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?

Beyond fiction

August 8th, 2018

I now know firsthand what it’s like to be arrested by armed police officers, handcuffed, and sharply interrogated, while one’s wife and children look on helplessly.  This is not a prank post.

It happened in Philadelphia International Airport.  As someone who was born in Philadelphia, and who’s since visited ~40 countries on 6 continents and flies every week or two, I’ve long considered PHL possibly the most depressing airport on the planet (and the competition is fierce).

I’d just eaten dinner with my wife Dana and our two kids in a food court—after a day of travel that had already, before this happened, involved a missed flight and a lost suitcase, owing to a chain of mishaps that I’d (probably melodramatically) been describing to Dana as insane beyond the collective imagination of Homer and Shakespeare and Tolstoy and the world’s other literary giants to invent.  Again, that was before my arrest.

Two large uniformed men with holstered pistols saw me as we were exiting the airport, surrounded and handcuffed me, and demanded that I confess.

“I’m … sorry, officers,” I managed.  “I don’t understand what this is about.”

“Stop the games.  You know exactly what you took.  We have it all on video.  Where is it?”

Me, a thief?  I felt terrified to be at the beginning of a Kafka story.  But if I’m going to be brutally honest about it, I also felt … secretly vindicated in my irrational yet unshakeable beliefs that

  1. the laws of probability are broken, capricious horribleness reigning supreme over the universe,
  2. I’m despised by a large fraction of the world just for being who I am, and
  3. it’s only a matter of time until big, scary armed guys come for me, as they came for so many other nerdy misfits.

I almost wanted to say to the police: where have you been?  I’ve been expecting you my whole life.  And I wanted to say to Dana: you see??  see what I’ve been telling you all these years, about the nature of the universe we were born into?

Dana, for her part, was remonstrating with the officers that there must be some misunderstanding, that her husband was often absentminded but it’s completely impossible that he stole anything.  The officers brushed her away, told her to remove the kids from the situation.

“Are you gonna come clean?” one of the cops barked at me.  “We know you took it.”

“I didn’t take anything.”  Then I thought it over more.  “Or if somehow I did … then I’m certain that it would’ve been an accident, and I’d be more than happy to fix the…”

“Wait, if you did?  It sounds like you just confessed!”

“No, I definitely didn’t steal anything.  I’m just saying it’s possible that I might have mistakenly…”

“Your answers are rambling and all over the place.  Stop making up stories.  We know you did it.”

I’m not proud of myself for the next part, but the officers were so serious, and somehow I had to make them realize the sheer comical absurdity of what was happening.  “Look, I’m a computer science professor,” I said.  “I’ve never stolen a penny in my life, and it’s not something I’d ever…”

“Yeah, well I’m a police officer.  I’ve seen a lot in my thirty years in this job.  This is not about who you are, it’s about what you did.”

But what did I do?  After many more attempts to intimidate me, I was finally informed of the charge: “that smoothie place over there says you stole cash from their tip jar.”  Huh? How much?  One of the officers returned from the smoothie bar, and said, a bit sheepishly: “they say it was $4.”

Now a vague recollection came into sharper focus.  Yes, I had bought a berry smoothie for my daughter and a sparkling grapefruit juice for me.  I’d paid with a debit card, for reasons that I don’t remember, even though I normally pay cash.  My mind was elsewhere: on the missed flight, the lost suitcase, the brazen behavior of American Airlines (about which more later).  Then, completely forgetting I hadn’t paid cash this time, I looked down for my change: $4 in an unmarked plastic change cup.  I collected the change, put it in my wallet, then completely forgot about it.

After a minute, an employee angrily pointed down at a tray that the plastic cup was on (though not clearly at the cup itself), and said “hey, the tips go here!”  So I took a dollar from my wallet and put it on the tray.  I thought: this guy has some chutzpah, to demand a tip, and for an over-the-counter smoothie!  But whatever, he probably needs the dollar more than I do.  So if it will make him stop being angry…

But he was still angry.  He repeated: “this here is for tips!”

I said something to the effect of: “yeah, I know–that’s what you just told me, isn’t it?  So that’s why I just left you a tip!”  Sheesh.

At no point did he ever say, “you accidentally took from the tip jar,” or any other statement that would’ve clarified his meaning.

As I turned and walked away, I thought: yes, this is the strange world I was born into.  A world where people yell at me for not tipping at a smoothie bar–is that expected? I didn’t think it was–and then continue yelling even after I do.  But what did I expect?  Did I expect, as a nerdy outsider, to be able to buy normal people’s toleration with mere money?

As soon as I figured out what had happened, of course I offered to pay back the smoothie bar, not merely the $3 I still owed them, but $40 or whatever other amount would express my goodwill and compensate them for their trouble.  But the smoothie bar returned the $40 that I’d asked Dana to give them—I was unable to bring it myself on account of being handcuffed—and refused to press charges.  (In fact, apparently the employees hadn’t wanted to involve the police at all.  It was the manager, who hadn’t seen what happened, who’d insisted on it.)

So with no case, the police finally had no choice but to let me go–though not before giving me a stern lecture about never again putting my hands on stuff that’s not mine.


A week later, I’m still processing the experience.  In the rest of the post, I’d like to reflect on some lessons I think I learned from it.


First, it’s said that “a conservative is a liberal who’s been mugged; a liberal is a conservative who’s been arrested.”  It’s true: there are aspects of being arrested that are hard to understand until you’ve been through it.  While I’m white (well, insofar as Ashkenazim are), and while both officers who interrogated me happened to be African-Americans, what I went through further increased my sympathy for the many minority victims of aggressive policing.  Sitting in your armchair, it’s easy to think: in a liberal democracy, as long you know you did nothing wrong, even if you got arrested, frisked, detained, there’d probably be no real need to panic.  All you’d need to do is calmly clear up the misunderstanding and be back on your merry way.

But at least in my experience, an actual arrest isn’t like that.  The presumption of innocence, Miranda rights, all the things you might learn about in civics class—none of it seems to play any role.  From the very beginning, there’s an overwhelming presumption of guilt.  Everything you say gets interpreted as if you’re a red-handed criminal trying to fabricate a story, no matter how strained and how ludicrous such an interpretation might become.

And something strange happened: the officers seemed so certain I was guilty, that after only a few minutes I started to feel guilty.  I still had only a hazy sense of my “crime,” but I knew I was going to be punished for it, and I only hoped that the punishment wouldn’t tear me away from my family and previous life forever.

I came away from this incident with a visceral feel for just how easy it would be to procure a false confession from someone, which I didn’t have before but which will now stay with me as long as I live.


Second, it occurred to me that the sight of me, stuttering and potbellied complexity blogger, shackled and interrogated by armed policemen demanding that he confess to the theft of $3 from an airport stand, is a decent visual metaphor for much of my life.  If you doubt this, simply imagine Arthur Chu or Amanda Marcotte in place of the police officers.

It’s like: my accusers arrive on the scene committed to a specific, hostile theory of me: that I’m a petty thief of smoothie bars, let’s say, or a sexual-harassment-loving misogynist.  With all due modesty, people who know me might say that it’s not merely that I don’t fit the theory, that I happen to be innocent of the charge.  Rather, it’s that I’m one of the most astronomically, ridiculously unlikely people to fit the theory you could ever meet.  Not because I’m especially saintly, but simply because I already walk around all day feeling like my right to exist is conditional and might be revoked at any minute.  Breaking the normal people’s rules is the last thing on my agenda!  And yes, I still often feel that way, even as a professor with an endowed chair and awards and whatever.  The only times when I really relax, among strangers, is when everyone’s there to discuss ideas.

But my accusers don’t know any of that, or they refuse to believe it.  Everything I say gets interpreted in the light of the hostile theory, and therefore serves only as further confirmation of it.  Ironically—and this is key—the very unusual personality traits that make me so unlikely to be an offender, are also what throw off my accusers’ detection algorithms, and make them double down on their wrong theory.  When I’m trapped, I tend to fall back on the only tools I know: argument, openness, frank confession of my mistakes and failings, sometimes a little self-deprecating humor.  Unfortunately, I find this often backfires, as my accusers see in my vulnerability a golden opportunity to mount another wretched evildoer above their fireplace.

Or, to go even further out on a psychoanalytic limb: I sometimes get the sense that it gradually does dawn on my accusers that I’m not who they thought I was.  And then, far from prompting an apology, that realization seems to make my accusers even angrier, as if my throwing off their model of reality so badly, was an even worse offense than actually being guilty of whatever they thought!  A thief, a misogynist, they know how to handle.  But a living, breathing adversarial example for their worldview?

Dana, who watched the entire arrest, tells me that the central mistake I made was to try to reason with the police officers: “you say I took $3 that wasn’t mine?  If so, then I’m sure it was an accident, so let’s try to figure out what happened so we can fix it…”  In Dana’s view, what I saw as an earnest desire to get to the bottom of things, came across to grizzled cops only as evasiveness and guilt.  She says it would’ve been far better if I’d categorically denied: “no, I did not steal.  That’s completely absurd.  Please release me immediately.”

I’ve asked myself: how do you live in a world where, again and again, you can choose the hard right path over the easy wrong one, and then see your choice gleefully wielded against you?  Where you can spill your guts out to your accusers, in a desperate attempt to talk with them not as hardened warriors, but one confused and vulnerable human to another–and your reward is (to take one example) your picture in Salon above the headline “The Plight of the Bitter Nerd”?

The only way to live in such a world, as far as I can see, is to remind yourself that sometimes openness and vulnerability work.  In the course of my arrest, the two officers gradually differentiated themselves into a “good cop” and a “bad cop.”  While the “bad cop” treated me till the end like an unrepentant kleptomaniac being freed on a technicality, the “good cop,” who talked to me and Dana much more, became almost apologetic: “look man, when we get a call that someone stole money, we have to treat it like that’s the situation, you understand what I’m saying?  And then if it’s not, well then it’s not.”  Likewise, Arthur Chu recently tweeted that he’s “unhappy about [my] continued existence”–i.e., on a straightforward reading, that he wants me to die.  But I try to remind myself every day that the human race doesn’t consist solely of Arthur Chus (or Amanda Marcottes, or Lubos Motls, or SneerClub posters, or Paul Manaforts or Donald Trumps).  The world contains millions of women and men of every background and ideology who want actual dialogue, many of whom I’m lucky to count as friends, many of whom I met through this blog.  Vulnerability is possible because the world is not uniformly evil.


Third, I emerged from my arrest with a self-help technique that’s probably well-known to somebody, but that was new to me, and that I hope others will find as useful as I’m finding it.  Here it is: when something freakishly bad happens to you, draw a directed graph of all the known causes of the event, and the causes of the causes, and so forth as far back as you can trace them.  Also draw all the known measures that could have blocked the causal path leading to the bad event, and what prevented those measures from working or from being tried.

For example: why did I end up in handcuffs?  Firstly because, earlier in the day, Lily threw a temper tantrum that prevented us from packing and leaving for Logan Airport on time.  Because there was also heavy traffic on the way there.  Because we left from Harvard Square, and failed to factor in the extra 10 minutes to reach the airport, compared to if we’d left from MIT.  Because online check-in didn’t work.  Because when we did arrive, (barely) on time, the contemptuous American Airlines counter staff deliberately refused to check us in, chatting as we stewed impotently, so that we’d no longer be on time and they could legally give our seats away to others, and strand us in an airport with two young kids.  Because the only replacement flight was in a different terminal.  Because, in the stress of switching terminals–everything is stressful with two kids in an airport–I lost our suitcase.  Because the only shuttle to get back to the terminal went around the long way, and was slow as molasses, and by the time I returned our suitcase had been taken by the bomb squad.  Because the stress of such events bears down on me like an iron weight, and makes me unable to concentrate on the reality in front of me.  Because the guy at the smoothie counter and I failed to communicate.  Because the police chose to respond (or were trained to respond), not by politely questioning me to try to understand what had happened, but by handcuffing me and presuming guilt.

I actually drew the graph, filled a notebook page with it–and when I searched it for answers, neither I nor the world got off easily.  Looking over the strange chain of events that led to my arrest, I could find much to support my “default narrative,” that the laws of probability are broken and the universe is grotesquely awful.  But also, my belief in the universe’s grotesque awfulness clearly played a role in the events.  Had I been able maintain a calm demeanor, I would not have made so many mistakes.

Again and again, I screwed up.  Again and again, airport personnel responded to my honest mistakes with a maximum of cold bureaucracy rather than commonsense discussion: the booting from the flight, the bomb squad, the handcuffs.

We tend to think of bureaucracy as a mere nuisance, the person behind the counter at the Department of Motor Vehicles who makes you wait all day and then sends you home to get a different form of ID.  In my view, though, the bureaucratic impulse is one of the worst evils of which the human mind is capable.  It is, after all, the impulse that once sent trainloads of Jewish children to their deaths because that was the policy and there were no documents stating that any exception should be made in this case.  Today it’s the impulse that rounds up and deports people who’ve lived in the US for decades, sometimes served in the army, etc., and that separates screaming children from their parents.  To me, the mindset that willingly carries out such orders is almost more terrifying than the mindset that gives the orders in the first place.  I don’t mean to suggest, of course, that my arrest was even a trillionth as bad as those other things; at most I got a tiny, accidental taste of many less fortunate people’s daily reality.  But it’s worth remembering: every time you exercise official power over another person without even trying to talk it over first, clear up any honest misunderstandings, find out if there’s a reasonable explanation, you’re surrendering to one of the most destructive impulses in the history of civilization.

May we each strive to kill the bureaucrat in us and nurture the human being.


Unrelated Announcements:

I’m in Mexico City this week, to participate in a computer science and philosophy conference at UNAM and then give a broad quantum computing talk at CViCom 2018.  Because of this, responses to this post might be delayed.

(Update: But I’m having a wonderful time in Mexico!  Lots of delicious mole and horchata, and no arrests so far.  Today I gave my survey talk on P vs. NP.  I opened with the following icebreaker: “As a computer scientist speaking in a philosophy institute, I apologize that my talk will contain very little philosophy  Also, as an American speaking in Mexico, I apologize for our president.”)

My friend Elette Boyle asked me to announce that the 2018 CRYPTO conference, to be held in Santa Barbara, will be preceded by exciting workshops, including one that I’ll be speaking at myself entitled Beyond Crypto: A Theory Perspective.  Register now if you’re interested.

Huge congratulations to Costis Daskalakis, my former MIT colleague, for winning the Nevanlinna Prize for his work in algorithmic game theory!  While I don’t pretend to understand their work, congratulations to the four new Fields Medalists as well.

I put a new preprint online: Quantum Lower Bound for Approximate Counting Via Laurent Polynomials.

I’ve added a new blog to my blogroll: The Unit of Caring. I’ve been impressed by the author’s moral adeptness: when she addresses contentious debates among nerds, rationalists, feminists, SJWs, etc. etc., she often seems perfectly balanced on an atom-thin tightrope, even as some of us are plummetting left and right.

I forgot to mention this earlier, but I’m now a donor to the campaign of Beto O’Rourke, as he strives to unseat the quisling Ted Cruz in my adopted home state of Texas.  Americans: please consider donating as well!


Further Thoughts (Aug. 9):

  1. I wholeheartedly endorse an observation that many commenters (on this blog and elsewhere) made independently: that what really happened, is that I was forced to live out an episode of Seinfeld or Curb Your Enthusiasm.  To my detractors, I say the following: try for one minute to imagine how pathological, narcissistic, far outside the human norm, etc. etc. you could make Seinfeld or George or Kramer or Elaine seem, if their misadventures from any given episode were described and analyzed with clinical detachment.  (Or you were never a Seinfeld fan, then I guess this argument fails and we have nothing to say to each other.)
  2. I feel like some commenters are imposing their own after-the-fact knowledge (“c’mon, it was obviously a tip jar, he must be lying!”).  Dana, who’s generally more grounded than I am, saw their whole setup and agreed it was profoundly non-obvious that the tiny, unmarked plastic cup was supposed to be for tips, particularly to someone who was extremely stressed and not concentrating.  And when the employee later talked about tips, he didn’t indicate the cup so I didn’t make a connection.
  3. Most importantly: I wish to clarify that I don’t regard the police officers who handcuffed and interrogated me as having been “evil” in any sense.  I even took a liking to the “good cop,” the one who implicitly acknowledged the situation’s surreal absurdity by the end (although maybe that’s the whole point of a “good cop”?).  Having said that, I’m still rattled by the way the “bad cop” treated me as an unrepentant thief even to the end, even after the situation had been cleared up to everyone else’s satisfaction.  And I stand by my view that there was no need to handcuff me in front of my wife and young children, when I’d shown not a single subatomic particle of resistance.
  4. Speaking of which, let me now relate the most interesting and unexpected part of the reaction to my story.  Again and again, I found that fellow Americans, even nominally left-wing ones, sided with the police, said that I was crazy and guilty as charged and should’ve expected much worse, etc.  And again and again, commenters from Australia and New Zealand sided with me 300%, said that handcuffing someone over such a trivial mishap was a ludicrous overreaction, which would be totally unheard of in their countries and which confirms all the bad things they’ve heard about the US.  So maybe the rational conclusion is that I should be learning to enjoy vegemite in preparation for a move down under?

Summer recapitulates life

July 24th, 2018

Last week, I was back at the IAS in Princeton, to speak at a wonderful PITP summer school entitled “From Qubits to Spacetime,” co-organized by Juan Maldacena and Edward Witten. This week, I’ll be back in Waterloo, to visit old and new friends at the Perimeter Institute and Institute for Quantum Computing and give a couple talks.  Then, over the weekend, I’ll be back in Boston to see old friends, colleagues, and students.  After some other miscellaneous travel, I’ll then return to Austin in late August when the semester begins.  The particular sequence IAS → Waterloo → Boston → Austin is of course one that I’ve followed before, over a longer timescale.

Two quick announcements:

First, at the suggestion of reader Sanketh Menda, I’m thinking of holding a Shtetl-Optimized meetup in Waterloo this week.  Please send me an email if you’re interested, and we’ll figure out a time and place that work for everyone.

Second, many of the videos from the IAS summer school are now available, including mine: Part I and Part II.  I cover some basics of complexity theory, the complexity of quantum states and unitary transformations, the Harlow-Hayden argument about the complexity of turning a black hole event horizon into a firewall (with my refinement), and my and Lenny Susskind’s work on circuit complexity, wormholes, and AdS/CFT.  As a special bonus, check out the super-embarrassing goof at the beginning of my first lecture—claiming a mistaken symmetry of conditional entropy and even attributing it to Edward Witten’s lecture!  (But Witten, who I met for the first time on this visit, was kind enough to call my talk “lots of fun” anyway, and give me other positive comments, which I should put on my CV or something.)

Addendum: Many of the PITP videos are well worth watching!  As one example, I found Witten’s talks to be shockingly accessible.  I’d been to a previous talk of his involving Khovanov homology, but beyond the first few minutes, it went so far over my head that I couldn’t tell you how it was for its intended audience.  I’d also been to a popular talk of Witten’s on string theory, but that’s something he could do with only 3 awake brain cells.  In these talks, by contrast, Witten proves some basic inequalities of classical and quantum information theory, then proves the Reeh-Schlieder Theorem of quantum field theory and the Hawking and Penrose singularity theorems of GR, and finally uses quantum information theory to prove positive energy conditions from quantum field theory that are often needed to make statements about GR.

Customers who liked this quantum recommendation engine might also like its dequantization

July 12th, 2018

I’m in Boulder, CO right now for the wonderful Boulder summer school on quantum information, where I’ll be lecturing today and tomorrow on introductory quantum algorithms.  But I now face the happy obligation of taking a break from all the lecture-preparing and schmoozing, to blog about a striking new result by a student of mine—a result that will probably make an appearance in my lectures as well.

Yesterday, Ewin Tang—an 18-year-old who just finished a bachelor’s at UT Austin, and who will be starting a PhD in CS at the University of Washington in the fall—posted a preprint entitled A quantum-inspired classical algorithm for recommendation systems. Ewin’s new algorithm solves the following problem, very loosely stated: given m users and n products, and incomplete data about which users like which products, organized into a convenient binary tree data structure; and given also the assumption that the full m×n preference matrix is low-rank (i.e., that there are not too many ways the users vary in their preferences), sample some products that a given user is likely to want to buy.  This is an abstraction of the problem that’s famously faced by Amazon and Netflix, every time they tell you which books or movies you “might enjoy.”  What’s striking about Ewin’s algorithm is that it uses only polylogarithmic time: that is, time polynomial in log(m), log(n), the matrix rank, and the inverses of the relevant error parameters.  Admittedly, the polynomial involves exponents of 33 and 24: so, not exactly “practical”!  But it seems likely to me that the algorithm will run much, much faster in practice than it can be guaranteed to run in theory.  Indeed, if any readers would like to implement the thing and test it out, please let us know in the comments section!

As the title suggests, Ewin’s algorithm was directly inspired by a quantum algorithm for the same problem, which Kerenidis and Prakash (henceforth KP) gave in 2016, and whose claim to fame was that it, too, ran in polylog(m,n) time.  Prior to Ewin’s result, the KP algorithm was arguably the strongest candidate there was for an exponential quantum speedup for a real-world machine learning problem.  The new result thus, I think, significantly changes the landscape of quantum machine learning, by killing off one of its flagship applications.  (Note that whether KP gives a real exponential speedup was one of the main open problems mentioned in John Preskill’s survey on the applications of near-term quantum computers.)  At the same time, Ewin’s result yields a new algorithm that can be run on today’s computers, that could conceivably be useful to those who need to recommend products to customers, and that was only discovered by exploiting intuition that came from quantum computing. So I’d consider this both a defeat and a victory for quantum algorithms research.

This result was the outcome of Ewin’s undergraduate thesis project (!), which I supervised. A year and a half ago, Ewin took my intro quantum information class, whereupon it quickly became clear that I should offer this person an independent project.  So I gave Ewin the problem of proving a poly(m,n) lower bound on the number of queries that any classical randomized algorithm would need to make to the user preference data, in order to generate product recommendations for a given user, in exactly the same setting that KP had studied.  This seemed obvious to me: in their algorithm, KP made essential use of quantum phase estimation, the same primitive used in Shor’s factoring algorithm.  Without phase estimation, you seemed to be stuck doing linear algebra on the full m×n matrix, which of course would take poly(m,n) time.  But KP had left the problem open, I didn’t know how to solve it either, and nailing it down seemed like an obvious challenge, if we wanted to establish the reality of quantum speedups for at least one practical machine learning problem.  (For the difficulties in finding such speedups, see my essay for Nature Physics, much of which is still relevant even though it was written prior to KP.)

Anyway, for a year, Ewin tried and failed to rule out a superfast classical algorithm for the KP problem—eventually, of course, discovering the unexpected reason for the failure!  Throughout this journey, I served as Ewin’s occasional sounding board, but can take no further credit for the result.  Indeed, I admit that I was initially skeptical when Ewin told me that phase estimation did not look essential after all for generating superfast recommendations—that a classical algorithm could get a similar effect by randomly sampling a tiny submatrix of the user preference matrix, and then carefully exploiting a variant of a 2004 result by Frieze, Kannan, and Vempala.  So when I was in Berkeley a few weeks ago for the Simons quantum computing program, I had the idea of flying Ewin over to explain the new result to the experts, including Kerenidis and Prakash themselves.  After four hours of lectures and Q&A, a consensus emerged that the thing looked solid.  Only after that gauntlet did I advise Ewin to put the preprint online.

So what’s next?  Well, one obvious challenge is to bring down the running time of Ewin’s algorithm, and (as I mentioned before) to investigate whether or not it could give a practical benefit today.  A different challenge is to find some other example of a quantum algorithm that solves a real-world machine learning problem with only a polylogarithmic number of queries … one for which the exponential quantum speedup will hopefully be Ewin-proof, ideally even provably so!  The field is now wide open.  It’s possible that my Forrelation problem, which Raz and Tal recently used for their breakthrough oracle separation between BQP and PH, could be an ingredient in such a separation.

Anyway, there’s much more to say about Ewin’s achievement, but I now need to run to lecture about quantum algorithms like Simon’s and Shor’s, which do achieve provable exponential speedups in query complexity!  Please join me in offering hearty congratulations, see Ewin’s nicely-written paper for details, and if you have any questions for me or (better yet) Ewin, feel free to ask in the comments.


Update: On the Hacker News thread, some commenters are lamenting that such a brilliant mind as Ewin’s would spend its time figuring out how to entice consumers to buy even more products that they don’t need. I confess that that’s an angle that hadn’t even occurred to me: I simply thought that it was a beautiful question whether you actually need a quantum computer to sample the rows of a partially-specified low-rank matrix in polylogarithmic time, and if the application to recommendation systems helped to motivate that question, then so much the better. Now, though, I feel compelled to point out that, in addition to the potentially lucrative application to Amazon and Netflix, research on low-rank matrix sampling algorithms might someday find many other, more economically worthless applications as well.

Another Update: For those who are interested, streaming video of my quantum algorithms lectures in Boulder are now available:

You can also see all the other lectures here.

My Y Combinator podcast

June 29th, 2018

Here it is, recorded last week at Y Combinator’s office in San Francisco.  For regular readers of this blog, there will be a few things that are new—research projects I’ve been working on this year—and many things that are old.  Hope you enjoy it!  Thanks so much to Craig Cannon of Y Combinator for inviting me.

Associated with the podcast, Hacker News will be doing an AMA with me later today.  I’ll post a link to that when it’s available.  Update: here it is.

I’m at STOC’2018 TheoryFest in Los Angeles right now, where theoretical computer scientists celebrated the 50th anniversary of the conference that in some sense was the birthplace of the P vs. NP problem.  (Two participants in the very first STOC in 1969, Richard Karp and Allan Borodin, were on a panel to share their memories, along with Ronitt Rubinfeld and Avrim Blum, who joined the action in the 1980s.)  There’s been a great program this year—if you’d like to ask me about it, maybe do so in the comments of this post rather than in the AMA.