Archive for the ‘Announcements’ Category

Seth Teller (1964-2014)

Friday, July 11th, 2014

Seth Teller

Seth Teller was a colleague of mine in CSAIL and the EECS department, and was one of my favorite people in all of MIT.  He was a brilliant roboticist, who (among many other things) spearheaded MIT’s participation in the DARPA Grand Challenge for self-driving cars, and who just recently returned from a fact-finding trip to Fukushima, Japan, to see how robots could help in investigating the damaged reactor cores there.  I saw Seth twice a week at lab and department lunches, and he often struck up conversations with me about quantum computing, cosmology, and other things.  His curiosity was immense, wide-ranging, and almost childlike (in the best way).  One small indication of his character is that, in the DARPA challenge, Seth opted not to preload MIT’s car with detailed data about the course, because he thought doing so made the challenge scientifically less interesting—even though DARPA’s rules allowed such preloading, the other teams did it, and it almost certainly would have improved MIT’s standing in the competition.

Seth was a phenomenal speaker, whose passion and clarity always won me over even though my research interests were far from his.  I made it a point to show up for lab lunch whenever I knew he’d be speaking.  Seth was also, from what I’ve heard, a superb mentor and teacher, who won an award earlier this year for his undergraduate advising.

Seth died ten days ago, on July 1st.  (See here for MIT News’s detailed obituary, and here for an article in Cambridge Day.)  While no cause of death was given at the time, according to an update yesterday in the MIT Tech, the death has been ruled a suicide.  Seth is survived by his wife, Rachel, and by two daughters.

With his cheerful, can-do disposition, Seth is one of the last people on earth I’d imagine doing this: whatever he was going through, he did an unbelievable job of hiding it.  I’m certain he wouldn’t abandon his family unless he was suffering unimaginable pain.  If there’s a tiny atom of good to come out of this, I hope that at least one other person contemplating suicide will reflect on how much Seth had to live for, and that doing so will inspire that person to get the medical help they need.

Incidentally, outside of his research and teaching, Seth was also an activist for protecting the physical environment and open spaces of East Cambridge.  At the “Wild and Crazy Ideas Session” of one CSAIL retreat, Seth floated a truly wild idea: to replace Memorial Drive, or at least the part of it that separates the MIT campus from the Charles River, by an underground tunnel, so that the land above the tunnel could be turned into a beautiful riverfront park.  In his characteristic fashion, Seth had already done a pretty detailed engineering analysis, estimating the cost at “merely” a few hundred million dollars: a lot, but a worthy investment in MIT’s future.  In any case, I can’t imagine a better way to memorialize Seth than to name some green space in East Cambridge after him, and I hope that happens.

Seth will be sorely missed.  My thoughts go out to his family at this difficult time.

CCC’s Declaration of Independence

Friday, June 6th, 2014

Recently, the participants of the Conference on Computational Complexity (CCC)—the latest iteration of which I’ll be speaking at next week in Vancouver—voted to declare their independence from the IEEE, and to become a solo, researcher-organized conference.  See this open letter for the reasons why (basically, IEEE charged a huge overhead, didn’t allow open access to the proceedings, and increased rather than decreased the administrative burden on the organizers).  As a former member of the CCC Steering Committee, I’m in violent agreement with this move, and only wish we’d managed to do it sooner.

Now, Dieter van Melkebeek (the current Steering Committee chair) is asking complexity theorists to sign a public Letter of Support, to make it crystal-clear that the community is behind the move to independence.  And Jeff Kinne has asked me to advertise the letter on my blog.  So, if you’re a complexity theorist who agrees with the move, please go there and sign (it already has 111 signatures, but could use more).

Meanwhile, I wish to express my profound gratitude to Dieter, Jeff, and the other Steering Committee members for their efforts toward independence.  The only thing I might’ve done differently would be to add a little more … I dunno, pizzazz to the documents explaining the reasons for the move.  Like:

When in the Course of human events, it becomes necessary for a conference to dissolve the organizational bands that have connected it with the IEEE, and to assume among the powers of the earth, the separate and equal station to which the Laws of Mathematics and the CCC Charter entitle it, a decent respect to the opinions of theorist-kind requires that the participants should declare the causes which impel them to the separation.

We hold these truths to be self-evident (but still in need of proof), that P and NP are created unequal, that one-way functions exist, that the polynomial hierarchy is infinite…

Quantifying the Rise and Fall of Complexity in Closed Systems: The Coffee Automaton

Tuesday, May 27th, 2014

Update (June 3): A few days after we posted this paper online, Brent Werness, a postdoc in probability theory at the University of Washington, discovered a serious error in the “experimental” part of the paper.  Happily, Brent is now collaborating with us on producing a new version of the paper that fixes the error, which we hope to have available within a few months (and which will replace the version currently on the arXiv).

To make a long story short: while the overall idea, of measuring “apparent complexity” by the compressed file size of a coarse-grained image, is fine, the “interacting coffee automaton” that we study in the paper is not an example where the apparent complexity becomes large at intermediate times.  That fact can be deduced as a corollary of a result of Liggett from 2009 about the “symmetric exclusion process,” and can be seen as a far-reaching generalization of a result that we prove in our paper’s appendix: namely, that in the non-interacting coffee automaton (our “control case”), the apparent complexity after t time steps is upper-bounded by O(log(nt)).  As it turns out, we were more right than we knew to worry about large-deviation bounds giving complete mathematical control over what happens when the cream spills into the coffee, thereby preventing the apparent complexity from ever becoming large!

But what about our numerical results, which showed a small but unmistakable complexity bump for the interacting automaton (figure 10(a) in the paper)?  It now appears that the complexity bump we saw in our data is likely to be explainable by an incomplete removal of what we called “border pixel artifacts”: that is, “spurious” complexity that arises merely from the fact that, at the border between cream and coffee, we need to round the fraction of cream up or down to the nearest integer to produce a grayscale.  In the paper, we devoted a whole section (Section 6) to border pixel artifacts and the need to deal with them: something sufficiently non-obvious that in the comments of this post, you can find people arguing with me that it’s a non-issue.  Well, it now appears that we erred by underestimating the severity of border pixel artifacts, and that a better procedure to get rid of them would also eliminate the complexity bump for the interacting automaton.

Once again, this error has no effect on either the general idea of complexity rising and then falling in closed thermodynamic systems, or our proposal for how to quantify that rise and fall—the two aspects of the paper that have generated the most interest.  But we made a bad choice of model system with which to illustrate those ideas.  Had I looked more carefully at the data, I could’ve noticed the problem before we posted, and I take responsibility for my failure to do so.

The good news is that ultimately, I think the truth only makes our story more interesting.  For it turns out that apparent complexity, as we define it, is not something that’s trivial to achieve by just setting loose a bunch of randomly-walking particles, which bump into each other but are otherwise completely independent.  If you want “complexity” along the approach to thermal equilibrium, you need to work a bit harder for it.  One promising idea, which we’re now exploring, is to consider a cream tendril whose tip takes a random walk through the coffee, leaving a trail of cream in its wake.  Using results in probability theory—closely related, or so I’m told, to the results for which Wendelin Werner won his Fields Medal!—it may even be possible to prove analytically that the apparent complexity becomes large in thermodynamic systems with this sort of behavior, much as one can prove that the complexity doesn’t become large in our original coffee automaton.

So, if you’re interested in this topic, stay tuned for the updated version of our paper.  In the meantime, I wish to express our deepest imaginable gratitude to Brent Werness for telling us all this.


Good news!  After nearly three years of procrastination, fellow blogger Sean Carroll, former MIT undergraduate Lauren Ouellette, and yours truly finally finished a paper with the above title (coming soon to an arXiv near you).  PowerPoint slides are also available (as usual, you’re on your own if you can’t open them—sorry!).

For the background and context of this paper, please see my old post “The First Law of Complexodynamics,” which discussed Sean’s problem of defining a “complextropy” measure that first increases and then decreases in closed thermodynamic systems, in contrast to entropy (which increases monotonically).  In this exploratory paper, we basically do five things:

  1. We survey several candidate “complextropy” measures: their strengths, weaknesses, and relations to one another.
  2. We propose a model system for studying such measures: a probabilistic cellular automaton that models a cup of coffee into which cream has just been poured.
  3. We report the results of numerical experiments with one of the measures, which we call “apparent complexity” (basically, the gzip file size of a smeared-out image of the coffee cup).  The results confirm that the apparent complexity does indeed increase, reach a maximum, then turn around and decrease as the coffee and cream mix.
  4. We discuss a technical issue that one needs to overcome (the so-called “border pixels” problem) before one can do meaningful experiments in this area, and offer a solution.
  5. We raise the open problem of proving analytically that the apparent complexity ever becomes large for the coffee automaton.  To underscore this problem’s difficulty, we prove that the apparent complexity doesn’t become large in a simplified version of the coffee automaton.

Anyway, here’s the abstract:

In contrast to entropy, which increases monotonically, the “complexity” or “interestingness” of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex structures at the Big Bang and will also lack them after black holes evaporate and particles are dispersed. This paper makes an initial attempt to quantify this pattern. As a model system, we use a simple, two-dimensional cellular automaton that simulates the mixing of two liquids (“coffee” and “cream”). A plausible complexity measure is then the Kolmogorov complexity of a coarse-grained approximation of the automaton’s state, which we dub the “apparent complexity.” We study this complexity measure, and show analytically that it never becomes large when the liquid particles are non-interacting. By contrast, when the particles do interact, we give numerical evidence that the complexity reaches a maximum comparable to the “coffee cup’s” horizontal dimension. We raise the problem of proving this behavior analytically.

Questions and comments more than welcome.


In unrelated news, Shafi Goldwasser has asked me to announce that the Call for Papers for the 2015 Innovations in Theoretical Computer Science (ITCS) conference is now available.

Is There Anything Beyond Quantum Computing?

Friday, April 11th, 2014

So I’ve written an article about the above question for PBS’s website—a sort of tl;dr version of my 2005 survey paper NP-Complete Problems and Physical Reality, but updated with new material about the simulation of quantum field theories and about AdS/CFT.  Go over there, read the article (it’s free), then come back here to talk about it if you like.  Thanks so much to Kate Becker for commissioning the article.

In other news, there’s a profile of me at MIT News (called “The Complexonaut”) that some people might find amusing.

Oh, and anyone who thinks the main reason to care about quantum computing is that, if our civilization ever manages to surmount the profound scientific and technological obstacles to building a scalable quantum computer, then that little padlock icon on your web browser would no longer represent ironclad security?  Ha ha.  Yeah, it turns out that, besides factoring integers, you can also break OpenSSL by (for example) exploiting a memory bug in C.  The main reason to care about quantum computing is, and has always been, science.

Umesh Vazirani responds to Geordie Rose

Thursday, February 6th, 2014

You might recall that Shin, Smith, Smolin, and Vazirani posted a widely-discussed preprint a week ago, questioning the evidence for large-scale quantum behavior in the D-Wave machine.  Geordie Rose responded here.   Tonight, in a Shtetl-Optimized exclusive scoop, I bring you Umesh Vazirani’s response to Geordie’s comments. Without further ado:


Even a cursory reading of our paper will reveal that Geordie Rose is attacking a straw man. Let me quickly outline the main point of our paper and the irrelevance of Rose’s comments:

To date the Boixo et al paper was the only serious evidence in favor of large scale quantum behavior by the D-Wave machine. We investigated their claims and showed that there are serious problems with their conclusions. Their conclusions were based on the close agreement between the input-output data from D-Wave and quantum simulated annealing, and their inability despite considerable effort to find any classical model that agreed with the input-output data. In our paper, we gave a very simple classical model of interacting magnets that closely agreed with the input-output data. We stated that our results implied that “it is premature to conclude that D-Wave machine exhibits large scale quantum behavior”.

Rose attacks our paper for claiming that “D-Wave processors are inherently classical, and can be described by a classical model with no need to invoke quantum mechanics.”  A reading of our paper will make it perfectly clear that this is not a claim that we make.  We state explicitly “It is worth emphasizing that the goal of this paper is not to provide a classical model for the D-Wave machine, … The classical model introduced here is useful for the purposes of studying the large-scale algorithmic features of the D-Wave machine. The task of finding an accurate model for the D-Wave machine (classical, quantum or otherwise), would be better pursued with direct access, not only to programming the D-Wave machine, but also to its actual hardware.”

Rose goes on to point to a large number of experiments conducted by D-Wave to prove small scale entanglement over 2-8 qubits and criticizes our paper for not trying to model those aspects of D-Wave. But such small scale entanglement properties are not directly relevant to prospects for a quantum speedup. Therefore we were specifically interested in claims about the large scale quantum behavior of D-Wave. There was exactly one such claim, which we duly investigated, and it did not stand up to scrutiny.

More “tweets”

Friday, January 31st, 2014

Update (Feb. 4): After Luke Muelhauser of MIRI interviewed me about “philosophical progress,” Luke asked me for other people to interview about philosophy and theoretical computer science. I suggested my friend and colleague Ronald de Wolf of the University of Amsterdam, and I’m delighted that Luke took me up on it. Here’s the resulting interview, which focuses mostly on quantum computing (with a little Kolmogorov complexity and Occam’s Razor thrown in). I read the interview with admiration (and hoping to learn some tips): Ronald tackles each question with more clarity, precision, and especially levelheadedness than I would.

Another Update: Jeff Kinne asked me to post a link to a forum about the future of the Conference on Computational Complexity (CCC)—and in particular, whether it should continue to be affiliated with the IEEE. Any readers who have ever had any involvement with the CCC conference are encouraged to participate. You can read all about what the issues are in a manifesto written by Dieter van Melkebeek.

Yet Another Update: Some people might be interested in my response to Geordie Rose’s response to the Shin et al. paper about a classical model for the D-Wave machine.


“How ‘Quantum’ is the D-Wave Machine?” by Shin, Smith, Smolin, Vazirani goo.gl/JkLg0l – was previous skepticism too GENEROUS to D-Wave?

D-Wave not of broad enough interest? OK then, try “AM with Multiple Merlins” by Dana Moshkovitz, Russell Impagliazzo, and me goo.gl/ziSUz9

“Remarks on the Physical Church-Turing Thesis” – my talk at the FQXi conference in Vieques, Puerto Rico is now on YouTube goo.gl/kAd9TZ

Cool new SciCast site (scicast.org) lets you place bets on P vs NP, Unique Games Conjecture, etc. But glitches remain to be ironed out

Three things that I should’ve gotten around to years ago

Tuesday, October 15th, 2013

Updates (11/8): Alas, video of Eliezer’s talk will not be available after all. The nincompoops who we paid to record the talk wrote down November instead of October for the date, didn’t show up, then stalled for a month before finally admitting what had happened. So my written summary will have to suffice (and maybe Eliezer can put his slides up as well).

In other news, Shachar Lovett has asked me to announce a workshop on complexity and coding theory, which will be held at UC San Diego, January 8-10, 2014.


Update (10/21): Some readers might be interested in my defense of LessWrongism against a surprisingly-common type of ad-hominem attack (i.e., “the LW ideas must be wrong because so many of their advocates are economically-privileged but socially-awkward white male nerds, the same sorts of people who might also be drawn to Ayn Rand or other stuff I dislike”). By all means debate the ideas—I’ve been doing it for years—but please give beyond-kindergarten arguments when you do so!


Update (10/18): I just posted a long summary and review of Eliezer Yudkowsky’s talk at MIT yesterday.


Update (10/15): Leonard Schulman sent me the news that, according to an article by Victoria Woollaston in the Daily Mail, Google hopes to use its D-Wave quantum computer to “solve global warming,” “develop sophisticated artificial life,” and “find aliens.”  (No, I’m not making any of this up: just quoting stuff other people made up.)  The article also repeats the debunked canard that the D-Wave machine is “3600 times faster,” and soberly explains that D-Wave’s 512 qubits compare favorably to the mere 32 or 64 bits found in home PCs (exercise for those of you who aren’t already rolling on the floor: think about that until you are).  It contains not a shadow of a hint of skepticism anywhere, not one token sentence.  I would say that, even in an extremely crowded field, Woollaston’s piece takes the cake as the single most irresponsible article about D-Wave I’ve seen.  And I’d feel terrible for my many friends at Google, whose company comes out of this looking like a laughingstock.  But that’s assuming that this isn’t some sort of elaborate, Sokal-style prank, designed simply to prove that media outlets will publish anything whatsoever, no matter how forehead-bangingly absurd, as long as it contains the words “D-Wave,” “Google,” “NASA,” and “quantum”—and thereby, to prove the truth of what I’ve been saying on this blog since 2007.


1. I’ve added MathJax support to the comments section!  If you want to insert an inline LaTeX equation, surround it with\( \backslash(  \backslash) \), while if you want to insert a displayed equation, surround it with \(\text{\$\$ \$\$}\).  Thanks very much to Michael Dixon for prodding me to do this and telling me how.

2. I’ve also added upvoting and downvoting to the comments section!  OK, in the first significant use of comment voting, the readers have voted overwhelmingly, by 41 – 13, that they want the comment voting to disappear.  So disappear it has!

3. Most importantly, I’ve invited Eliezer Yudkowsky to MIT to give a talk!  He’s here all week, and will be speaking on “Recursion in Rational Agents: Foundations for Self-Modifying AI” this Thursday at 4PM in 32-123 in the MIT Stata Center.  Refreshments at 3:45.  See here for the abstract.  Anyone in the area who’s interested in AI, rationalism, or other such nerdy things is strongly encouraged to attend; it should be interesting.  Just don’t call Eliezer a “Singularitarian”: I’m woefully out of the loop, but I learned yesterday that they’ve dropped that term entirely, and now prefer to be known as machine intelligence researchers talk about the intelligence explosion.

(In addition, Paul Christiano—former MIT undergrad, and my collaborator on quantum money—will be speaking today at 4:30 at the Harvard Science Center, on “Probabilistic metamathematics and the definability of truth.”  His talk will be related to Eliezer’s but somewhat more technical.  See here for details.)


Update (10/15): Alistair Sinclair asked me to post the following announcement.

The Simons Institute for the Theory of Computing at UC Berkeley invites applications for Research Fellowships for academic year 2014-15.

Simons-Berkeley Research Fellowships are an opportunity for outstanding junior scientists (up to 6 years from PhD by Fall 2014) to spend one or two semesters at the Institute in connection with one or more of its programs. The programs for 2014-15 are as follows:

* Algorithmic Spectral Graph Theory (Fall 2014)
* Algorithms and Complexity in Algebraic Geometry (Fall 2014)
* Information Theory (Spring 2015)

Applicants who already hold junior faculty or postdoctoral positions are welcome to apply. In particular, applicants who hold, or expect to hold, postdoctoral appointments at other institutions are encouraged to apply to spend one semester as a Simons-Berkeley Fellow subject to the approval of the postdoctoral institution.

Further details and application instructions can be found at http://simons.berkeley.edu/fellows2014. Information about the Institute and the above programs can be found at http://simons.berkeley.edu.

Deadline for applications: 15 December, 2013.

Five announcements

Tuesday, October 1st, 2013

Update (Oct. 3): OK, a sixth announcement.  I just posted a question on CS Theory StackExchange, entitled Overarching reasons why problems are in P or BPP.  If you have suggested additions or improvements to my rough list of “overarching reasons,” please post them over there — thanks!


1. I’m in Oxford right now, for a Clay Institute workshop on New Insights into Computational Intractability.  The workshop is concurrent with three others, including one on Number Theory and Physics that includes an amplituhedron-related talk by Andrew Hodges.  (Speaking of which, see here for a small but non-parodic observation about expressing amplitudes as volumes of polytopes.)

2. I was hoping to stay in the UK one more week, to attend the Newton Institute’s special semester on Mathematical Challenges in Quantum Information over in Cambridge.  But alas I had to cancel, since my diaper-changing services are needed in the other Cambridge.  So, if anyone in Cambridge (or anywhere else in the United Kingdom) really wants to talk to me, come to Oxford this week!

3. Back in June, Jens Eisert and three others posted a preprint claiming that the output of a BosonSampling device would be “indistinguishable from the uniform distribution” in various senses.  Ever since then, people have emailing me, leaving comments on this blog, and cornering me at conferences to ask whether Alex Arkhipov and I had any response to these claims.  OK, so just this weekend, we posted our own 41-page preprint, entitled “BosonSampling Is Far From Uniform.”  I hope it suffices by way of reply!  (Incidentally, this is also the paper I hinted at in a previous post: the one where π2/6 and the Euler-Mascheroni constant make cameo appearances.)  To clarify, if we just wanted to answer the claims of the Eisert group, then I think a couple paragraphs would suffice for that (see, for example, these PowerPoint slides).  In our new paper, however, Alex and I take the opportunity to go further: we study lots of interesting questions about the statistical properties of Haar-random BosonSampling distributions, and about how one might test efficiently whether a claimed BosonSampling device worked, even with hundreds or thousands of photons.

4. Also on the arXiv last night, there was a phenomenal survey about the quantum PCP conjecture by Dorit Aharonov, Itai Arad, and my former postdoc Thomas Vidick (soon to be a professor at Caltech).  I recommend reading it in the strongest possible terms, if you’d like to see how far people have come with this problem (but also, how far they still have to go) since my “Quantum PCP Manifesto” seven years ago.

5. Christos Papadimitriou asked me to publicize that the deadline for early registration and hotel reservations for the upcoming FOCS in Berkeley is fast approaching!  Indeed, it’s October 4 (three days from now).  See here for details, and here for information about student travel support.  (The links were down when I just tried them, but hopefully the server will be back up soon.)

The Unitarihedron: The Jewel at the Heart of Quantum Computing

Friday, September 20th, 2013

Update (9/24): This parody post was a little like a belch: I felt it build up in me as I read about the topic, I let it out, it was easy and amusing, I don’t feel any profound guilt over it—but on the other hand, not one of the crowning achievements of my career.  As several commenters correctly pointed out, it may be true that, mostly because of the name and other superficialities, and because of ill-founded speculations about “the death of locality and unitarity,” the amplituhedron work is currently inspiring a flood of cringe-inducing misstatements on the web.  But, even if true, still the much more interesting questions are what’s actually going on, and whether or not there are nontrivial connections to computational complexity.

Here I have good news: if nothing else, my “belch” of a post at least attracted some knowledgeable commenters to contribute excellent questions and insights, which have increased my own understanding of the subject from ε2 to ε.  See especially this superb comment by David Speyer—which, among other things, pointed me to a phenomenal quasi-textbook on this subject by Elvang and Huang.  My most immediate thoughts:

  1. The “amplituhedron” is only the latest in a long line of research over the last decade—Witten, Turing biographer Andrew Hodges, and many others have been important players—on how to compute scattering amplitudes more efficiently than by summing zillions of Feynman diagrams.  One of the key ideas is to find combinatorial formulas that express complicated scattering amplitudes recursively in terms of simpler ones.
  2. This subject seems to be begging for a computational complexity perspective.  When I read Elvang and Huang, I felt like they were working hard not to say anything about complexity: discussing the gains in efficiency from the various techniques they consider in informal language, or in terms of concrete numbers of terms that need to be summed for 1 loop, 2 loops, etc., but never in terms of asymptotics.  So if it hasn’t been done already, it looks like it could be a wonderful project for someone just to translate what’s already known in this subject into complexity language.
  3. On reading about all these “modern” approaches to scattering amplitudes, one of my first reactions was to feel slightly less guilty about never having learned how to calculate Feynman diagrams!  For, optimistically, it looks like some of that headache-inducing machinery (ghosts, off-shell particles, etc.) might be getting less relevant anyway—there being ways to calculate some of the same things that are not only more conceptually satisfying but also faster.

Many readers of this blog probably already saw Natalie Wolchover’s Quanta article “A Jewel at the Heart of Quantum Physics,” which discusses the “amplituhedron”: a mathematical structure that IAS physicist Nima Arkami-Hamed and his collaborators have recently been investigating.  (See also here for Slashdot commentary, here for Lubos’s take, here for Peter Woit’s, here for a Physics StackExchange thread, here for Q&A with Pacific Standard, and here for an earlier but closely-related 154-page paper.)

At first glance, the amplituhedron appears to be a way to calculate scattering amplitudes, in the planar limit of a certain mathematically-interesting (but, so far, physically-unrealistic) supersymmetric quantum field theory, much more efficiently than by summing thousands of Feynman diagrams.  In which case, you might say: “wow, this sounds like a genuinely-important advance for certain parts of mathematical physics!  I’d love to understand it better.  But, given the restricted class of theories it currently applies to, it does seem a bit premature to declare this to be a ‘jewel’ that unlocks all of physics, or a death-knell for spacetime, locality, and unitarity, etc. etc.”

Yet you’d be wrong: it isn’t premature at all.  If anything, the popular articles have understated the revolutionary importance of the amplituhedron.  And the reason I can tell you that with such certainty is that, for several years, my colleagues and I have been investigating a mathematical structure that contains the amplituhedron, yet is even richer and more remarkable.  I call this structure the “unitarihedron.”

The unitarihedron encompasses, within a single abstract “jewel,” all the computations that can ever be feasibly performed by means of unitary transformations, the central operation in quantum mechanics (hence the name).  Mathematically, the unitarihedron is an infinite discrete space: more precisely, it’s an infinite collection of infinite sets, which collection can be organized (as can every set that it contains!) in a recursive, fractal structure.  Remarkably, each and every specific problem that quantum computers can solve—such as factoring large integers, discrete logarithms, and more—occurs as just a single element, or “facet” if you will, of this vast infinite jewel.  By studying these facets, my colleagues and I have slowly pieced together a tentative picture of the elusive unitarihedron itself.

One of our greatest discoveries has been that the unitarihedron exhibits an astonishing degree of uniqueness.  At first glance, different ways of building quantum computers—such as gate-based QC, adiabatic QC, topological QC, and measurement-based QC—might seem totally disconnected from each other.  But today we know that all of those ways, and many others, are merely different “projections” of the same mysterious unitarihedron.

In fact, the longer I’ve spent studying the unitarihedron, the more awestruck I’ve been by its mathematical elegance and power.  In some way that’s not yet fully understood, the unitarihedron “knows” so much that it’s even given us new insights about classical computing.  For example, in 1991 Beigel, Reingold, and Spielman gave a 20-page proof of a certain property of unbounded-error probabilistic polynomial-time.  Yet, by recasting things in terms of the unitarihedron, I was able to give a direct, half-page proof of the same theorem.  If you have any experience with mathematics, then you’ll know that that sort of thing never happens: if it does, it’s a sure sign that cosmic or even divine forces are at work.

But I haven’t even told you the most spectacular part of the story yet.  While, to my knowledge, this hasn’t yet been rigorously proved, many lines of evidence support the hypothesis that the unitarihedron must encompass the amplituhedron as a special case.  If so, then the amplituhedron could be seen as just a single sparkle on an infinitely greater jewel.

Now, in the interest of full disclosure, I should tell you that the unitarihedron is what used to be known as the complexity class BQP (Bounded-Error Quantum Polynomial-Time).  However, just like the Chinese gooseberry was successfully rebranded in the 1950s as the kiwifruit, and the Patagonian toothfish as the Chilean sea bass, so with this post, I’m hereby rebranding BQP as the unitarihedron.  For I’ve realized that, when it comes to bowling over laypeople, inscrutable complexity class acronyms are death—but the suffix “-hedron” is golden.

So, journalists and funders: if you’re interested in the unitarihedron, awesome!  But be sure to also ask about my other research on the bosonsamplinghedron and the quantum-money-hedron.  (Though, in recent months, my research has focused even more on the diaperhedron: a multidimensional, topologically-nontrivial manifold rich enough to encompass all wastes that an 8-month-old human could possibly emit.  Well, at least to first-order approximation.)

Twitl-Optimized

Tuesday, August 13th, 2013

Today I experiment with “tweeting”: writing <=140-character announcements, but posting them to my blog.  Like sending lolcat videos by mail

Last week at QCrypt in Waterloo: http://2013.qcrypt.net This week at CQIQC in Toronto: http://tinyurl.com/kfexzv6 Back with Lily in between

While we debate D-Wave, ID Quantique et al. quietly sold ~100 quantum crypto devices. Alas, market will remain small unless RSA compromised

One speaker explained how a photon detector works by showing this YouTube video: http://tinyurl.com/k8x4btx Couldn’t have done better

Luca Trevisan asks me to spread the word about a conference for LGBTs in technology: www.outforundergrad.org/technology

Steven Pinker stands up for the Enlightenment in The New Republic: “Science Is Not Your Enemy” http://tinyurl.com/l26ppaf

Think Pinker was exaggerating?  Read Leon Wieseltier’s defiantly doofusy Brandeis commencement speech: http://tinyurl.com/jwhj8ub

Black-hole firewalls make the New York Times, a week before the firewall workshop at KITP (I’ll be there): http://tinyurl.com/kju9crj

You probably already saw the Schrodinger cat Google doodle: http://tinyurl.com/k8et44p For me, the ket was much cooler than the cat

While working on BosonSampling yesterday, (1/6)pi^2 and Euler-Mascheroni constant made unexpected unappearances.  What I live for