course. Also at Epsilon Camp, unexpectedly, was a woman who I knew well back when we were undergrads at Cornell, both of took taking the theoretical computer science graduate sequence, but who I’d barely seen since. She, as it turned out, was accompanying her 8-year-old son, who got to know my 8-year-old. They played together every day and traded math facts.

It occurred to me that the course I taught, on theoretical computer science, was one of the most accessible I’ve ever done, and therefore more people might be interested. So I advertised on this blog for someone to help me LaTeX up the notes for wider distribution. I was thrilled to find a talented student to volunteer. Alas, because of where that student lives, he needs to stay anonymous for now. I thank him, pray for his safety, and hope to be able to reveal his name in the future. I’m also thrilled to have gotten three great high school students—Ian Ko, Tzak Lau, and Sunetra Rao—to help with the figures. Thanks to them as well.

You can read the notes here [59 pages, PDF]

If you’re curious, here’s the table of contents:

• Lecture 1: Bits
• Lecture 2: Gates
• Lecture 3: Finite Automata
• Lecture 4: Turing Machines
• Lecture 5: Big Numbers
• Lecture 6: Complexity, or Number of Operations
• Lecture 7: Polynomial vs. Exponential
• Lecture 8: The P vs. NP Problem
• Lecture 9: NP-completeness
• Lecture 10: Foundations of Cryptography
• Lecture 11: Public-Key Cryptography and Quantum Computing

Happy as always to receive comments and corrections. Enjoy!

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I’m on a spring break vacation-plus-lecture-tour with Dana and the kids in Mexico City this week, and wasn’t planning to blog, but I see that I need to make an exception. Charles Bennett and Gilles Brassard have won the Turing Award, for their seminal contributions to quantum computing and information including the BB84 quantum key distribution scheme. This is the first-ever Turing Award specifically for quantum stuff (though previous Turing Award winners, including Andy Yao, Leslie Valiant, and Avi Wigderson, have had quantum among their interests).

As a practical proposal, BB84 is already technologically feasible but has struggled to find an economic niche, in a world where conventional public-key encryption already solves much the same problem using only the standard Internet—and where, even after scalable quantum computers become able to break many of our current encryption schemes, post-quantum encryption (again running on the standard Internet) stands ready to replace those schemes. Nevertheless, as an idea, BB84 has already been transformative, playing a central role in the birth of quantum information science itself. Beyond BB84, Bennett and Brassard have made dozens of other major contributions to quantum information science, with a personal favorite of mine being the 1994 BBBV (Bennett Bernstein Brassard Vazirani) paper, which first established the limitations of quantum computers at solving unstructured search problems (and indeed, proved the optimality of Grover’s algorithm even before Grover’s algorithm had been discovered to exist).

While I take my kids to see Aztec artifacts, you can learn much more from Ben Brubaker’s Quanta article, to which I contributed without even knowing that it would be about Bennett and Brassard winning the Turing Award (info that was strictly embargoed before today). It’s an honor to have known Charlie and Gilles as well as I have for decades, and to have been able to celebrate one of their previous honors, the Wolf Prize, with them in Jerusalem. Huge congrats to two of the founders of our field!

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Scott’s foreword: I’ve known fellow quantum computing theorist Daniel Gottesman, now at the University of Maryland, for a quarter-century at this point. Daniel has been a friend, colleague, coauthor, and one of the people from whom I’ve learned the most in my career. Today he writes about a topic close to my heart, and one to which I’ve regularly lent this blog over the decades: namely, the struggle to protect enrichment and acceleration in the United States (in this case, the public magnet programs in Montgomery County, Maryland) from the constant attempts to weaken or dismantle them. Thanks so much to Daniel for doing this, and please help out if you can!

Without further ado, Daniel Gottesman:

Scott has kindly let me write this guest post because I’d like to ask the readers of Shtetl-Optimized for help.  I live in Montgomery County, Maryland, and the county is getting ready to replace our current handful of great magnet programs with a plethora of mediocre ones.

Montgomery County has a generally quite good school system, but its gifted education programs are really inadequate at the elementary and middle school level.  Montgomery County Public Schools (MCPS) offers nothing at all for gifted children until 4th grade.  Starting in 4th grade, magnet programs are available, but there are not enough spaces for everyone who meets the minimum qualifications.  A few years ago, the elementary and middle school magnets were switched to a lottery system, meaning the highest-achieving students, who most need special programming, might or might not get in, based purely on luck of the draw.

The remaining bright spot has been the high school magnets.  Montgomery County has two well-known and high-performing magnets, a STEM magnet at Montgomery Blair high school and an International Baccalaureate (IB) program at Richard Montgomery.  The Richard Montgomery IB program draws students from the whole county and the Blair Magnet draws from 2/3 of the county (with the remaining 1/3 eligible to go to another successful but less well-known magnet at Poolesville).  And these programs have so far resisted the lottery: They pick the best students from the application pool.

So with inadequate magnets in the lower grades and stellar magnets in high school, you can guess which one is up for a change.

MCPS now wants to reconfigure the high school magnet programs by splitting the county up into 6 regions.  Students will only be allowed to apply to programs in their home region.  Each region will have its own STEM magnet and its own IB program, as well as programs in the arts, medicine, and leadership.  And actually there are multiple program strands in each of these subjects, sometimes in different schools.  The whole plan is big and complicated, with close to 100 different programs around the county, more than half of them new.

The stated purpose of this plan is to expand access to these programs by admitting more students and reducing travel times to the programs.  And who could object to that?  There are definitely places in the county that are far from the current magnets and there are certainly more students that can benefit from high-quality magnets than there is currently space for.

The problem is that making high-quality magnets has not been a priority in the design process.  The last time MCPS tried adding regional magnets was about 7 years ago, when they added 3 regional IB programs while keeping Richard Montgomery available to students all over the county.  It was a failure: Test scores at the regional IB programs are far below those at Richard Montgomery (the worst-performing regional IB had only 24% getting a passing grade in even one subject in 2024, compared to 99% at Richard Montgomery) and all 3 are underenrolled.  Now MCPS has decided they can solve this problem by preventing students from going to Richard Montgomery to try to force them to go to the regional IBs.  In addition, they want to repeat the same mistakes with the STEM and other magnets.  The best programs in the county will shrink and only be accessible to a small fraction of students, leaving everyone else with new programs of likely highly-varying quality.

And if that were not enough, they want to do this revamp on a ridiculously short timeline.  The new programs are supposed to start in the 2027-8 school year, and between now and then, they need to recruit and train teachers for these 100 programs, create all the curricula for the first year of the programs (they are only planning to do one year at a time), and much much more.  The probability of a train wreck in the early years of the new system seems high.

Equity is certainly a concern driving this change.  And let me be clear: I am totally in favor of improving equity in the school system.  But I agree with Scott on this point: strong magnet programs in the public schools are pro-equity and weakening magnet programs is anti-equity.  Magnet programs are pro-equity even if the magnets are disproportionally populated by more affluent students, which is admittedly the case in MCPS: Affluent students will always have access to enrichment outside school and to private schools for the most affluent, whereas the public magnet programs are the only source of enrichment for those without those resources.

If MCPS really wants to address the difference in achievement between richer and poorer students, the way to do that is to create gifted programming starting from kindergarten.  If you wait until high school, it is unreasonable to expect even brilliant students to catch up to their also highly-capable peers who have been doing math and science camps and extracurriculars and contests and whatnot since they were little.  Some can manage it, but it is certainly not easy.  Unfortunately, MCPS’s notion of equity seems more focused on optimizing the demographic breakdown of magnet programs, which is most easily achieved by techniques which don’t improve — and usually degrade — the quality of the education provided.

So how can you help?  The Board of Education (BOE) is supposed to vote on this plan on Mar. 26.  Those of us opposed to it are hoping to sway enough members to vote to tell MCPS to investigate alternatives.  For instance, I have proposed a model with only 3 regions, which could also substantially improve access while preserving the strong existing magnets.

If you live in Montgomery County, write to BOE members telling them you oppose this change.  You can also sign a petition — there are many, but my favorite is here.

If you are an alumnus of one of the MCPS magnets, write to the BOE telling them how your education there was valuable to you and how a smaller program would not have served you as well.

If you are unconnected to Montgomery County, you can still spread the word.  If the BOE gets enough press inquiries asking about the many things that don’t add up in the MCPS proposal, perhaps they will recognize that this is a bad idea.

If you are really really interested in this topic and want to learn more: Last fall, I put together a long analysis of some of the flaws in MCPS’s plan and their claims, and of the alternative 3-region model.  You can find it here.

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To start on a somber note: those of us at UT Austin are in mourning this week for Savitha Shan, an undergrad double major here in economics and information systems, who was murdered over the weekend by an Islamist terrorist who started randomly shooting people on Sixth Street, apparently angry about the war in Iran. Two other innocents were also killed.

As it happens, these murders happened just a few hours after the end of my daughter’s bat mitzvah, and in walking distance from the venue. The bat mitzvah itself was an incredibly joyful and successful event that consumed most of my time lately, and which I might or might not say more about—the nastier the online trolls get, the more I need to think about my family’s privacy.

Of all the many quantum computing podcasts/interviews I’ve done recently, I’m probably happiest with this one, with Yuval Boger of QuEra. It covers all the main points about where the hardware currently is, the threat to public-key cryptography, my decades-long battle against quantum applications hype, etc. etc., and there’s even an AI-created transcript that eliminates my verbal infelicities!

A month ago, I blogged about “The Time I Didn’t Meet Jeffrey Epstein” (basically, because my mom warned me not to). Now the story has been written up in Science magazine, under the clickbaity headline “Meet Three Scientists Who Said No to Epstein.” (Besides yours truly, the other two scientists are friend-of-the-blog Sean Carroll, whose not-meeting-Epstein story I’d already heard directly from him, and David Agus, whose story I hadn’t heard.)

To be clear: as I explained in my post, I never actually said “no” to Epstein. Instead, based on my mom’s advice, I simply failed to follow up with his emissary, to the point where no meeting ever happened.

Anyway, ever since Science ran this story and it started making the rounds on social media, my mom has been getting congratulatory messages from friends of hers who saw it!

I’ve been a huge fan of the philosopher-novelist Rebecca Newberger Goldstein ever since I read her celebrated debut work, The Mind-Body Problem, back in 2005. Getting to know Rebecca and her husband, Steven Pinker, was a highlight of my last years at MIT. So I’m thrilled that Rebecca will be visiting UT Austin next week to give a talk on Spinoza, related to her latest book The Mattering Instinct (which I’m reading right now), and hosted by me and my colleague Galen Strawson in UT’s philosophy department. More info is in the poster below. If you’re in Austin, I hope to see you there!

The 88-year-old Donald Knuth has published a 5-page document about how Claude was able to solve a tricky graph theory problem that arose while he was working on the latest volume of The Art of Computer Programming—a series that Knuth is still writing after half a century. As you’d expect from Knuth, the document is almost entirely about the graph theory problem itself and Claude’s solution to it, eschewing broader questions about the nature of machine intelligence and how LLMs are changing life on Earth. To anyone who’s been following AI-for-math lately, the fact that Claude now can help with this sort of problem won’t come as a great shock. The virality is presumably because Knuth is such a legend that to watch him interact productively with an LLM is sort of like watching Leibniz, Babbage, or Turing do the same.

John Baez is a brilliant mathematical physicist and writer, who was blogging about science before the concept of “blogging” even existed, and from whom I’ve learned an enormous amount. But regarding John’s quest for the past 15 years — namely, to use category theory to help solve the climate crisis (!) — I always felt like the Cookie Monster would, with equal intellectual justification, say that the key to arresting climate change was for him to eat more Oreos. Then I read this Quanta article on the details of Baez’s project, and … uh … I confess it failed to change my view. Maybe someday I’ll understand why it’s better to say using category theory what I would’ve said in a 100x simpler way without category theory, but I fear that day is not today.

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I don’t have time to write a full post right now, but hopefully this is self-explanatory.

Regardless of their broader views on the AI industry, the eventual risks from AI, or American politics, right every person of conscience needs to stand behind Anthropic, as they stand up for their right to [checks notes] not be effectively nationalized by the Trump administration and forced to build murderbots and to help surveil American citizens. No, I wouldn’t have believed this either in a science-fiction movie, but it’s now just the straightforward reality of our world, years ahead of schedule. In particular, I call on all other AI companies, in the strongest possible terms, to do the right thing and stand behind Anthropic, in this make-or-break moment for the AI industry and the entire world.

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1. The STOC’2026 accepted papers list is out. It seems to me that there’s an emperor’s bounty of amazing stuff this year. I felt especially gratified to see the paper on the determination of BusyBeaver(5) on the list, reflecting a broad view of what theory of computing is about.
   
2. There’s a phenomenal profile of Henry Yuen in Quanta magazine. Henry is now one of the world leaders of quantum complexity theory, involved in breakthroughs like MIP*=RE and now pioneering the complexity theory of quantum states and unitary transformations (the main focus of this interview). I’m proud that Henry tells Quanta that learned about the field in 2007 or 2008 from a blog called … what was it again? … Shtetl-Optimized? I’m also proud that I got to help mentor Henry when he was a PhD student of my wife Dana Moshkovitz at MIT. Before I read this Quanta profile, I didn’t even know the backstory about Henry’s parents surviving and fleeing the Cambodian genocide, or about Henry growing up working in his parents’ restaurant. Henry never brought any of that up!
   
3. See Lance’s blog for an obituary of Joe Halpern, a pioneer of the branch of theoretical computer science that deals with reasoning about knowledge (e.g., the muddy children puzzle), who sadly passed away last week. I knew Prof. Halpern a bit when I was an undergrad at Cornell. He was a huge presence in the Cornell CS department who’ll be sorely missed.
   
4. UT Austin has announced the formation of a School of Computing, which will bring together the CS department (where I work) with statistics, data science, and several other departments. Many of UT’s peer institutions have recently done the same. Naturally, I’m excited for what this says about the expanded role of computing at UT going forward. We’ll be looking to hire even more new faculty than we were before!
   
5. When I glanced at the Chronicle of Higher Education to see what was new, I learned that researchers at OpenAI had proposed a technical solution, called “watermarking,” that might help tackle the crisis of students relying on AI to write all their papers … but that OpenAI had declined to deploy that solution. The piece strongly advocates a legislative mandate in favor of watermarking LLM outputs, and addresses some of the main counterarguments to that position.
   
6. For those who can’t get enough podcasts of me, here are the ones I’ve done recently. Quantum: Science vs. Mythology on the Peggy Smedley Show. AI Alignment, Complexity Theory, and the Computability of Physics, on Alexander Chin’s Philosophy Podcast. And last but not least, What Is Quantum Computing? on the Robinson Erhardt Podcast.
   
7. Also, here’s an article that quotes me entitled “Bitcoin needs a quantum upgrade. So why isn’t it happening?” Also, here’s a piece that interviews me in Investor’s Business Daily, entitled “Is quantum computing the next big tech shift?” (I have no say over these titles.)

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This is just a quick announcement that I’ll be hosting Nate Soares—who coauthored the self-explanatorily titled If Anyone Builds It, Everyone Dies with Eliezer Yudkowsky—tomorrow (Tuesday) at 5PM at UT Austin, for a brief talk followed by what I’m sure will be an extremely lively Q&A about his book. Anyone in the Austin area is welcome to join us.

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Friend-of-the-blog Salil Vadhan has asked me to share the following.

The Trevisan Award for Expository Work is a new SIGACT award created in memory of Luca Trevisan (1971-2024), with a nomination deadline of April 10, 2026.

The award is intended to promote and recognize high-impact work expositing ideas and results from the Theory of Computation. The exposition can have various target audiences, e.g. people in this field, people in adjacent or remote academic fields, as well as the general public. The form of exposition can vary, and can include books, surveys, lectures, course materials, video, audio (e.g. podcasts), blogs and other media products. The award may be given to a single piece of work or a series produced over time. The award may be given to an individual, or a small group who together produced this expository work.

The awardee will receive USD$2000 (to be divided among the awardees if multiple), as well as travel support if needed to attend STOC, where the award will be presented. STOC’2026 is June 22-26 in Salt Lake City, Utah.

The endowment for this prize was initiated by a gift from Avi Wigderson, drawing on his Turing Award, and has been subsequently augmented by other individuals.

For more details see here.

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