The NP genie

December 11th, 2018

Hi from the Q2B conference!

Every nerd has surely considered the scenario where an all-knowing genie—or an enlightened guru, or a superintelligent AI, or God—appears and offers to answer any question of your choice.  (Possibly subject to restrictions on the length or complexity of the question, to prevent glomming together every imaginable question.)  What do you ask?

(Standard joke: “What question should I ask, oh wise master, and what is its answer?”  “The question you should ask me is the one you just asked, and its answer is the one I am giving.”)

The other day, it occurred to me that theoretical computer science offers a systematic way to generate interesting variations on the genie scenario, which have been contemplated less—variations where the genie is no longer omniscient, but “merely” more scient than any entity that humankind has ever seen.  One simple example, which I gather is often discussed in the AI-risk and rationality communities, is an oracle for the halting problem: what computer program can you write, such that knowing whether it halts would provide the most useful information to civilization?  Can you solve global warming with such an oracle?  Cure cancer?

But there are many other examples.  Here’s one: suppose what pops out of your lamp is a genie for NP questions.  Here I don’t mean NP in the technical sense (that would just be a pared-down version of the halting genie discussed above), but in the human sense.  The genie can only answer questions by pointing you to ordinary evidence that, once you know where to find it, makes the answer to the question clear to every competent person who examines the evidence, with no further need to trust the genie.  Or, of course, the genie could fail to provide such evidence, which itself provides the valuable information that there’s no such evidence out there.

More-or-less equivalently (because of binary search), the genie could do what my parents used to do when my brother and I searched the house for Hanukkah presents, and give us “hotter” or “colder” hints as we searched for the evidence ourselves.

To make things concrete, let’s assume that the NP genie will only provide answers of 1000 characters or fewer, in plain English text with no fancy encodings.  Here are the candidates for NP questions that I came up with after about 20 seconds of contemplation:

  • Which pieces of physics beyond the Standard Model and general relativity can be experimentally confirmed with the technology of 2018? What are the experiments we need to do?
  • What’s the current location of the Ark of the Covenant, or its remains, if any still exist?  (Similar: where can we dig to find physical records, if any exist, pertaining to the Exodus from Egypt, or to Jesus of Nazareth?)
  • What’s a sketch of a resolution of P vs. NP, from which experts would stand a good chance of filling in the details?  (Similar for other any famous unsolved math problem.)
  • Where, if anywhere, can we point radio telescopes to get irrefutable evidence for the existence of extraterrestrial life?
  • What happened to Malaysia Flight 370, and where are the remains by which it could be verified?  (Similar for Amelia Earhart.)
  • Where, if anywhere, can we find intact DNA of non-avian dinosaurs?

Which NP questions would you ask the genie?  And what other complexity-theoretic genies would be interesting to consider?  (I thought briefly about a ⊕P genie, but I’m guessing that the yearning to know whether the number of sand grains in the Sahara is even or odd is limited.)


Update: I just read Lenny Susskind’s Y Combinator interview, and found it delightful—pure Lenny, and covering tons of ground that should interest anyone who reads this blog.

Airport idiocy

November 28th, 2018

On Sunday, I returned to Austin with Dana and the kids from Thanksgiving in Pennsylvania.  The good news is that I didn’t get arrested this time, didn’t mistake any tips for change, and didn’t even miss the flight!  But I did experience two airports that changed decisively for the worse.

In Newark Terminal C—i.e., one of the most important terminals of one of the most important airports in the world—there’s now a gigantic wing without a single restaurant or concession stand that, quickly and for a sane price, serves the sort of food that a child (say) might plausibly want to eat.  No fast food, not even an Asian place with rice and teriyaki to go.  Just one upscale eatery after the next, with complicated artisanal foods at brain-exploding prices, and—crucially—“servers” who won’t even acknowledge or make eye contact with the customers, because you have to do everything through a digital ordering system that gives you no idea how long the food might take to be ready, and whether your flight is going to board first.  The experience was like waking up in some sci-fi dystopia, where all the people have been removed from a familiar environment and replaced with glassy-eyed cyborgs.  And had we not thought to pack a few snacks with us, our kids would’ve starved.

Based on this and other recent experiences, I propose the following principle: if a customer’s digitally-mediated order to your company is eventually going to need to get processed by a human being anyhow—a fallible human who could screw things up—and if you’re less competent at designing user interfaces than Amazon (which means: anyone other than Amazon), then you must make it easy for the customer to talk to one of the humans behind the curtain.  Besides making the customer happy, such a policy is good business, since when you do screw things up due to miscommunications caused by poor user interfaces—and you will—it will be on you to fix things anyway, which will eat into your profit margin.  To take another example, besides Newark Terminal C, all these comments apply with 3000% force to the delivery service DoorDash.

Returning to airports, though: whichever geniuses ruined Terminal C at Newark are amateurs compared to those in my adopted home city of Austin.  Austin-Bergstrom International Airport (ABIA) chose Thanksgiving break—i.e., the busiest travel time of the year—to roll out a universally despised redesign where you now need to journey for an extra 5-10 minutes (or 15 with screaming kids in tow), up and down elevators and across three parking lots, to reach the place where taxis and Ubers are.  The previous system was that you simply walked out of the terminal, crossed one street, and the line of taxis was there.

Supposedly this is to “reduce congestion” … except that, compared to other airports, ABIA never had any significant congestion caused by taxis.  I’d typically be the only person walking to them at a given time, or I’d join a line of just 3 or 4 people.  Nor does this do anything for the environment, since the city of Austin has no magical alternative, no subway or monorail to whisk you from the airport to downtown.  Just as many people will need a taxi or Uber as before; the only difference is that they’ll need to go ten times further out of their way as they’d need to go at a ten times busier airport.  For new visitors, this means their first experience of Austin will be one of confusion and anger; for Austin residents who fly a few times per month, it means that days or weeks have been erased from their lives.  From the conversations I’ve had so far, it appears that every single passenger of ABIA, and every single taxi and Uber driver, is livid about the change.  With one boneheaded decision, ABIA singlehandedly made Austin a less attractive place to live and work.

Postscript I.  But if you’re a prospective grad student, postdoc, or faculty member, you should still come to UT!  The death of reason, and the triumph of the blank-faced bureaucrats, is a worldwide problem, not something in any way unique to Austin.

Postscript II.  No, I don’t harbor any illusions that posts like this, or anything else I can realistically say or do, will change anything for the better, at my local airport let alone in the wider world.  Indeed, I sometimes wonder whether, for the bureaucrats, the point of ruining facilities and services that thousands rely on is precisely to grind down people’s sense of autonomy, to make them realize the futility of argument and protest.  Even so, if someone responsible for the doofus decisions in question happened to come across this post, and if they felt even the tiniest twinge of fear or guilt, felt like their victory over common sense wouldn’t be quite as easy or painless as they’d hoped—well, that would be reason enough for the post.

Teaching quantum in junior high: special Thanksgiving guest post by Terry Rudolph

November 22nd, 2018

Happy Thanksgiving!

People have sometimes asked me: “how do you do it?  how do you do your research, write papers, teach classes, mentor grad students, build up the quantum center at UT, travel and give talks every week or two, serve on program committees, raise two rambunctious young kids, and also blog and also participate in the comments and also get depressed about people saying mean things on social media?”  The answer is that increasingly I don’t.  Something has to give, and this semester, alas, that something has often been blogging.

And that’s why, today, I’m delighted to have a special guest post by my good friend Terry Rudolph.  Terry, who happens to be Erwin Schrödinger’s grandson, has done lots of fascinating work over the years in quantum computing and the foundations of quantum mechanics, and previously came up on this blog in the context of the PBR (Pusey-Barrett-Rudolph) Theorem.  Today, he’s a cofounder and chief architect at PsiQuantum, a startup in Palo Alto that’s trying to build silicon-photonic quantum computers.

Terry’s guest post is about the prospects for teaching quantum theory at the junior high school level—something he thought about a lot in the context of writing his interesting recent book Q is for Quantum.  I should stress that the opinions in this post are Terry’s, and don’t necessarily reflect the official editorial positions of Shtetl-Optimized.  Personally, I have taught the basics of quantum information to sharp junior high and high school students, so I certainly know that it’s possible.  (By undergrad, it’s not only possible, but maybe should become standard for both physics and CS majors.)  But I would also say that, given the current state of junior high and high school education in the US, it would be a huge step up if most students graduated fully understanding what’s a probability, what’s a classical bit, what’s a complex number, and any of dozens of other topics that feed into quantum information—so why not start by teaching the simpler stuff well?  And also, if students don’t learn the rules of classical probability first, then how will they be properly shocked when they come to quantum? 🙂

But without further ado, here’s Terry—who’s also graciously agreed to stick around and answer some comments.


Can we/should we teach Quantum Theory in Junior High?

by Terry Rudolph

Should we?

Reasons which suggest the answer is “yes” include:

Economic: We are apparently into a labor market shortage in quantum engineers.  We should not, however, need the recent hype around quantum computing to make the economic case – the frontier of many disparate regions of the modern science and technology landscape is quantum.  Surely if students do decide to drop out of school at 16 they should at least be equipped to get an entry-level job as a quantum physicist?

Educational: If young peoples’ first exposures to science are counterintuitive and “cutting edge,” it could help excite them into STEM.  The strong modern quantum information theoretic connections between quantum physics, computer science and math can help all three subjects constructively generate common interest.

Pseudo-Philosophical: Perhaps our issues with understanding/accepting quantum theory are because we come to it late and have lost the mental plasticity for a “quantum reset” of our brain when we eventually require it late in an undergraduate degree.  It may be easier to achieve fluency in the “language of quantum” with early exposure.

Can we?

There are two distinct aspects to this question: Firstly, is it possible at the level of “fitting it in” – training teachers, adjusting curricula and so on?  Secondly, can a nontrivial, worthwhile fraction of quantum theory even be taught at all to pre-calculus students?

With regards to the first question, as the child of two schoolteachers I am very aware that an academic advocating for such disruption will not be viewed kindly by all.  As I don’t have relevant experience to say anything useful about this aspect, I have to leave it for others to consider.

Let me focus for the remainder of this post on the second aspect, namely whether it is even possible to appropriately simplify the content of the theory.  This month it is exactly 20 years since I lectured the first of many varied quantum courses I have taught at multiple universities. For most of that period I would have said it simply wasn’t possible to teach any but the most precocious of high school students nontrivial technical content of quantum theory – despite some brave attempts like Feynman’s use of arrows in QED: The Strange Theory of Light and Matter (a technique that cannot easily get at the mysteries of two-particle quantum theory, which is where the fun really starts).  I now believe, however, that it is actually possible.

A pedagogical method covering nontrivial quantum theory using only basic arithmetic

My experience talking about quantum theory to 12-15 year olds has only been in the idealized setting of spending a few hours with them at science fairs, camps and similar.  In fact it was on the way to a math camp for very young students, desperately trying to plan something non-trivial to engage them with, that I came up with a pedagogical method which I (and a few colleagues) have found does work.

I eventually wrote the method into a short book Q is for Quantum, but if you don’t want to purchase the book then here is a pdf of Part I,, which takes a student knowing only the rules of basic arithmetic through to learning enough quantum computing they can understand the Deutsch–Jozsa algorithm.  In fact not only can they do a calculation to see how it works in detail, they can appreciate conceptual nuances often under-appreciated in popular expositions, such as why gate speed doesn’t matter – it’s all about the number of steps, why classical computing also can have exponential growth in “possible states” so interference is critical, why quantum computers do not compute the uncomputable and so on.

Before pointing out a few features of the approach, here are some rules I set myself while writing the book:

  • No analogies, no jargon – if it can’t be explained quantitatively then leave it out.
  • No math more than basic arithmetic and distribution across brackets.
  • Keep clear the distinction between mathematical objects and the observed physical events they are describing.
  • Be interpretationally neutral.
  • No soap opera: Motivate by intriguing with science, not by regurgitating quasi-mythological stories about the founders of the theory.
  • No using the word “quantum” in the main text! This was partly to amuse myself, but I also thought if I was succeeding in the other points then I should be able to avoid a word almost synonymous with “hard and mysterious.”

One of the main issues to confront is how to represent and explain superposition.  It is typical in popular expositions to draw analogies between a superposition of, say, a cat which is dead and a cat which is alive by saying it is dead “and” alive.  But if superposition was equivalent to logical “and”, or, for that matter, logical “or”, then quantum computing wouldn’t be interesting, and in this and other ways the analogy is ultimately misleading.  The approach I use is closer to the latter – an unordered list of possible states for a system (which is most like an “or”) can be used to represent a superposition. Using a list has some advantages – it is natural to apply a transformation to all elements of a list, for instance doubling the list of ingredients in a recipe.  More critically, given two independent lists of possibilities the new joint list of combined possibilities is a natural concept.  This makes teaching the equivalent of the Kronecker (tensor) product for multiple systems easy, something often a bit tricky even for undergrads to become comfortable with.

Conceptually the weirdest part of the whole construction, particularly for someone biased by the standard formalism, is that I use a standard mathematical object (a negative or minus sign) applied to a diagram of a physical object (a black or white ball).  Moreover, positive and negative balls in a diagram can cancel out (interfere).  This greatly simplifies the exposition, by removing a whole level of abstraction in the standard theory (we do not need to use a vector containing entries whose specific ordering must be remembered in order to equate them to the physical objects).  While it initially seemed odd to me personally to do this, I have yet to have any young person think of it as any more weird than using the negative sign on a number.  And if it is always kept clear that drawing and manipulating the whole diagram is an abstract thing we do, which may or may not have any correspondence to what is “really going on” in the physical setups we are describing, then there really is no difference.

There are some subtleties about the whole approach – while the formalism is universal for quantum computing, it can only make use of unitary evolution which is proportional to a matrix with integer entries.  Thus the Hadamard gate (PETE box) is ok, the Controlled-NOT and Toffoli likewise, but a seemingly innocuous gate like the controlled-Hadamard is not capable of being incorporated (without adding a whole bunch of unintuitive and unjustified rules).  The fact the approach covers a universal gate set means some amazing things can be explained in this simple diagrammatic language.  For example, the recent paper Quantum theory cannot consistently describe the use of itself, which led to considerable discussion on this blog, can be fully reproduced.  That is, a high school student can in principle understand the technical details of a contemporary argument between professional physicists.  I find this amazing.

Based on communication with readers I have come to realize the people at most risk of being confused by the book are actually those already with a little knowledge – someone who has done a year or two’s worth of undergraduate quantum courses, or someone who has taken things they read in pop-sci books too literally.  Initially, as I was developing the method, I thought it would be easy to keep “touching base” with the standard vector space formalism.  But in fact it becomes very messy to do so (and irrelevant for someone learning quantum theory for the first time).  In the end I dropped that goal, but now realize I need to develop some supplementary notes to help someone in that situation.

Q is for Quantum is certainly not designed to be used as a classroom text – if nothing else my particular style and choice of topics will not be to others’ tastes, and I haven’t included all the many, many simple examples and exercises I have students doing along with me in class when I actually teach this stuff.  It should be thought of as more a “proof of principle,” that the expository challenge can be met.  Several colleagues have used parts of these ideas already for teaching, and they have given me some great feedback.  As such I am planning on doing a revised and slightly expanded version at some point, so if you read it and have thoughts for improvement please send me them.

Ten updates

November 7th, 2018

If you like quantum, complexity, etc., then please read to the end! I’ve gotten a bunch of emails lately of the form “why haven’t you ever blogged about such-and-such?,” when it turned out that I damn well did blog about it; it was just somewhere down in a multi-item post.

1. Like many of you, I watched the US midterm election results with (mostly…) disappointment and dismay.  I think that history will judge us harshly for not totally and unequivocally rebuking everything Trump stands for and every politician associated with him.  But that’s not what I wanted to blog about today.

2. There was a breakthrough in communication complexity by Arkadev Chattopadhyay, Nikhil Mande, and Suhail Sherif: the first exponential separation between randomized communication complexity and log approximate rank for a total Boolean function f.  This falsifies the longstanding conjecture that these measures are polynomially related (though it doesn’t resolve the original log rank conjecture).  For those of you keeping score at home, the quantum communication complexity of f is sandwiched in between randomized CC and log approximate rank.  So, at least one of the following must now be true: either randomized CC is exponentially separated from quantum CC, or else quantum CC is exponentially separated from log approximate rank.  My money’s on the latter.

3. Ewin Tang, who achieved fame with a quantum-inspired classical algorithm for recommendation systems (which I blogged about in July), is now back with quantum-inspired classical algorithms for principal component analysis and supervised clustering.  Well, with the announcements of such algorithms; details of the analysis are to come later.

4. A bunch of people asked me about the paper by Sergey Bravyi, David Gosset, and Robert Koenig, Quantum advantage with shallow circuits.  tl;dr: it’s great!  And it was deservedly a highlight of the QIP conference back in January!  That’s why it confused me when everyone started asking about it a couple weeks ago.  The resolution is that the paper was just recently published in Science magazine, which led to popular coverage like this, which in turn led to people asking me whether this result unconditionally proves P≠BQP (that is, quantum computers can solve more problems in polynomial time than classical computers), and if not why not.  The answer is no: the paper proves an unconditional separation, but one that’s a long long way from P≠BQP, or anything else that would entail solving the central open problems of complexity theory like P vs. PSPACE.  Basically, it shows there are problems solvable in constant time with a quantum computer that aren’t solvable in constant time classically, for suitable meanings of “problem” (namely, a relation problem) and “in constant time” (namely, NC0 circuits, in which each output bit depends on only a constant number of input bits).  I understand that a stronger separation has since been achieved, between quantum NC0 and classical AC0, in work that’s not yet on the arXiv.  The problems in question, however, are all easy to solve in P, or even in classical logarithmic time, given a polynomial number of parallel processors.

5. A bunch of people also asked me about the paper by Xun Gao and Luming Duan, Efficient classical simulation of noisy quantum computation.  This paper tries to formalize something that many of us have suspected/feared for years, namely that random quantum circuits (the whole thing is specific to random circuits) can tolerate only a tiny amount of noise and decoherence before they become efficiently simulable classically.  If true, this has obvious implications for the sampling-based quantum supremacy experiments that Google and others are planning for the next few years: namely, that all the engineering effort they’ve already been investing anyway to push down the noise rate, will actually be necessary!  However, correspondence with the authors revealed that there’s a significant gap in the analysis as it currently stands: namely, the current proof applies only to closed quantum systems, which would (for example) rule out all the techniques that people eventually hope to use to achieve quantum fault-tolerance—all of which are based on constantly measuring subsets of the qubits, doing essentially error-free classical computation on the measurement outcomes, throwing away noisy qubits, and pumping in fresh qubits.  Xun and Duan say that they’re currently working on an extension to open systems; in my personal view, such an extension seems essential for this interesting result to have the informal interpretation that the authors want.

6. My friend Bram Cohen asked me to announce that his company, Chia, has launched a competition for best implementation of its Verifiable Delay Functions (VDFs), with real money rewards.  You can find the details at this Github page.

7. The second Q2B (“Quantum 2 Business”) conference, organized by QC Ware Corp., will be held this coming December 10-12, at the Computer History Museum in Mountain View.  There will be two keynote addresses, one by John Preskill and the other by me.  I hope I’ll get a chance to meet some of you there!

8. Longtime colleague and friend-of-the-blog Ashwin Nayak asked me to announce that the 2019 Conference on Computational Complexity, to be held July 18-20 in exciting New Brunswick, NJ, is now accepting submissions.  I hope to be there!

9. OK, what the hell: the 21st annual, and nearly impossible to capitalize correctly, SQuInT (Southwest Quantum Information and Technology) workshop will be held February 2019 in Albuquerque, NM.  UT Austin is now a node of the SQuInT network, and I’ll hopefully be attending along with a posse of students and postdocs.  The deadline for abstract submission is coming up soon: Monday November 12!

10. I went to morning Shabbat services in Austin this past weekend, exactly one week after the tragedy in Pittsburgh.  There was massively increased security, with armed guards interrogating us, Israeli-style, about why we had no membership sticker on our car, whether we knew the name of the rabbi, etc.  Attendance was maybe a factor of three higher than usual.  About thirty priests, ministers, and Christian seminary students, and one Muslim, came up to the bima to say a prayer of solidarity with Jews.  The mayor of Austin, Steve Adler, was also on hand to give a speech.  Then the rabbi read a letter to the synagogue by Sen. Ted Cruz denouncing antisemitism (well, parts of it; he said the letter was really long).  There were murmurs of disapproval from the crowd when Cruz’s name was mentioned, but then everyone quieted down and listened.  The thing is, the US and large parts of the world are now so far outside the norms of liberal democracy, in territory so terrifyingly uncharted since the end of World War II, that shooting up synagogues is bad is actually something that it’s better than not for powerful people to affirm explicitly.  Anyway, while I’m neither a believer nor much of a synagogue-goer, I found the show of unity moving.

Boof

October 2nd, 2018

(Just a few politics-related comments to get off my chest.  Feel free to skip if American politics isn’t your 5-liter bottle of Coke.)

FiveThirtyEight currently gives Beto O’Rourke a ~29% chance of winning Ted Cruz’s Senate seat.  I wish it were higher, but I think this will be such a spectacular upset if it happens, and so transformative for Texas, that it’s well worth our support.  I’ve also been impressed by the enthusiasm of Beto’s campaign—including a rally in Austin this weekend where the 85-year-old Willie Nelson, headlining the first political event of his 60-year music career, performed a new song (“Vote ‘Em Out”).  I’ll tell you what: if anyone donates to Beto’s campaign within the next two days as a result of reading this post, and emails or leaves a comment to tell me about it, I’ll match their donation, up to my personal Tsirelson bound of $853.

Speaking of which, if you’re a US citizen and are not currently registered to vote, please do so!  And then show up and vote in the midterms!  My personal preference is to treat voting as simply a categorical imperative.  But if you’d like a mathematical discussion of the expected utility of voting, then check out this, by my former MIT undergraduate advisee Shaunak Kishore.

But what about the highest questions currently facing the American republic: namely, the exact meanings of “boofing,” “Devil’s triangle,” and “Renate alumnius”?  I’ve been reading the same articles and analyses as everybody else, and have no privileged insight.  For what it’s worth, though, I think it’s likely that Blasey Ford is teling the truth.  And I think it’s likely that Kavanaugh is lying—if not about the assault itself (which he might genuinely have no memory of—blackout is a real phenomenon), then certainly about his teenage drinking and other matters.  And while, absent some breakthrough in the FBI investigation, none of this rises to the beyond-a-reasonable-doubt standard, I think it likely should be seen as disqualifying for the Supreme Court.  (Admittedly, I’m not a good arbiter of that question, since there are about 200 unrelated reasons why I don’t want Kavanaugh near the Court.)  I also think it’s perfectly reasonable of Senate Democrats to fight this one to the bitter end, particularly after what the Republicans did to Merrick Garland, and what Kavanaugh himself did to Bill Clinton.  If you’re worried about the scorched-earth, all-defect equilibrium that seems to prevail in Congress—well, the Democrats are not the ones who started it.

All of that would be one thing, coming from some hardened social-justice type who might have happily convicted Kavanaugh of aggravated white male douchiness even before his umbilical cord was cut.  But I daresay that it means a bit more, coming from an individual who hundreds of online activists once denounced just as fervently as they now denounce Kavanaugh—someone who understands perfectly well that not even the allegation of wrongdoing is needed any longer for a person to be marked for flattening by the steamroller of Progress.  What can I say?  The enemy of my enemy is sometimes still my enemy.  My friend is anybody, of whatever party or creed, who puts their humanity above their ideology.  Justice is no respecter of persons.  Sometimes those who earn the mob’s ire are nevertheless guilty.

I was actually in the DC area the week of the Kavanaugh hearings, to speak at a quantum information panel on Capitol Hill convened by the House Science Committee, to participate in a quantum machine learning workshop at UMD, and to deliver the Nathan Krasnopoler Memorial Lecture at Johns Hopkins, which included the incredibly moving experience of meeting Nathan’s parents.

The panel went fine, I think.  Twenty or thirty Congressional staffers attended, including many of those involved in the National Quantum Initiative bill.  They asked us about the US’s standing relative to China in QIS; the relations among academia, industry, and national labs; and how to train a ‘quantum workforce.’  We panelists came prepared with a slide about what qubits and interference are, but ended up never needing it: the focus was emphatically on policy, not science.

Kamala Harris (D-CA) is the leader in the Senate for what’s now called the Quantum Computing Research Act.  One of Sen. Harris’s staffers conveyed to me that, given her great enthusiasm for quantum computing, the Senator would have been delighted to meet with me, but was unfortunately too busy with Kavanaugh-related matters.  This was better than what I’d feared, namely: “following the lead of various keyboard warriors on Twitter and Reddit, Sen. Harris denounces you, Dr. Aaronson, as a privileged white male techbro and STEMlord, and an enemy of the people.”  So once again I was face-to-face with the question: is it conceivable that social-media discourse is a bit … unrepresentative of the wider world?

It’s hard to think when someone Hadamards your brain

September 25th, 2018

“Unperformed measurements have no results.” —Asher Peres


With two looming paper deadlines, two rambunctious kids, an undergrad class, program committee work, faculty recruiting, and an imminent trip to Capitol Hill to answer congressional staffers’ questions about quantum computing (and for good measure, to give talks at UMD and Johns Hopkins), the only sensible thing to do is to spend my time writing a blog post.

So: a bunch of people asked for my reaction to the new Nature Communications paper by Daniela Frauchiger and Renato Renner, provocatively titled “Quantum theory cannot consistently describe the use of itself.”  Here’s the abstract:

Quantum theory provides an extremely accurate description of fundamental processes in physics.  It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally.  Here, we propose a Gedankenexperiment to investigate the question whether quantum theory can, in principle, have universal validity.  The idea is that, if the answer was yes, it must be possible to employ quantum theory to model complex systems that include agents who are themselves using quantum theory.  Analysing the experiment under this presumption, we find that one agent, upon observing a particular measurement outcome, must conclude that another agent has predicted the opposite outcome with certainty.  The agents’ conclusions, although all derived within quantum theory, are thus inconsistent.  This indicates that quantum theory cannot be extrapolated to complex systems, at least not in a straightforward manner.

I first encountered Frauchiger and Renner’s argument back in July, when Renner (who I’ve known for years, and who has many beautiful results in quantum information) presented it at a summer school in Boulder, CO where I was also lecturing.  I was sufficiently interested (or annoyed?) that I pulled an all-nighter working through the argument, then discussed it at lunch with Renner as well as John Preskill.  I enjoyed figuring out exactly where I get off Frauchiger and Renner’s train—since I do get off their train.  While I found their paper thought-provoking, I reject the contention that there’s any new problem with QM’s logical consistency: for reasons I’ll explain, I think there’s only the same quantum weirdness that (to put it mildly) we’ve known about for quite some time.

In more detail, the paper makes a big deal about how the new argument rests on just three assumptions (briefly, QM works, measurements have definite outcomes, and the “transitivity of knowledge”); and how if you reject the argument, then you must reject at least one of the three assumptions; and how different interpretations (Copenhagen, Many-Worlds, Bohmian mechanics, etc.) make different choices about what to reject.

But I reject an assumption that Frauchiger and Renner never formalize.  That assumption is, basically: “it makes sense to chain together statements that involve superposed agents measuring each other’s brains in different incompatible bases, as if the statements still referred to a world where these measurements weren’t being done.”  I say: in QM, even statements that look “certain” in isolation might really mean something like “if measurement X is performed, then Y will certainly be a property of the outcome.”  The trouble arises when we have multiple such statements, involving different measurements X1, X2, …, and (let’s say) performing X1 destroys the original situation in which we were talking about performing X2.

But I’m getting ahead of myself.  The first thing to understand about Frauchiger and Renner’s argument is that, as they acknowledge, it’s not entirely new.  As Preskill helped me realize, the argument can be understood as simply the “Wigner’s-friendification” of Hardy’s Paradox.  In other words, the new paradox is exactly what you get if you take Hardy’s paradox from 1992, and promote its entangled qubits to the status of conscious observers who are in superpositions over thinking different thoughts.  Having talked to Renner about it, I don’t think he fully endorses the preceding statement.  But since I fully endorse it, let me explain the two ingredients that I think are getting combined here—starting with Hardy’s paradox, which I confess I didn’t know (despite knowing Lucien Hardy himself!) before the Frauchiger-Renner paper forced me to learn it.

Hardy’s paradox involves the two-qubit entangled state

$$\left|\psi\right\rangle = \frac{\left|00\right\rangle + \left|01\right\rangle + \left|10\right\rangle}{\sqrt{3}}.$$

And it involves two agents, Alice and Bob, who measure the left and right qubits respectively, both in the {|+〉,|-〉} basis.  Using the Born rule, we can straightforwardly calculate the probability that Alice and Bob both see the outcome |-〉 as 1/12.

So what’s the paradox?  Well, let me now “prove” to you that Alice and Bob can never both get |-〉.  Looking at |ψ〉, we see that conditioned on Alice’s qubit being in the state |0〉, Bob’s qubit is in the state |+〉, so Bob can never see |-〉.  And conversely, conditioned on Bob’s qubit being in the state |0〉, Alice’s qubit is in the state |+〉, so Alice can never see |-〉.  OK, but since |ψ〉 has no |11〉 component, at least one of the two qubits must be in the state |0〉, so therefore at least one of Alice and Bob must see |+〉!

When it’s spelled out so plainly, the error is apparent.  Namely, what do we even mean by a phrase like “conditioned on Bob’s qubit being in the state |0〉,” unless Bob actually measured his qubit in the {|0〉,|1〉} basis?  But if Bob measured his qubit in the {|0〉,|1〉} basis, then we’d be talking about a different, counterfactual experiment.  In the actual experiment, Bob measures his qubit only in the {|+〉,|-〉} basis, and Alice does likewise.  As Asher Peres put it, “unperformed measurements have no results.”

Anyway, as I said, if you strip away the words and look only at the actual setup, it seems to me that Frauchiger and Renner’s contribution is basically to combine Hardy’s paradox with the earlier Wigner’s friend paradox.  They thereby create something that doesn’t involve counterfactuals quite as obviously as Hardy’s paradox does, and so requires a new discussion.

But to back up: what is Wigner’s friend?  Well, it’s basically just Schrödinger’s cat, except that now it’s no longer a cat being maintained in coherent superposition but a person, and we’re emphatic in demanding that this person be treated as a quantum-mechanical observer.  Thus, suppose Wigner entangles his friend with a qubit, like so:

$$ \left|\psi\right\rangle = \frac{\left|0\right\rangle \left|FriendSeeing0\right\rangle + \left|1\right\rangle \left|FriendSeeing1\right\rangle}{\sqrt{2}}. $$

From the friend’s perspective, the qubit has been measured and has collapsed to either |0〉 or |1〉.  From Wigner’s perspective, no such thing has happened—there’s only been unitary evolution—and in principle, Wigner could even confirm that by measuring |ψ〉 in a basis that included |ψ〉 as one of the basis vectors.  But how can they both be right?

Many-Worlders will yawn at this question, since for them, of course “the collapse of the wavefunction” is just an illusion created by the branching worlds, and with sufficiently advanced technology, one observer might experience the illusion even while a nearby observer doesn’t.  Ironically, the neo-Copenhagenists / Quantum Bayesians / whatever they now call themselves, though they consider themselves diametrically opposed to the Many-Worlders (and vice versa), will also yawn at the question, since their whole philosophy is about how physics is observer-relative and it’s sinful even to think about an objective, God-given “quantum state of the universe.”  If, on the other hand, you believed both that

  1. collapse is an objective physical event, and
  2. human mental states can be superposed just like anything else in the physical universe,

then Wigner’s thought experiment probably should rock your world.

OK, but how do we Wigner’s-friendify Hardy’s paradox?  Simple: in the state

$$\left|\psi\right\rangle = \frac{\left|00\right\rangle + \left|01\right\rangle + \left|10\right\rangle}{\sqrt{3}},$$

we “promote” Alice’s and Bob’s entangled qubits to two conscious observers, call them Charlie and Diane respectively, who can think two different thoughts that we represent by the states |0〉 and |1〉.  Using far-future technology, Charlie and Diane have been not merely placed into coherent superpositions over mental states but also entangled with each other.

Then, as before, Alice will measure Charlie’s brain in the {|+〉,|-〉} basis, and Bob will measure Diane’s brain in the {|+〉,|-〉} basis.  Since the whole setup is mathematically identical to that of Hardy’s paradox, the probability that Alice and Bob both get the outcome |-〉 is again 1/12.

Ah, but now we can reason as follows:

  1. Whenever Alice gets the outcome |-〉, she knows that Diane must be in the |1〉 state (since, if Diane were in the |0〉 state, then Alice would’ve certainly seen |+〉).
  2. Whenever Diane is in the |1〉 state, she knows that Charlie must be in the |0〉 state (since there’s no |11〉 component).
  3. Whenever Charlie is in the |0〉 state, she knows that Diane is in the |+〉 state, and hence Bob can’t possibly see the outcome |-〉 when he measures Diane’s brain in the {|+〉,|-〉} basis.

So to summarize, Alice knows that Diane knows that Charlie knows that Bob can’t possibly see the outcome |-〉.  By the “transitivity of knowledge,” this implies that Alice herself knows that Bob can’t possibly see |-〉.  And yet, as we pointed out before, quantum mechanics predicts that Bob can see |-〉, even when Alice has also seen |-〉.  And Alice and Bob could even do the experiment, and compare notes, and see that their “certain knowledge” was false.  Ergo, “quantum theory can’t consistently describe its own use”!

You might wonder: compared to Hardy’s original paradox, what have we gained by waving a magic wand over our two entangled qubits, and calling them “conscious observers”?  Frauchiger and Renner’s central claim is that, by this gambit, they’ve gotten rid of the illegal counterfactual reasoning that we needed to reach a contradiction in our analysis of Hardy’s paradox.  After all, they say, none of the steps in their argument involve any measurements that aren’t actually performed!  But clearly, even if no one literally measures Charlie in the {|0〉,|1〉} basis, he’s still there, thinking either the thought corresponding to |0〉 or the thought corresponding to |1〉.  And likewise Diane.  Just as much as Alice and Bob, Charlie and Diane both exist even if no one measures them, and they can reason about what they know and what they know that others know.  So then we’re free to chain together the “certainties” of Alice, Bob, Charlie, and Diane in order to produce our contradiction.

As I already indicated, I reject this line of reasoning.  Specifically, I get off the train at what I called step 3 above.  Why?  Because the inference from Charlie being in the |0〉 state to Bob seeing the outcome |+〉 holds for the original state |ψ〉, but in my view it ceases to hold once we know that Alice is going to measure Charlie in the {|+〉,|-〉} basis, which would involve a drastic unitary transformation (specifically, a “Hadamard”) on the quantum state of Charlie’s brain.  I.e., I don’t accept that we can take knowledge inferences that would hold in a hypothetical world where |ψ〉 remained unmeasured, with a particular “branching structure” (as a Many-Worlder might put it), and extend them to the situation where Alice performs a rather violent measurement on |ψ〉 that changes the branching structure by scrambling Charlie’s brain.

In quantum mechanics, measure or measure not: there is no if you hadn’t measured.


Unrelated Announcement: My awesome former PhD student Michael Forbes, who’s now on the faculty at the University of Illinois Urbana-Champaign, asked me to advertise that the UIUC CS department is hiring this year in all areas, emphatically including quantum computing. And, well, I guess my desire to do Michael a solid outweighed my fear of being tried for treason by my own department’s recruiting committee…


Another Unrelated Announcement: As of Sept. 25, 2018, it is the official editorial stance of Shtetl-Optimized that the Riemann Hypothesis and the abc conjecture both remain open problems.

CS and quantum information at UT Austin: come join us!

September 19th, 2018

Merry Yom Kippur!

This is my annual post where I tell you about opportunities available at UT Austin, which has long been a safe space for CS research, and which we hope will rapidly become (or return to its historical role as…) a safe space for quantum computing and information.

If you’re interested in faculty positions in computer science at UT, I have some great news: we plan to do a lot of hiring this year!  Because of the sheer volume of interviews we’ll be doing, we’d like to start our recruiting season already in the fall.  So we’re extending an unusual invitation: if you already have your materials ready, we encourage you to apply for faculty positions right now.  If you’re chosen for an interview, we could schedule it for the next few months.

We’ll be looking for great candidates across all parts of CS, but one particular interest is hiring another quantum computing theorist in CS (i.e., besides me), most likely a junior person.  While not everyone who reads this blog is a plausible candidate, and not every plausible candidate reads this blog, the intersection is surely non-negligible!  So again: we encourage you to apply right now, so we can start scheduling interviews already.

I’m also on the lookout for postdocs, mainly in theoretical quantum computing and information.  (I, and others in the theory group, are also collectively interested in postdocs in classical computational complexity.)  If you’re interested in doing a postdoc with me starting in Fall 2019, the procedure, like in previous years, is this:

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

We’ll set a deadline for this of December 15.

Finally, if you’re interested in pursuing a PhD in CS at UT, please apply here!  The deadline, again, is December 15.  Just like every year, I’m on the lookout for superb, complexity-loving, quantum- or quantum-curious, lower-bound-hungry students of every background, and if you specify that you want to work with me, I’ll be sure to see your application.  Emailing me won’t help: everything is done through the application process.

As we like to say down here in Texas, hook ’em Hadamards!  (Well OK, no, we don’t especially like to say that.  It’s just a slogan that I found amusing a few years ago.)

My Tomassoni-Chisesi Prize talk

September 15th, 2018

Update (Sep. 21) Video of Philip Kim’s and my talks is now available! (But not streaming, just a giant mp4 that you can download.)


On Thursday, I had the incredible honor of accepting the 2018 Tomassoni-Chisesi Prize in Physics at Università “La Sapienza” in Rome—“incredible” mostly because I’m of course not a physicist.  (I kept worrying they’d revoke the award when they realized I could barely solve the wave equation.)  This is not the first time quantum information was recognized; the prize has previously gone to Serge Haroche and Alain Aspect.  This year, for the first time, there was both an under-40 and an over-40 award; the latter went to Philip Kim, a quantum materials researcher at Harvard who I had the privilege to meet on this trip (he’s the taller one below).

I’m unbelievably grateful, not only to the committee, and its chair Giorgio Parisi (whose seminal work on phase transitions and satisfiability I’d long known, but who I met for the first time on this trip), but to Fabio Sciarrino, Paolo Mataloni, Fernanda Lupinacci, and everyone else who graciously hosted me and helped make my hastily-planned visit to Europe a success.

The department I visited has a storied history: here are the notes that Enrico Fermi left, documenting what he covered each day in his physics class in 1938.  The reason the last squares are blank is that, when Fermi and his Jewish wife left for Stockholm on the occasion of Fermi’s Nobel Prize, they continued directly to the US rather than return to an Italy that had just passed the racial laws.

On my way to Rome, I also gave two talks at a “quantum computing hackathon” in Zurich, called QuID (Quantum Information for Developers).  Thanks so much to Lidia del Rio for arranging that visit, which was fantastic as well.

To accept the Tomassoni-Chisesi prize, I had to give a 40-minute talk summarizing all my research from 2000 to the present—the hardest part being that I had to do it while wearing a suit, and sweating at least half my body weight.  (I also had a cold and a hacking cough.)  I think there will eventually be video of my and Prof. Kim’s talks, but it’s not yet available.  In the meantime, for those who are interested, here are my PowerPoint slides, and here’s the title and abstract:

Three Questions About Quantum Computing
Scott Aaronson (University of Texas at Austin)

I’ll discuss some of my work in quantum computing over the past 18 years, organizing it in terms of three questions.  First, how can we demonstrate, using near-future hardware, that quantum computers can get any genuine speedups at all over classical computers (ideally useful speedups)?  Second, what sorts of problems would be hard even for quantum computers, and can we turn the intractability of those problems to our advantage?  Third, are there physically reasonable models of computation even more powerful than quantum computing, or does quantum computing represent an ultimate limit?

If you’re a regular reader here, most of the content will be stuff you’ve seen before, with the exception of a story or two like the following:

Last night I was talking to my mom about my grandfather, who as it happens came through Rome 73 years ago, as an engineer with the US Army.  Disabling landmines was, ironically, one of the safer ways to be a Jew in Europe at that time.  If you’d told him then that, three-quarters of a century later, his grandson would be back here in Rome to accept an award for research in quantum computational complexity … well, I’m sure he’d have any number of questions about it.  But one thing I clearly remember is that my grandfather was always full of effusive praise for the warmth of the people he met in Italy—how, for example, Italian farmers would share food with the hungry and inadequately-provisioned Allied soldiers, despite supposedly being on the opposing side.  Today, every time I’m in Italy for a conference or a talk, I get to experience that warmth myself, and certainly the food part.

(Awww!  But I meant it.  Italians are super-warm.)

There’s a view that scientists should just pursue the truth and be serenely unaffected by prizes, recognition, and other baubles.  I think that view has a great deal to be said for it.  But thinking it over recently, I struck the following mental bargain: if I’m going to get depressed on a semi-regular basis by people attacking me online—and experience shows that I will—well then, I also get to enjoy whatever’s the opposite of that with a clear conscience.  It’s not arrogance or self-importance; it’s just trying to balance things out a bit!

So again, thanks so much—to the physics department of La Sapienza, but also to my family, friends, mentors, readers, colleagues at UT Austin and around the world, and everyone else who helps make possible whatever it is that I do.

Lecture notes! Intro to Quantum Information Science

August 26th, 2018

Someone recently wrote that my blog is “too high on nerd whining content and too low on actual compsci content to be worth checking too regularly.”  While that’s surely one of the mildest criticisms I’ve ever received, I hope that today’s post will help to even things out.

In Spring 2017, I taught a new undergraduate course at UT Austin, entitled Introduction to Quantum Information Science.  There were about 60 students, mostly CS but also with strong representation from physics, math, and electrical engineering.  One student, Ewin Tang, made a previous appearance on this blog.  But today belongs to another student, Paulo Alves, who took it upon himself to make detailed notes of all of my lectures.  Using Paulo’s notes as a starting point, and after a full year of procrastination and delays, I’m now happy to release the full lecture notes for the course.  Among other things, I’ll be using these notes when I teach the course a second time, starting … holy smokes … this Wednesday.

I don’t pretend that these notes break any new ground.  Even if we restrict to undergrad courses only (which rules out, e.g., Preskill’s legendary notes), there are already other great quantum information lecture notes available on the web, such as these from Berkeley (based on a course taught by, among others, my former adviser Umesh Vazirani and committee member Birgitta Whaley), and these from John Watrous in Waterloo.  There are also dozens of books—including Mermin’s, which we used in this course.  The only difference with these notes is that … well, they cover exactly the topics I’d cover, in exactly the order I’d cover them, and with exactly the stupid jokes and stories I’d tell in a given situation.  So if you like my lecturing style, you’ll probably like these, and if not, not (but given that you’re here, there’s hopefully some bias toward the former).

The only prerequisite for these notes is some minimal previous exposure to linear algebra and algorithms.  If you read them all, you might not be ready yet to do research in quantum information—that’s what a grad course is for—but I feel good that you’ll have an honest understanding of what quantum information is all about and where it currently stands.  (In fact, where it already stood by the late 1990s and early 2000s, but with many comments about the theoretical and experimental progress that’s been made since then.)

Also, if you’re one of the people who read Quantum Computing Since Democritus and who was disappointed by the lack of basic quantum algorithms in that book—a function of the book’s origins, as notes of lectures given to graduate students who already knew basic quantum algorithms—then consider these new notes my restitution.  If nothing else, no one can complain about a dearth of basic quantum algorithms here.

I welcome comments, bugfixes, etc.  Thanks so much, not only to Paulo for transcribing the lectures (and making the figures!), but also to Patrick Rall and Corey Ostrove for TA’ing the course, to Tom Wong and Supartha Podder for giving guest lectures, and of course, to all the students for making the course what it was.

  • Lecture 1: Course Intro, Church-Turing Thesis (3 pages)
  • Lecture 2: Probability Theory and QM (5 pages)
  • Lecture 3: Basic Rules of QM (4 pages)
  • Lecture 4: Quantum Gates and Circuits, Zeno Effect, Elitzur-Vaidman Bomb (5 pages)
  • Lecture 5: Coin Problem, Inner Products, Multi-Qubit States, Entanglement (5 pages)
  • Lecture 6: Mixed States (6 pages)
  • Lecture 7: Bloch Sphere, No-Cloning, Wiesner’s Quantum Money (6 pages)
  • Lecture 8: More on Quantum Money, BB84 Quantum Key Distribution (5 pages)
  • Lecture 9: Superdense Coding (2 pages)
  • Lecture 10: Teleportation, Entanglement Swapping, GHZ State, Monogamy (5 pages)
  • Lecture 11: Quantifying Entanglement, Mixed State Entanglement (4 pages)
  • Lecture 12: Interpretation of QM (Copenhagen, Dynamical Collapse, MWI, Decoherence) (10 pages)
  • Lecture 13: Hidden Variables, Bell’s Inequality (5 pages)
  • Lecture 14: Nonlocal Games (7 pages)
  • Lecture 15: Einstein-Certified Randomness (4 pages)
  • Lecture 16: Quantum Computing, Universal Gate Sets (8 pages)
  • Lecture 17: Quantum Query Complexity, Deutsch-Jozsa (8 pages)
  • Lecture 18: Bernstein-Vazirani, Simon (7 pages)
  • Lecture 19: RSA and Shor’s Algorithm (6 pages)
  • Lecture 20: Shor, Quantum Fourier Transform (8 pages)
  • Lecture 21: Continued Fractions, Shor Wrap-Up (4 pages)
  • Lecture 22: Grover (9 pages)
  • Lecture 23: BBBV, Applications of Grover (7 pages)
  • Lecture 24: Collision and Other Applications of Grover (6 pages)
  • Lecture 25: Hamiltonians (10 pages)
  • Lecture 26: Adiabatic Algorithm (10 pages)
  • Lecture 27: Quantum Error Correction (8 pages)
  • Lecture 28: Stabilizer Formalism (9 pages)
  • Lecture 29: Experimental Realizations of QC (9 pages)

And by popular request, here are the 2017 problem sets!

I might post solutions at a later date.

Note: If you’re taking the course in 2018 or a later year, these sets should be considered outdated and for study purposes only.


Notes and Updates (Aug. 27)

Here’s a 184-page combined file. Thanks so much to Robert Rand, Oscar Cunningham, Petter S, and Noon van der Silk for their help with this.

If it wasn’t explicit: these notes are copyright Scott Aaronson 2018, free for personal or academic use, but not for modification or sale.

I’ve freely moved material between lectures so that it wasn’t arbitrarily cut across lecture boundaries. This is one of the reasons why some lectures are much longer than others.

I apologize that some of the displayed equations are ugly. This is because we never found an elegant way to edit equations in Google Docs.

If you finish these notes and are still hankering for more, try my Quantum Complexity Theory or Great Ideas in Theoretical Computer Science lecture notes, or my Barbados lecture notes.  I now have links to all of them on the sidebar on the right.

Thank you, world!

August 15th, 2018

1. This post has no technical content.  As the tag indicates, it’s entirely “Nerd Self-Help”—thoughts I’ve recently found extremely helpful to me, and that I’m hopeful some others might be able to apply to their own life situations.  If that doesn’t interest you, feel free to skip.

2. I’m using the numbered list format simply because I have a large number of interrelated things to say, and getting each one down precisely seems more important than fashioning them into some coherent narrative.

3. For someone who walks around every day wracked by neurosis, social anxiety, tics, and depression, I’m living an unbelievably happy and fulfilling life.  For this I’m profoundly grateful—to “the universe,” but much more so, to the family and friends and colleagues who’ve made it possible.

4. On bad days, I’ve cursed fate for having placed me in a world to which my social skills were so poorly adapted.  On good days, though, I’ve thanked fate for letting me thrive in such a world, despite my social skills being so maladapted to it.  My ability to thrive in this world owes everything to the gifts of modernity, to the stuff Steven Pinker talks about in Enlightenment Now: the decline of violence, the rule of law, the freedom from hunger, disease, and war, but most of all the rise of science.  So I have a personal reason to be grateful for modernity and to care deeply about its preservation—and to detest Trump and all the other would-be autocrats who’d gleefully take an ax to it.  Like hothouse plants, nerds can flourish only in artificially safe environments.  I don’t often enough express my gratitude for having been born into a world that contains such environments, so I’m taking the opportunity to do so today.

5. I got back a few days ago from a wonderful visit to Mexico City—thanks so much to Sergio Rajsbaum, Luis González, and all my other new friends there for helping to organize it.  I gave three talks at UNAM, one of the largest universities on earth.  I ate … well, the best Mexican food I ever tasted.  I saw amazing sights, including the National Museum of Anthropology, which has hall after hall full of Aztec and Maya artifacts of a grandeur one normally associates with ancient Egypt, Greece, or Rome.  Go there if you want a visceral sense for the scale of the tragedy wrought by the conquistadors.  (On the other hand, having seen the decorated ceremonial knives, the skulls of children whose hearts were ripped out while still beating, I do have to count the end of human sacrifice as a net positive.)

6. The trip was surreal: I discussed quantum computing and philosophy and Mexican history over enchiladas and tequila.  I signed copies of my book, lectured, met fans of this blog.  There was lots of good-natured laughter about the tale of my arrest, and stern reminders to be careful when ordering smoothies.  A few people I met shared their own stories of being harassed by US police over trivial mishaps (e.g., “put your hands on the car,” rifle aimed, over a parking violation), exacerbated of course by their being Mexicans.  One colleague opined that he preferred the Mexican system, wherein you and the officer just calmly, politely discussed how many pesos would make the problem go away.  But then, from time to time, I’d check my phone and find fresh comments accusing me of being a thief, a nutcase incapable of functioning in society, a racist who wants to be treated differently from blacks and Latinos (the actual view expressed in my post was precisely the opposite of that), or even a money-grubbing Jew hyperventilating about “anuddah Shoah.”

7. The real world has a lot to be said for it.  Maybe I should spend more time there.

8. Thanks so much to everyone who sent emails or left comments expressing sympathy about my arrest—or even who simply found the story crazy and amusing, like a Seinfeld episode.  Meanwhile, to those who berated me for being unable to function in society: does it bother you, does it present a puzzle for your theory, that rather than starving under a bridge, I’m enjoying a career doing what I love, traveling the world giving lectures, happily married with two kids?  Do I not, if nothing else, illustrate how functional a non-functional person can be?

9. It’s possible that my kids will grow up with none of the anxiety or depression or neuroticism or absentmindedness that I’ve had.  But if they do have those problems … well, I’m thankful that I can provide them at least one example of what it’s possible to do in life in spite of it!

10. On SneerClub, someone opined that not only was I an oblivious idiot at the smoothie counter, I must also be oblivious to how bad the incident makes me look—since otherwise, I would never have blogged about it.  I ask my detractors: can you imagine, for one second, being so drunk on the love of truth that you’d take the experiences that made you look the most pathetic and awkward, and share them with the world in every embarrassing detail—because “that which can be destroyed by the truth should be”?  This drunkenness on truth is scary, it’s destabilizing, it means that every day you run a new risk of looking foolish.  But as far as I can introspect, it’s also barely distinguishable from the impulse that leads to doing good science: asking the questions everyone else knows better than to ask, clarifying the obvious, confessing one’s own doofus mistakes.  So as a scientist, I’m grateful to have this massive advantage, for all its downsides.

11. Of the hundreds of reactions to my arrest, some blamed me, some the police, some both and some neither.  As I mentioned before, there was an extremely strong and surprising national split, with Americans siding with the police and non-Americans siding with me.  But there was also an even deeper split: namely, almost everyone who already liked me found the story funny or endearing or whatever, while almost everyone who already hated me found in it new reasons for their hate.  I’ve observed this to be a general phenomenon: within the range of choices I’d realistically consider, none of them seem to do anything to turn enemies into friends or friends into enemies.  If so, then that’s a profoundly liberating realization.  It means that I might as well just continue being myself, saying and doing what seem reasonable to me, without worrying about either winning over the SneerClubbers or losing the people who like this blog.  For neither of those is likely to happen–even if we ignore all the other reasons to eschew overreliance on external validation.

12. Every week or so I get emails from people wanting to share their spiritual theories with me, and to illustrate them with color diagrams.  Most such emails go straight to my trash folder.  This week, however, I received one that contained a little gem of insight:

I realize you are professionally reluctant to admit that Spirit actually exists. However, it is obvious to me from your blog that you are personally committed to what I might label “spiritual development.” You are continually pushing yourself and others to be more self-aware, reflect on our actions and assumptions, and choose to become our best selves.

I can only imagine how much pain and psychic energy it costs you to do that so publicly and vulnerably. But that is precisely why so many of us love you; and others hate you, because they are understandably terrified of paying that same price.

13. To those who’ve called me a terrible person, based on how they imagine I’d respond in hypothetical scenarios of their own construction, I make one request.  Before passing final judgment, at least exchange emails with me, or meet me, or otherwise give me a chance to differentiate myself from your internal bogeyman.  Ask me for grad school advice, or comments on your CS idea, or whatever—and with nothing in it for me, and swamped with similar requests, see how much time I spend trying to help you.  Or ask me to donate to your favorite charity, and see if I do it.  Or tell me about misconduct by a prominent member of my community, and see how I respond.  See if any of this is noticeably affected by your race, religion, gender, sexual orientation, or anything else besides the honesty of your request.

14. None of the above are hypotheticals for me.  Once I was given firsthand reports, which I judged to be extremely credible, about a serial sexual harasser of women in the math and TCS communities.  The victims had already pursued formal complaints, but with an unsatisfactory resolution.  In response, I immediately offered to publish the perpetrator’s name on this blog along with the evidence and accusations, or help in any other way desired.  My offer was declined, but it still stands if the victims were to change their minds.

15. My mom once told me that, having been hippies concerned about overpopulation, she and my dad weren’t planning to have any kids.  When they finally decided to do so, it was in order to “spite Hitler.”  I felt incredibly proud to have that be the reason for my birth.  Every time I think about it, it fills me with a renewed urge to stand up for whatever seems most human and compassionate, regardless of how unpopular.

16. Going forward, if I ever (hypothetically) experience a relapse of the suicidal thoughts that characterized part of my life, I’m going to say to myself: no.  Not only will I remain alive, I’ll continue to enjoy my family and friends and research and teaching, and mentor students, and get involved in issues I care about, and otherwise make the most of life.  And if for no other reason, I’d do this in order that Arthur Chu could remain, as he put it, “unhappy about [my] continued existence”!  Admittedly, spiting Chu and his chorus of SneerClubbers is far from the only reason to continue living, but it’s a perfectly sufficient reason in itself.  And this will be an impenetrable shield against suicidal thoughts.  So thanks, Arthur!

17. Four years ago, I received hundreds of moving responses to comment 171.  But perhaps the most touching were from several female classmates who I’d had crushes on back in the depressed period I wrote about, and who said some variant of: “it’s a shame you never asked me, because I liked you and would’ve gladly said yes.”  One of these classmates, bless her heart, recently asked me to share this information, as an encouragement to young nerdy readers who might find themselves in the same situation I was in.  Four years ago, a few feminists lectured me that the crippling fear I’d suffered was good, a feature rather than a bug: if only every other predatory nerdbro would be paralyzed by the same fear!  (That is, when they weren’t also lecturing me that the fears were ridiculous and existed only in my head.)  But the women who wrote to me are also left-wing feminists.  So if you confess your feelings to someone, know that no one who despises that decision, who considers it ‘problematic’ and ‘entitled’ and ‘privileged’ and all the rest of the modern litany of just-die-already words, can pretend to speak for all feminists.  I love my wife and my children, and wouldn’t go back in time to change my life’s trajectory if I could.  But you, readers, armed with wisdom I lacked, can reach a happy place in your lives a hell of a lot faster than I did.

18. While this has been beneath the surface of a huge number of my posts, it seems worth bringing out explicitly.  On certain blogs and social media sites, I’m regularly described as a “leftist troll,” a “pathetic, mewling feminist,” or a “rabid establishment liberal.”  On others I’m called a “far-right Zionist” or an “anti-feminist men’s rights advocate.”  It’s enough to make even me confused.  But here’s how I choose to define my stance: my party is the Party of Psychological Complexity.  Our party platform consists of Shakespeare’s plays, the movie The Breakfast Club, the novels of Mark Twain and Philip Roth and Rebecca Goldstein, classic Simpsons and Futurama, and anything else that tries to grapple with human nature honestly.  For most of the past few centuries, the Party of Psychological Complexity has been in a coalition with the political left, because both were interested in advancing Enlightenment ideals, ending slavery and female subjugation and other evils, and broadening humankind’s circles of empathy.  But the PoPC and the political left already split once, over the question of Communism, and today they split again over the morality and the wisdom of social justice vigilantism.

19. Here in the PoPC, our emphasis on the staggering complexity of the individual conscience might seem hard to square with utilitarian ethics: with public health campaigns, Effective Altruism, doing the greatest good for the greatest number, etc.  But the two philosophies actually fit beautifully.  In the PoPC, our interest (you might say) is in the psychological prerequisites to utilitarianism: in the “safe spaces” for the weird and nerdy and convention-defying and literal-minded in human nature that need to get established, before discussion about the best ways to fight malaria or global warming or nuclear proliferation or plastic in the oceans can even begin.

20. On leftist forums like SneerClub, whenever I’m brought up, I’m considered a dangerous reactionary—basically Richard Spencer or Alex Jones except with more quantum query complexity.  Yet, while there are differences in emphasis, and while my not being in politics gives me more freedom to venture outside the Overton window, my views on most contemporary American issues are hard to distinguish from those of Barack Obama, who I consider to have been a superb president and a model of thoughtful leadership.  If you want to understand how racist demagogues managed to take over the US—well, there was a perfect storm of horribleness, with no one decisive factor.  But it surely didn’t help that the modern social-justice left so completely disdains coalition-building, so values the purity of the Elect above all else, that it cast even progressive Obama supporters like me into its lowest circle of Hell.

21. Open yourself up to the complicated and the true in human nature.  Don’t be like Donald Trump or Arthur Chu, two men who represent opposite poles of ideology, yet who have in common that they both purposefully killed what was complicated in themselves.  For those two, winning is all that matters—they’ve explicitly said so, and have organized their entire lives around that principle.  But winning is not all that matters.  When I stand before the Lord of Song, even though it all went wrong, the only word on my lips will be “hallelujah”–because while I have many faults, I did make some room in life for beauty and truth, even at the expense of winning.  Though everything temporal turns to dust, I experienced some moments of eternity.

22. I can already predict the tweets: “No, Scott Aaronson, your weird numbered ruminations won’t save you from being the privileged douchebag who you fundamentally are.”  How was that?  Let me try another: “Aaronson embarrasses himself yet again, proves he doesn’t get why nerd culture is totally f-cked up.”  Here in the Party of Psychological Complexity, we’re used to this stuff.  We don’t fare well in social media wars, and we’ll gladly lose rather than become what we detest.  And yet, over the long run—which might be the very long run—we do mean to win, much like heliocentrism and quantum mechanics ultimately triumphed over simpler, more soundbite-friendly rivals.  Complex ideas win not through 140-character flinged excrement but through conversations, long-form essays, discourse, verbal technologies able to transfer large interconnected bundles of thoughts and emotions from one mind to another one that’s ready for such things.

23. Try every hour of every day to extend your sympathetic imagination to those who are unlike you (those who are like you don’t need such a strenuous effort).  And carve this message of universal compassion onto your doorposts, and bind it to your wrists, and put it for a sign on your foreheads.  There is no ideology that relieves us of the need to think and to feel: that’s my ideology.

24. When people give feedback about this blog’s topics, they seem roughly evenly split between those who beg for more quantum computing and other technical posts that they can actually learn from, and those who beg for more nontechnical posts that they can actually understand!  The truth is that, from the very beginning, this has never been a quantum computing or theoretical computer science blog—or rather it has been, but only incidentally.  If you had to sum it up in one sentence, I suppose this blog has been about surviving and thriving as a quantum complexity theorist in a world that isn’t designed for quantum complexity theorists?

25. But I’ll tell you what: my next post will be a quantum computing one, and I’ll make it worth the wait.  What else could I do by way of thanks to the world, and (more to the point) my family, friends, and readers?