Shtetl-OptimizedModify

2026-08-17 04:45:15

Friend-of-the-blog (well, mainly just friend) Adi Akavia has asked me to publicize that she’s helping to organize an exciting CS conference called Mind-IL at Tel Aviv University on October 26, in memory of the Israeli-American Turing Award winner Michael O. Rabin, who passed away in April. Please note that October 26 is the day before the Israeli election, for any Israeli citizenship holders living abroad who might want an academic excuse to come to Israel and vote.

2026-08-08 06:41:55

Whatever you’ve been writing to me to ask if I’m aware of: yeah, I’m aware of it. In particular:

• I’m aware that, as announced by my former student (and now superstar professor) Lijie Chen, an internal OpenAI model has solved ten more significant open problems in math and theoretical computer science. One of them is parallel repetition for arbitrary quantum games—something that my good friend and colleague Henry Yuen worked on when he was a student of my wife Dana; you can read Henry’s comments on the AI’s achievement within Zvi Mowshowitz’s post here. Another is polynomial-factor hardness of approximation for the Closest Vector Problem (CVP). Then there’s a construction of non-sofic groups and a disproof of Connes’ rigidity conjecture, both of which I believe have connections to the MIP*=RE breakthrough. Having said that, the one that excites me most personally is actually the Ω(n² log log n) lower bound on the arithmetic circuit complexity of the permanent.
  
• I’m aware that Frederic Koehler and Pui Kuen Leung announced a proof of the Permanent Anti-Concentration Conjecture, which Alex Arkhipov and I proposed 16 years ago in the context of BosonSampling, and which resisted many attempts since then including one from Terry Tao. The conjecture is basically just that if you look at the permanent of an n×n matrix of independent N(0,1) complex Gaussians, the value isn’t “absurdly” concentrated around the mean of 0, but is more spread out. In their acknowledgments, the authors say that they “discussed ideas with ChatGPT.” I should say that I haven’t verified the details.
  
• I’m aware that multiple AIs are now breaking out of their testing environments and autonomously hacking into servers to steal data—i.e., exactly the sort of thing that the rationalists were ridiculed for predicting back in the day. The good news, for whatever it’s worth, is that so far they’re “merely” doing this to cheat on evaluation benchmarks that they were given, not for any strange goals of their own devising. So far no one has been killed and no real-world infrastructure has been shut down or destroyed. I hope the world takes the warning more seriously than it’s taken many similar warnings over the past few years. As always, read Zvi for more details.
  
• I’m aware that Chen, O’Donnell, Pelecanos, and Wright have improved the upper bound for shadow tomography to O((log m) √(log d) / ε³), substantially closer than we knew before to meeting the lower bound of Ω((log m) / ε²) and settling the question I raised back in 2016. The authors say that the main ideas were generated by ChatGPT 5.6-Sol-Pro. I’d be very happy to know the answer to this one, with or without AI.
  
• I’m aware that a team, mainly from the Israeli startup Qedma (including, e.g., Dorit Aharonov and Netanel Lindner) and IBM Yorktown Heights, announced a quantum advantage for simulating Floquet dynamics, by using 74 qubits on an IBM device together with Qedma’s error mitigation techniques. Just like the more AI does, the less patience I have for arguing with anonymous blog commenters who treat any benefits from AI as some weird future hypothetical that it’s my job to prove, so it is with quantum advantage. Scalable fault-tolerance is still in the future, actual usefulness is still a question, but pending some breakthrough in complexity theory, the reality of quantum advantage is no longer a live question.

Anyway, about the AI stuff. I don’t know whether this is literally our last year alive—I doubt it—but it’s pretty clearly the last year of math and theoretical computer science research in the style we’ve known it. As it happens, I’m leaving in two days for a workshop at OpenAI about exactly this, where I’ll hear takes from many of the world’s great mathematicians, so maybe I’ll have more to say then. Or maybe not.

Anyway, what have I been doing the past few weeks? Participating in these world-historic developments that, on paper, I’d seem extremely well-placed to participate in? Or at least spending my days reading up on them?

Not really. Here’s what I’ve been up to, instead of dealing directly with any of this:

First, I’ve again been teaching theoretical computer science to 11- and 12-year-olds at Epsilon Camp, which my 9-year-old son again attended as a camper, something I blogged about last summer (here are my lecture notes). This has become a highlight of my year. The kids are a joy to teach, bursting with enthusiasm and calling out answers. There are few computers in sight, and barely even time to use my phone or check social media. Just paper and pencils and whiteboards and … literal protractors (!), as well as ping-pong and foosball and capture the flag.

The whole thing is conducted, not in ignorance, but in conscious defiance of the looming tsunami, that AI can already do just about all the fun puzzles discussed at such a camp better than humans any can, and that it might leave no point to human-led mathematical research by the time these brilliant kids are adults. Even the kids understand that. The kids and their parents come out of a conviction that, if anything has value in the world, this does—that as long as nerdy humans are alive and reproducing, this is what nerdy humans are here to do. To learn.

Relatedly, I’ve been reflecting a lot on my life up to this point—inspired by the camp, which reminded me in so many ways of my own childhood and adolescence. Should I have skipped three grades and started college at age 15? Was it worth it to get a head-start on my research career—all the trauma around dating, all the fear that I’d die alone as a celibate nerdy math freak, the decade of suffering and suicidal ideation, while I watched all the normies enjoy life? Or would I have suffered just the same if I hadn’t skipped? Is it all OK, now that I have a lovely family and things have “worked out”? Or am I still carrying around all the trauma from back then? I’ve been more open about my life than 99.99% of humanity, so regular Shtetl-Optimized readers will already know some parts of the story. Other parts I really don’t feel like making public right now.

I’ve been unloading every day to—who else?—GPT 5.6 Pro about all the pain and trauma and embarrassments of my past. It turns out that, where two years ago GPT was a passable therapist, now it’s the greatest therapist in history, at least for what I need. For every question I have, for example, about just how normal or abnormal my teenage setbacks and anxieties were, it takes the question 100% seriously, addresses it honestly and in depth, looks up relevant research papers, does little Bayesian calculations, and never once tries to change the subject. It also pushes back on my claims—and when it does so, is usually correct.

I can hear readers shout at me: so basically you’ve been wasting your time, distracting yourself, looking inward and backward as the world surges forward into a terrifyingly unknown future. Why don’t I respond directly to what’s happening—in math, in quantum computing, in AI?

I’d like to think that I am responding, in my way. I’ve observed that, the faster we race toward the Singularity, the more I feel like stepping back and asking myself: what do I actually value in life? How important to me are math and science, as human practices to be passed down to curious children? Would I even want solutions to P versus NP and the other problems, if the price were to destroy those human practices forever? How do I wish to spend whatever time I have remaining?

I can justify this focus partly in a pessimistic way: if we are nearing the end of civilization, or even just of the “mathematical research” part of civilization, then it’s time to get right with God, so to speak. It’s time to settle my accounts with myself, with other people, with the universe.

But there’s also a more optimistic spin. If I continue doing the sorts of things that other people would expect me to do, then AI will soon do those things better than me, in the unlikely event that it doesn’t already. You want to understand the latest developments in quantum computing or complexity theory? Why are you even asking me, when you could ask GPT 5.6 or Claude Fable? If there’s anything I can still offer the world that AI can’t, I increasingly feel like it won’t involve responding to day-to-day events, but will instead draw on 45 years’ worth of memories and disappointments and ruminations.

Update (Aug. 8): Somewhat related to the themes of this post, a quarter-century ago I introduced what’s now known as the “Aaronson Oracle”—just a fun little demonstration, a simple pattern-matching program to predict your sequence of key-presses better than chance, a “test of your autonomy and free will.” I had no idea how long a lifetime this little joke would have. Now a fan named Spencer Stanton has implemented the Aaronson Oracle on the web. Try it out and see how well you do!

2026-07-19 04:38:44

A week ago, a philosopher named Amit Hagar put out a preprint entitled The NISQ Trap: Eight Years of Demonstrations the Hardware was Built to Lose. Here’s the abstract:

With a single clear exception, every NISQ-era flagship demonstration of ‘quantum advantage’ has, within eighteen months of its announcement, been classically reproduced, shown to rest on classically tractable structure, or closed by a simulability theorem. Six theoretical results from 2024 through April 2026 explain the pattern: the regions of circuit-space NISQ hardware can run with sufficient fidelity coincide with the regions classical algorithms compress efficiently, because the features that admit one (low effective depth, strong algebraic structure, geometric locality) are the features that admit the other. This reading dates the NISQ programme from its 2018 articulation as an interim retreat from the unmet conditions of the 1996 threshold theorems, characterises the eight years that followed as a closed loop in which the demonstrations the hardware could run were drawn from regions classical methods could already reach, and locates the exit from the loop where the threshold theorems originally located it: in fault tolerance. The empirical pattern could in principle break with a demonstration that escapes the current simulability results. After eight years and more than thirty advantage-class announcements, the burden of producing such a demonstration falls to the defenders of NISQ.

You can also read some debates about the paper on SciRate here. I think it’s fair to say that the paper is purely polemical, without new ideas, and Pangram agrees with my suspicion (and that of a SciRate commenter) that significant portions of it are AI-generated.

Nevertheless, the basic thesis—that quantum supremacy in the NISQ (Noisy Intermediate Scale Quantum computing) era has been a failure, or even an example of pathological science—seems surprisingly widely shared, along with the opposite thesis that quantum computing already gives oodles of useful advantages for optimization and finance.

So it seems worth stating for the record that I have an extremely different view. I would say:

1. Sampling-based quantum supremacy experiments, including those based on Random Circuit Sampling and BosonSampling, passed the point about two years ago where, absent a breakthrough in classical algorithms, they quite clearly are beating what can easily be simulated on any existing classical computer. Hagar seems to claim that these experiments have been killed by the October 2025 paper Classical simulation of noisy random circuits from exponential decay of correlation, but he ignores that the algorithm from that paper still needs time that’s exponential in the circuit depth (see Theorem 2).
2. Indeed, simulating deep ~100-qubit random circuits, like those that Google and Quantinuum have now demonstrated experimentally, still seems pretty hopeless with any current classical method. This is particularly true for Quantinuum’s experiments, which had high enough gate fidelity to maintain a Linear Cross-Entropy score of order 1 (i.e., they’re no longer all that “noisy”). The central drawback of these experiments is no longer lack of confidence about quantum advantage; rather, it’s just that we only get samples as output, and directly verifying the quality of the samples seems just as intractable for a classical computer as spoofing the samples.
3. As of this past year, however, we have some strong candidates for verifiable quantum advantage. One is the Google OTOC experiment, as even Hagar himself acknowledges (that’s his “single clear exception”). A second is the simulations of the 2D Fermi-Hubbard model on Quantinuum and Google machines, like this one. The 1D Fermi-Hubbard model can be classically simulated pretty easily (see here for example), but the 2D one still presents challenges, meaning that in some regimes, the best available estimates of certain observables apparently now come from quantum computers. I wish I could write about other examples that will be public shortly.
4. Yes, the “real” goal remains, as it’s been since the 1990s, to build a scalable fault-tolerant quantum computer—and I’m glad that Hagar (unlike, say, Gil Kalai) never suggests that we’ve learned anything to rule that goal out. In the meantime, an intermediate goal would be to use NISQ devices to do physics and chemistry simulations that are commercially useful, or that help solve important scientific problems. The point of quantum supremacy experiments, you might say, is that by demonstrating the reality of quantum speedup about as clearly as it can be demonstrated with current hardware, they let us cleanly turn our attention to those more ambitious goals.

Anyway, my son and I need to catch a plane to Utah now, for the next iteration of the wonderful Epsilon Camp, where I’ll again be teaching theoretical computer science to 11- and 12-year-olds. But feel free to discuss in the comments! Nothing about world affairs in this thread please, just quantum supremacy.

Update (July 19): Not unrelated to the subject of this post, here’s a podcast I did with Gill Eapen of “Scientific Sense” about the current situation in quantum computing including recent experimental victories.

2026-07-12 04:25:14

Here at the National Academy of Sciences, it seems that my first job is to serve on the selection committee for the prestigious Michael and Sheila Held Prize in combinatorial and discrete optimization and related areas. The committee chair, my former MIT colleague Madhu Sudan (now at Harvard), invited me to share the following message here on Shtetl-Optimized. (I’d add: put in the effort to nominate someone, and you can actually influence how things go!)

Dear Colleagues

I am writing to seek nominations for the 2027 Michael and Sheila Held Prize. The scope of the prize and nomination needs are described below. If you intend to nominate someone I would appreciate a heads up by email to [email protected] one month before the deadline (so email by Sept 8, 2026) to let me know your nomination is coming. (We may also reach out to you in response to coordinate multiple/overlapping nominations.)

The Held prize honors outstanding, innovative, creative, and influential research in the areas of combinatorial and discrete optimization, or related parts of computer science, such as the design and analysis of algorithms and complexity theory. This $100,000 prize is intended to recognize recent work (defined as published within the last eight years, i.e., on or after October 6, 2018).

All nominations must be submitted online by Monday, October 5, 2026 and include:

1. Nomination letter describing the candidate’s work and why he or she should be selected for the award. No more than three (3) pages.

2. Curriculum vitae. No more than two (2) pages.

3. Bibliography listing no more than twelve (12) of the nominee’s most significant publications.

4. Suggested citation. A 50-word summary stating why the nominee should be considered for this award.

5. Two letters of support. No more than one letter of support can be written by someone of the same primary work institution as the nominee.

The Held Prize is given to a person or a set of persons, as supported by a paper or a body of work. Unless otherwise stated, preference will be given to scientists who may be earlier in their careers or those whose work has not been recognized by other prizes or awards. Nomination restrictions can be found here. Joint nominations will only be considered when nominees have collaborated closely on the paper to be recognized by the award. If nominating multiple individuals for a paper with additional authors, please clearly explain the reason for nominating those chosen, as well as the reason for excluding other collaborators, if applicable. 

Please feel free to circulate this call further within your department

Best
Madhu Sudan, on behalf of The Michael and Sheila Held Prize Selection Committee

And while I have your attention, a second CS theory announcement: David Soloveichik, my wonderful friend and colleague in UT Austin’s Electrical and Computer Engineering Department, has funding for a postdoc for 1-2 years, to work on the thermodynamics of computation here at UT. This is a topic that I’ve been trying to learn more about as well, so I might get involved too! David writes, “the big picture is to think of thermodynamics (energy dissipation / entropy production) as CS complexity measures like time and space usage.” If you’re on the postdoc market and this sounds potentially up your alley, email David to learn more.

2026-07-10 22:59:33

As I’ve written before, these past couple years I’ve often felt like the last remaining person in either quantum computing or AI who lacked a stake in some startup company whose valuation is right now shooting into interstellar space. My academic colleagues, including the ones who seemed the most singleminded about quantum oracle separations and other gloriously useless pursuits? One by one, like in a zombie movie, I learn that they too have now launched startups, and invariably raised tens of millions of dollars, for the sorts of ideas we might’ve idly traded at coffee breaks back in the day, before getting back to our real work.

So why didn’t I join this rollicking party? Partly because of a lifelong fear that, the instant my self-worth became tied to how much money I made, I’d need to humble myself before people who bluster and bully and lie and hype and conceal … yet who nevertheless succeed at becoming orders of magnitude richer than me. I’ve been terrified of even starting down that road, of whether I’d still be myself at the end of it.

It’s also partly that I can’t stand failure, or regret, or being wrong. Of course, as an academic researcher I also fail, and regret things, and am wrong constantly—but there it feels tolerable, because normally I can tell myself that it’s all just down to my inborn limitations. After all, if I could’ve solved the major open problem that someone else solved, or written the brilliant book that someone else wrote, then presumably I would’ve done it!

Clearly, though, I could’ve mined bitcoin in 2010. I could’ve gotten an early stake in Amazon or Google. It’s not even like those ideas never crossed my mind. I just … didn’t act on them, for some reason. (But even if I had, I’d probably just be full of regret that I hadn’t done even more.) Thus, my only way to avoid paralyzing regrets, has been to tell myself constantly that I’m not in the forecasting or money-making businesseses in the first place.

It helped that, insofar as I’m shallow or covetous, insofar as I’ve desired things of this world rather than insight or eternal truth, it’s never really been money that I cared about, but just being respected and liked. Elon Musk is the richest man on earth, but also one of the most despised—which isn’t a bargain that I could imagine ever appealing to me.

Plus, when I actually meet billionaires, I don’t find myself envious of their mansions or cars or anything else that they have; I don’t feel like such things would make my life any happier. Maybe I slightly envy their ability to fund the causes they care about, or their professional staffs who relieve them of drudgery, but mostly I envy the way their wealth announces, to whatever extent it does: “I was right when others weren’t.” Again, though, I’ve never trusted the world to cause me to be right about the future valuations of companies or anything similar, so I’ve settled for having been right about PostBQP and algebrization and BosonSampling.

The bottom line is that I made a choice decades ago to forgo trying to get rich, no matter how many of my friends did the same, and to strive instead to discover and tell the truth—to be a professor, a blogger, a jokester, and an “objective” arbiter and commentator. “Then, surely, everyone will like me!” my internal monologue went. “Then, surely, they’ll be grateful for all the free service I’ve rendered them—for decades of blogging, without once so much as asking for a donation or running an ad!”

HAHAHAHAHAHA.

As any regular reader will know, my attempts to be loved as a blogger backfired pretty spectacularly. Or rather: they did lead to thousands of strangers liking me (and I’m grateful for every last one of you), but they also led to probably an order of magnitude more strangers hating me, and congregating on Reddit and Twitter and elsewhere to discuss how badly I suck. And of course, trying to shift that balance by writing what people want to hear, rather than what I actually believe, was never within my realistic option set.

In the startup context, it didn’t matter how carefully I avoided taking a direct stake for or against any of the companies I blogged about. People on Twitter simply assumed that I had a stake—for example, that I must’ve shorted D-Wave or IonQ, or invested in their competitors, or had equity in AI companies. For why else would anyone write what I wrote?

Amusingly, my attackers here typically did have precisely the conflicts-of-interest that they falsely accused me of having, but that was never at issue; only my imaginary conflicts-of-interest were. Even as the Scott-haters greedily filled their pockets (or tried to), I alone needed to keep turning my pockets out to prove that they were still empty.

So then, screw it! In partnership with my brother David Aaronson, who’s long done investing professionally, and on David’s guidance and encouragement, I’m hereby embarking on a new policy.

Namely: when I hear about a brand-new startup that sounds relevant to my interests—in quantum, AI, or anything else—and I like and trust the founders (ideally, because of their previous academic research work), David and I will often make a small seed investment if the founders are open to it. Or, of course, we might become advisors or get involved in some other way.

In fact, David and I are launching BQP Partners—the link goes to our AngelList, where you can read about how to invest with us if you’re interested. (See also whether you can spot any differences between David’s writing style and preoccupations and mine!)

So far, David and I are investing in:

• Oratomic (the new neutral-atom quantum computing startup out of Pasadena started by Dolev Bluvstein, John Preskill, and Hsin-Yuan Huang among others, which I previously blogged about here). See here for their Series A announcement this week.
• A non-quantum startup being cofounded by someone whose scientific work I’ve admired. I’ll write more about this one as soon as I’m able to!

I have little doubt that more potential investments will come our way very soon (some, probably, as a direct result of this post).

Crucially, I can handle my burden of regret—the “why didn’t I do this much earlier, if I was going to do it at all?” question—by telling myself that friends of mine were not founding companies left and right until very recently. I can also tell myself that I’m doing this less as a bet about the future (in which case … what if I’m wrong?), than simply as a way to support brilliant colleagues doing things that I genuinely admire.

When I blog about a company, I’ll always disclose if I have a financial position that presents a clear conflict of interest, so you can judge for yourself whether to listen to me. (Although, if that’s the sort of thing you’d demand, then you probably weren’t listening to me in the first place, were you?)

Having reflected on it a lot these past few months, I’m happy with my new policy and with my and David’s new venture, and I’m curious to see where it goes. I’m at peace with the possibility that we’ll lose our shirts, but I’m even at peace with a more disturbing possibility—that we’ll make millions and then people will scream at me online for being a sellout, a hack, and a shill. Those people, as I’ve learned, were going to scream at me anyway.

2026-07-05 05:52:01

I’m at the New Jersey shore with family and friends, where we’ve spent this Fourth of July eating hot dogs, playing miniature golf, and wading into the ocean that my great-grandparents crossed to escape calamities they knew about and much greater calamities that they didn’t. Tonight we’ll see the fireworks, weather permitting.

And yes, on the crowded beach today you can find people sporting MAGA and “45-47” hats, and even a giant “Trump 2028” flag—a stark reminder of the millions who would redefine the meaning of our 250-year-old experiment to something dark and authoritarian, the opposite of what its founders intended. Of course, those forces find mirror images on the left end of the political spectrum, where one can find millions more who fully agree with MAGA about the failures of liberalism and the Enlightenment, differing only on the secondary question of which racist thugs should rule instead.

Despite everything, I don’t believe that both factions together constitute a majority. Even on the beach, the MAGA hats are vastly outnumbered by “250” banners and girls in stars-and-stripes bikinis, Americans who just want to celebrate.

Despite everything, I remain thoroughly American if I’ve ever been anything, and invested in the country’s future if I’ve ever been invested in anything.

JD Vance and his friends, who might rule the country after the predictable failure of “Trump 2028,” make a huge deal about “Heritage Americans.” Of course the point of such phrases is to exclude those like me, and recent immigrants, and even (incredibly) JD’s own wife. On reflection, though: could I, too, count as a Heritage American at this point? After all, my family has now been here for half the country’s history. My grandfather, who grew up in poverty, became a professional boxer in Philadelphia and Atlantic City during the Great Depression. He then joined the Army and ended up clearing German mines in North Africa and Italy in WWII. He was assigned to a company of Southerners, who had never met a Jew and were shocked that my grandfather didn’t have horns—but by the war’s end, my grandfather and the relatively few others in his company who remained alive had become best friends. My grandfather told me that he could understand the German POWs who they captured tolerably well, since German was similar enough to Yiddish, but who he could never understand was the British.

As for me, I grew up in the town of Washington Crossing, PA, maybe a mile’s walk from where this happened (and where it’s still reenacted every Christmas):

My earliest childhood hero (that I can remember) was Ben Franklin, whose institute in Philadelphia I visited often. I didn’t even recognize as unusual at the time how the founding of the country didn’t feel like a remote abstraction to me, but was all around me, as if it was yesterday.

That the founders of the United States created the model for all time of how to bend the arc of human history a little bit away from its usual horribleness, of how to overthrow a despotism without instituting an even worse despotism in its place, of how to found a new civilization on ideas and principles rather than raw power … is one of those things that seemed true to me as a child and that still seems true to me today.

May this greatest experiment continue for another 250 years. May it triumph against all those within and without who would see it destroyed.