Ever since the movie Transcendence came out, it seems like the idea of the ‘technological singularity‘ has been in the air. Maybe it’s because I run in an unorthodox circle of deep thinkers, but over the past couple months, I’ve been roped into three conversations related to this topic. The conversations usually end with some version of “ah shucks, machine learning is developing at a fast rate, so we are all doomed. And have you seen those deep learning videos? Computers are learning to play 35 year old video games?! Put this on an exponential trend and we are D00M3d!”

So what is the technological singularity? My personal translation is: are we on the verge of narcissistic flesh-eating robots stealing our lunch money while we commute to the ‘special school for slow sapiens’?

This is an especially hyperbolic view, and I want to be clear to distinguish ‘machine learning‘ from ‘artificial consciousness.’ The former seems poised for explosive growth but the latter seems to require breakthroughs in our understanding of the fundamental science. The two concepts are often equated when defining the singularity, or even artificial intelligence, but I think it’s important to distinguish these two concepts. Without distinguishing them, people sometimes make the faulty association: machine_learning_progress=>AI_progress=>artificial_consciousness_progress.

I’m generally an optimistic person, but on this topic, I’m especially optimistic about humanity’s status as machine overlords for at least the next ~100 years. Why am I so optimistic? Quantum information (QI) theory has a secret weapon. And that secret weapon is obviously Scott Aaronson (and his brilliant friends+colleagues+sidekicks; especially Alex Arkhipov in this case.) Over the past few years they have done absolutely stunning work related to understanding the computational complexity of linear optics. They colloquially call this work Boson sampling.

What I’m about to say is probably extremely obvious to most people in the QI community, but I’ve had conversations with exquisitely well educated people–including a Nobel Laureate–and very few people outside of QI seem to be aware of Aaronson and Arkhipov’s (AA’s) results. Here’s a thought experiment: does a computer have all the hardware required to simulate the human brain? For a long time, many people thought yes, and they even created a more general hypothesis called the “extended Church-Turring hypothesis.”

An interdisciplinary group of scientists has long speculated that quantum mechanics may stand as an obstruction towards this hypothesis. In particular, it’s believed that quantum computers would be able to efficiently solve some problems that are hard for a classical computer. These results led people, possibly Roger Penrose most notably, to speculate that consciousness may leverage these quantum effects. However, for many years, there was a huge gap between quantum experiments and the biology of the human brain. If I ever broached this topic at a dinner party, my biologist friends would retort: “but the brain is warm and wet, good luck managing decoherence.” And this seems to be a valid argument against the brain as a universal quantum computer. However, one of AA’s many breakthroughs is that they paved the way towards showing that a rather elementary physical system can gain speed-ups on certain classes of problems over classical computers. Maybe the human brain has a Boson sampling module?

More specifically, AA’s physical setup involves being able to: generate identical photons; send them through a network of beamsplitters, phase shifters and mirrors; and then count the number of photons in each mode through ‘nonadaptive’ measurements. This setup computes the permanent of a matrix, which is known to be a hard problem classically. AA showed that if there exists a polynomial-time classical algorithm which samples from the same probability distribution, then the polynomial hierarchy would collapse to the third level (this last statement would be very bad for theoretical computer science and therefore for humans; ergo probably not true.) I should also mention that when I learned the details of these results, during Scott’s lectures this past January at the Israeli Insitute of Advanced Studies’ Winter School in Theoretical Physics, that there was one step in the proof which was not rigorous. Namely, they rely on a conjecture in random matrix theory–but at least they have simulations indicating the conjecture should be true.

Nitty gritty details aside, I find the possibility that this simple system is gaining a classical speed-up compelling in the conversation about consciousness. Especially considering that finding permanents is actually useful for some combinatorics problems. When you combine this with Nature’s mischievous manner of finding ways to use the tools available to it, it seems plausible to me that the brain is using something like Boson sampling for at least one non-trivial task towards consciousness. If not Boson sampling, then maybe ‘Fermion smashing’ or ‘minimal surface finding’ or some other crackpottery words I’m coming up with on the fly. The point is, this result opens a can of worms.

AA’s results have bred new life into my optimism towards humanity’s ability to rule the lands and interwebs for at least the next few decades. Or until some brilliant computer scientist proves that human consciousness is in P. If nothing else, it’s a fun topic for wild dinner party speculation.

I spent the past two weeks profoundly confused. I’ve been trying to get up to speed on this firewall business and I wanted to understand the picture below.

[Technical paragraph that you can skip.] I’ve been trying to understand why the picture on the left is correct, even though my intuition said the middle picture should be (intuition should never be trusted when thinking about quantum gravity.) The details of these pictures are technical and tangential to this post, but the brief explanation is that these pictures are called Penrose diagrams and they provide an intuitive way to think about the time dynamics of black holes. The two diagrams on the left represent the same physics as the schematic diagram on the right. I wanted to understand why during Hawking radiation, the radial momentum for partner modes is in the same direction. John Preskill gave me the initial reasoning, that “radial momentum is not an isometry of Schwarzchild or Rindler geometries,” then I struggled for a few weeks to unpack this, and then Dan Harlow rescued me with some beautiful derivations that make it crystal clear that the picture on the left is indeed correct. I wanted to understand this because if the central picture is correct, then it would be hard to catch up to an infalling Hawking mode and therefore to verify firewall weirdness. The images above are simple enough, but maybe the image below will give you a sense for how much of an uphill battle this was!

After four or five hours of maxing out my brain, it starts to throb. For the past couple of weeks, after breaking my brain with firewalls each day, I’ve been switching gears and reading about black hole astronomy (real-life honest-to-goodness science with data!) Beyond wanting to know the experimental state-of-the-art related to the fancy math I’ve been thinking about, I also had the selfish motivation that I wanted to do some PR maintenance after Nature’s headline: “Stephen Hawking: ‘There are no black holes’.” I found this headline infuriating when Nature posted it back in January. When taken out of context, this quote makes it seem like Stephen Hawking was saying “hey guys, my bad, we’ve been completely wrong all this time. Turn off the telescopes.” When in reality what he was saying was more like: “hey guys, I think this really hard modern firewall paradox is telling us that we’ve misunderstood an extremely subtle detail and we need to make corrections on the order of a few Planck lengths, but it matters!” When you combine this sensationalism with Nature’s lofty credibility, the result is that even a few of my intelligent scientist peers have interpreted this as the non-existence of astrophysical black holes. Not to mention that it opens a crack for the news media to say things like: ‘if even Stephen Hawking has been wrong all this time, then how can we possibly trust the rest of this scientist lot, especially related to climate change?’ So brain throbbing + sensationalism => learning black hole astronomy + PR maintenance.

Before presenting the evidence, I should wave my hands about what we’re looking for. You have all heard about black holes. They are objects where so much mass gets concentrated in such a small volume that Einstein’s general theory of relativity predicts that once an object passes beyond a certain distance (called the event horizon), then said object will never be able to escape, and must proceed to the center of the black hole. Even photons cannot escape once they pass beyond the event horizon (except when you start taking quantum mechanics into account, but this is a small correction which we won’t focus on here.) All of our current telescopes collect photons, and as I just mentioned, when photons get close to a black hole, they fall in, so this means a detection with current technology will only be indirect. What are these indirect detections we have made? Well, general relativity makes numerous predictions about black holes. After we confirm enough of these predictions to a high enough precision, and without a viable alternative theory, we can safely conclude that we have detected black holes. This is similar to how many other areas of science work, like particle physics finding new particles through detecting a particle’s decay products, for example.

Without further ado, I hope the following experimental evidence will convince you that black holes permeate our universe (and if not black holes, then something even weirder and more interesting!)

1. Sgr A*: There is overwhelming evidence that there is a supermassive black hole at the center of our galaxy, the Milky Way. As a quick note, most of the black holes we have detected are broken into two categories, solar mass, where they are only a few times more massive than our sun (5-30 solar masses), or supermassive, where the mass is about  solar masses. Some of the most convincing evidence comes from the picture below. Andrea Ghez and others tracked the orbits of several stars around the center of the Milky Way for over twenty years. We have learned that these stars orbit around a point-like object with a mass on the order of solar masses. Measurements in the radio spectrum show that there is a radio source located in the same location which we call Sagittarius A* (Sgr A*). Sgr A* is moving at less than and has a mass of at least solar masses. These bounds make it pretty clear that Sgr A* is the same object as what is at the focus of these orbits. A radio source is exactly what you would expect for this system because as dust particles get pulled towards the black hole, they collide and friction causes them to heat up, and hot objects radiate photons. These arguments together make it pretty clear that Sgr A* is a supermassive black hole at the center of the Milky Way!

2. Orbit of S2: During a recent talk that Andrea Ghez gave at Caltech, she said that S2 is “her favorite star.” S2 is a 15 solar mass star located near the black hole at the center of our galaxy. S2’s distance from this black hole is only about four times the distance from Neptune to the Sun (at closest point in orbit), and it’s orbital period is only 15 years. The Keck telescopes in Mauna Kea have followed almost two complete orbits of S2. This piece of evidence is redundant compared to point 1, but it’s such an amazing technological feat that I couldn’t resist including it.

3. Numerical studies: astrophysicists have done numerous numerical simulations which provide a different flavor of test. Christian Ott at Caltech is pretty famous for these types of studies.

4. Cyg A: Cygnus A is a galaxy located in the Cygnus constellation. It is an exceptionally bright radio source. As I mentioned in point 1, as dust falls towards a black hole, friction causes it to heat up and then hot objects radiate away photons. The image below demonstrates this. We are able to use the Eddington limit to convert luminosity measurements into estimates of the mass of Cyg A. Not necessarily in the case of Cyg A, but in the case of its cousins Active Galactic Nuclei (AGNs) and Quasars, we are also able to put bounds on their sizes. These two things together show that there is a huge amount of mass trapped in a small volume, which is therefore probably a black hole (alternative models can usually be ruled out.)

5. AGNs and Quasars: these are bright sources which are powered by supermassive black holes. Arguments similar to those used for Cyg A make us confident that they really are powered by black holes and not some alternative.

6. X-ray binaries: astronomers have detected ~20 stellar mass black holes by finding pairs consisting of a star and a black hole, where the star is close enough that the black hole is sucking in its mass. This leads to accretion which leads to the emission of X-Rays which we detect on Earth. Cygnus X-1 is a famous example of this.

7. Water masers: Messier 106 is the quintessential example.

8. Gamma ray bursts: most gamma ray bursts occur when a rapidly spinning high mass star goes supernova (or hypernova) and leaves a neutron star or black hole in its wake. However, it is believed that some of the “long” duration gamma ray bursts are powered by accretion around rapidly spinning black holes.

That’s only eight reasons but I hope you’re convinced that black holes really exist! To round out this list to include ten things, here are two interesting open questions related to black holes:

1. Firewalls: I mentioned this paradox at the beginning of this post. This is the cutting edge of quantum gravity which is causing hundreds of physicists to pull their hair out!

2. Feedback: there is an extremely strong correlation between the size of a galaxy’s supermassive black hole and many of the other properties in the galaxy. This connection was only realized about a decade ago and trying to understand how the black hole (which has a mass much smaller than the total mass of the galaxy) affects galaxy formation is an active area of research in astrophysics.

In addition to everything mentioned above, I want to emphasize that most of these results are only from the past decade. Not to mention that we seem to be close to the dawn of gravitational wave astronomy which will allow us to probe black holes more directly. There are also exciting instruments that have recently come online, such as NuSTAR. In other words, this is an extremely exciting time to be thinking about black holes–both from observational and theoretical perspectives–we have data and a paradox! In conclusion, black holes exist. They really do. And let’s all make a pact to read critically in the 21st century!

Cool resource from Sky and Telescope.

[* I want to thank my buddy Kaes Van’t Hof for letting me crash on his couch in NYC last week, which is where I did most of this work. ** I also want to thank Dan Harlow for saving me months of confusion by sharing a draft of his notes from his course on firewalls at the Israeli Institute for Advanced Study’s winter school in theoretical physics.]

I spent my childhood hacking computers. When I was seven, my cousin showed up for Thanksgiving with a box filled with computer parts and we built my first computer. I got into competitive computer gaming around age eleven, and hacking was a natural extension of these activities. Then when I was sixteen, after doing poorly at a Counterstrike tournament, I decided that I should probably apply myself to other things. Needless to say, my parents were thrilled. So that’s when I bought my first computer (instead of building my own), which for deliberate but now antediluvian reasons was a Mac. A few years later, when I was taking CS 106 at Stanford, I was the first student in the course’s history whose reason for buying a Mac was “so that I couldn’t play computer games!” And now you know the story of my childhood.

The hacker mentality is quite different than the norm and my childhood trained me to look at absolutist laws as opportunities to find loopholes (of course only when legal and socially responsible!) I’ve applied this same mentality as I’ve been doing physics and I’d like to share with you some of the loopholes that I’ve gathered.

Scharnhorst effect enables light to travel faster than in vacuum (c=299,792,458 m/s): this is about the grandaddy of all laws, that nothing can travel faster than light in a vacuum! This effect is the most controversial on my list, because it hasn’t yet been experimentally verified, but it seems obvious with the right picture in mind. Most people’s mental model for light traveling in a vacuum is of little particles/waves called photons traveling through empty space. However, the vacuum is not empty! It is filled with pairs of virtual particles which momentarily fleet into existence. Interactions with these virtual particles create a small amount of ‘resistance’ as photons zoom through the vacuum (photons get absorbed into virtual electron-positron pairs and then spit back out as photons ad infinitum.) Thus, if we could somehow reduce the rate at which virtual particles are created, photons would interact less strongly with the vacuum, and would be able to travel marginally faster than c. But this is exactly what leads to the Casimir effect: the experimentally verified fact that if you take two mirrors and put them ~10 nanometers apart, then they will attract each other because there are more virtual particles created outside the cavity than inside [low momenta virtual modes are inaccessible because the uncertainty principle requires .] This effect is extremely small, only predicting that light would travel one part in faster than c. However, it should remind us all to deeply question assumptions.

This first loophole used quantum effects to beat a relativistic bound, but the next few loopholes are purely quantum, and are mainly related to that most quantum of all limits, the Heisenberg uncertainty principle.

Smashing the standard quantum limit (SQL) with squeezed measurements: the Heisenberg uncertainty principle tells us that there is a fundamental tradeoff in nature: the more precise your information about an object’s position, the less precise your knowledge about its momentum. Or vice versa, or replace x and p with E and t, or any other conjugate variables. This uncertainty principle is oftentimes written as . For a variety of reasons, in the early days of quantum mechanics, it was hard enough to imagine creating a state with , but there was some hope because this is obtained in the ground state of a quantum harmonic oscillator. In this case, we have . However, it was harder still to imagine creating states with , these states would be said to ‘go beyond the standard quantum limit’ (SQL). Over the intervening years, not only have we figured out how to go beyond the SQL using squeezed coherent states, but this is actually essential in some of our most exciting current experiments, like LIGO.

LIGO is an incredibly ambitious experiment which has been talked about multiple times on this blog. It is trying to usher in a new era of astronomy–moving beyond detecting photons–to detecting gravitational waves, ripples in spacetime which are generated as exceptionally massive objects merge, such as when two black holes collide. The effects of these waves on our local spacetime as they travel past earth are minuscule, on the scale of , which is about one thousand times shorter than the ‘diameter’ of a proton, and is the same order of magnitude as . Remarkably, LIGO has exploited squeezed light to demonstrate sensitivities beyond the SQL. LIGO expects to start detecting gravitational waves on a frequent basis as its upgrades deemed ‘advanced LIGO’ are completed over the next few years.

Compressed sensing beats Nyquist-Shannon: let’s play a game. Imagine I’m sending you a radio signal. How often do you need to measure the signal in order to be able to reconstruct it perfectly? The Nyquist-Shannon sampling theorem is a path-breaking result which Claude Shannon proved in 1949. If you measure at least twice as often as the highest frequency, then you are guaranteed perfect recovery of the signal. This incredibly profound result laid the foundation for modern communications. Also, it is important to realize that your signal can be much more general than simply radio waves, such as with a signal of images. This theorem is a sufficient condition for reconstruction, but is it necessary? Not even close. And it took us over 50 years to understand this in generality.

Compressed sensing was proposed between 2004-2006 by Emmanuel Candes, David Donaho and Terry Tao with important early contributions by Justin Romberg. I should note that Candes and Romberg were at Caltech during this period. The Nyquist-Shannon theorem told us that with a small amount of knowledge (a bound on the highest frequency) that we could reconstruct a signal perfectly by only measuring at a rate twice faster than the highest frequency–instead of needing to measure continuously. Compressed sensing says that with one extra assumption, assuming that only sparsely few of your frequencies are being used (call it 10 out of 1000), that you can recover your signal with high accuracy using dramatically fewer measurements. And it turns out that this assumption is valid for a huge range of applications: enabling real-time MRIs using conventional technology or more relevant to this blog, increasing our ability to distinguish quantum states via tomography.

Unlike the other topics in this blog post, I have never worked with compressed sensing, but my intuition goes like this: instead of measuring in the basis in which you are sparse (frequency for example), measure in a different basis. With high probability each of these measurements will pick up a little piece from each of the occupied modes. Then, to reconstruct your signal, you want to use the L0-“norm” to interpolate in such a way that you use the fewest frequency components possible. Computing the L0-“norm” is not efficient, so one of the major breakthroughs of compressed sensing was showing that with high probability computing the L1-norm approximates the L0 solution, and all of this can be done using a highly efficient linear program. However, I really shouldn’t be speculating because I’ve never invested much time into mastering this new tool, and I’m friends with a couple of the quantum state tomography authors, so maybe they’ll chime in?

Wavelets as the mother of all bases: I previously wrote a post about the importance of choosing a convenient basis. Imagine you have an image which has a bunch of sharp contrasts, such as the outline of a person, or a horizon, or a table, basically anything. How do you store it efficiently? Due to the Gibbs phenomena, the Fourier basis is pretty awful for these applications. Here’s another motivating problem, imagine someone plays one note on an instrument. The sound is localized in both time and frequency. The Fourier basis is also pretty awful at storing/detecting this. Wavelets to the rescue! The theory of wavelets uses some beautiful math to solve the longstanding problem of finding a basis which is localized in both position and momenta space (or very close to it.) Wavelets have profound applications, some of my favorite include: modern image compression (JPEG 2000 onwards) is based on wavelets; Ingrid Daubechies and her colleagues used wavelets to detect forged paintings; recovering previously unrecoverable recordings of Brahms at the piano (I heard about this from Barry Simon, of Reed-Simon fame, who is currently teaching his last class ever); and even the FBI uses wavelets to compress images of fingerprints, obtaining a compression ratio of 20:1.

Postselection enables quantum cloning: the no-cloning theorem is well known in the field of quantum information. It says that you cannot find a machine (unitary operation U) which takes an arbitrary input state , and a known state , such that the machine maps to , and thereby cloning . This is very easy to prove using the linearity of quantum mechanics. However, there are loopholes. One of the most trivial loopholes is realizing that one can take the state and perform something called unambiguous state discrimination, which either spits out exactly which state is with some probability, or otherwise spits out “I don’t know which state.” You can postselect that the unambigious state discrimination succeeded and prepare a unitary which clones the relevant states. Peter Shor has a comment on physics stackexchange describing this. Seth Lloyd and John Preskill outlined a less trivial version of this in their recent paper which tries to circumvent firewalls by using postselected quantum teleportation.

In this blog post, I’ve only described a tiny fraction of the quantum loopholes that have been discovered. If I had more space/time, two of the next examples I would describe are beating classical correlations with quantum entanglement, in order to win at CHSH games. I would also describe weak measurements and some of the peculiar things they lead to. Beyond that, I would probably refer you to Yakir Aharonov’s amazingly fun book about quantum paradoxes.

After reading this, I hope that the next time you encounter an inviolable law of nature, you’ll apply the hacker mentality and attempt to strip it down to its essence, isolate assumptions, and potentially find a loophole. But while you’re doing this, remember that you should never argue with your mother, or with mathematics!

“What’s the hardest problem you’ve ever solved?”

Kids focus right in. Driven by a ruthless curiosity, they ask questions from which adults often shy away. Which is great, if you think you know the answer to everything a 7 year-old can possibly ask you…

Two Wednesdays ago, I was invited to participate in three Q&A sessions that quickly turned into Reddit-style AMA (ask-me-anything) sessions over Skype with four 5th grade classes and one 2nd grade class of students at Medina Elementary in Medina, Washington. When asked by the organizers what I would like the sessions to focus on, I initially thought of introducing students to the mod I helped design for Minecraft, called QCraft, which brings concepts like quantum entanglement and quantum superposition into the world of Minecraft. But then I changed my mind. I told the organizers that I would talk about anything the kids wanted to know more about. It dawned on me that maybe not all 5th graders are as excited about quantum physics as I am. Yet.

The students took the bait. They peppered me with questions for over two hours —everything from “What is a quantum physicist and how do you become one?” to “What is it like to work with a fashion designer (about my collaboration with Project Runway’s Alicia Hardesty on Project X Squared)?” and of course, “Why did you steal the cannon?” (learn more about the infamous Cannon Heist – yes kids, there is an ongoing war between the two schools and Caltech took the last (hot) shot just days ago.)”

Then they dug a little deeper: “If we have a quantum computer that knows the answer to everything, why do we need to go to school?” This question was a little tricky, so I framed the answer like this: I compared the computer to a sidekick, and the kids—the future scientists, artists and engineers —to superheroes. Sidekicks always look up to the superheroes for guidance and leadership. And then I got this question from a young girl: “If we are superheroes, what should we do with all this power?” I thought about it for a second and though my initial inclination was to go with: “You should make Angry Birds 3D!”, I went with this instead: “People often say, “Study hard so that one day you can cure cancer, figure out the theory of everything and save the world!” But I would rather see you all do things to understand the world. Sometimes you think you are saving the world when it does not need saving—it is just misunderstood. Find ways to understand one another and move to look for the value in others. Because there is always value in others, often hiding from us behind powerful emotions.” The kids listened in silence and, in that moment, I felt profoundly connected with them and their teachers.

I wasn’t expecting any more “deep” questions, until another young girl raised her hand and asked: “Can I be a quantum physicist, or is it only for the boys?” The ferocity of my answer caught me by surprise: “Of course you can! You can do anything you set your mind to and anyone who tells you otherwise, be it your teachers, your friends or even your parents, they are just wrong! In fact, you have the potential to leave all the boys in the class behind!” The applause and laughter from all the girls sounded even louder among the thunderous silence from the boys. Which is when I realized my mistake and added: “You boys can be superheroes too! Just make sure not to underestimate the girls. For your own sake.”

Why did I feel so strongly about this issue of women in science? Caltech has a notoriously bad reputation when it comes to the representation of women among our faculty and postdocs (graduate students too?) in areas such as Physics and Mathematics. IQIM has over a dozen male faculty members in its roster and only one woman: Prof. Nai-Chang Yeh. Anyone who meets Prof. Yeh quickly realizes that she is an intellectual powerhouse with boundless energy split among her research, her many students and requests for talks, conference organization and mentoring. Which is why, invariably, every one of the faculty members at IQIM feels really strongly about finding a balance and creating a more inclusive environment for women in science. This is a complex issue that requires a lot of introspection and creative ideas from all sides over the long term, but in the meantime, I just really wanted to tell the girls that I was counting on them to help with understanding our world, as much as I was counting on the boys. Quantum mechanics? They got it. Abstract math? No problem.*

It was of course inevitable that they would want to know why we created the Minecraft mod, a collaborative work between Google, MinecraftEDU and IQIM – after all, when I asked them if they had played Minecraft before, all hands shot up. Both IQIM and Google think it is important to educate younger generations about quantum computers and the complex ideas behind quantum physics; and more importantly, to meet kids where they play, in this case, inside the Minecraft game. I explained to the kids that the game was a place where they could experiment with concepts from quantum mechanics and that we were developing other resources to make sure they had a place to go to if they wanted to know more (see our animations with Jorge Cham at http://phdcomics.com/quantum).

As for the hardest problem I have ever solved? I described it in my first blog post here, An Intellectual Tornado. The kids sat listening in some sort of trance as I described the nearly perilous journey through the lands of “agony” and “self doubt” and into the valley of “grace”, the place one reaches when they learn to walk next to their worst fears, as understanding replaces fear and respect for a far superior opponent teaches true humility and instills in you a sense of adventure. By that time, I thought I was in the clear – as far as fielding difficult questions from 10 year-olds goes – but one little devil decided to ask me this simple question: “Can you explain in 2 minutes what quantum physics is?” Sure! You see kids, emptiness, what we call the quantum vacuum, underlies the emergence of spacetime through the build-up of correlations between disjoint degrees of freedom, we like to call entangled subsystems. The uniqueness of the Schmidt decomposition over generic quantum states, coupled with concentration of measure estimates over unequal bipartite decompositions gives rise to Schrodinger’s evolution and the concept of unitarity – which itself only emerges in the thermodynamic limit. In the remaining minute, let’s discuss the different interpretations of the following postulates of quantum mechanics: Let’s start with measurements…

Reaching out to elementary school kids is just one way we can make science come alive, and many of us here at IQIM look forward to sharing with kids of any age our love for adventuring far and wide to understand the world around us. In case you are an expert in anything, or just passionate about something, I highly recommend engaging the next generation through visits to classrooms and Skype sessions across state lines. Because, sometimes, you get something like this from their teacher:

Hello Dr. Michalakis,

My class was lucky enough to be able to participate in one of the Skype chats you did with Medina Elementary this morning. My students returned to the classroom with so many questions, wonderings, concerns, and ideas that we could spend the remainder of the year discussing them all.

Your ability to thoughtfully answer EVERY single question posed to you was amazing. I was so impressed and inspired by your responses that I am tempted to actually spend the remainder of the year discussing quantum mechanics J.

I particularly appreciated your point that our efforts should focus on trying to “understand the world” rather than “save” the world. I work each day to try and inspire curiosity and wonder in my students. You accomplished more towards my goal in about 40 minutes than I probably have all year. For that I am grateful.

All the best,
A.T.

* Several of my female classmates at MIT (where I did my undergraduate degree in Math with Computer Science) had a clarity of thought and a sense of perseverance that Seal Team Six would be envious of. So I would go to them for help with my hardest homework.

It was the summer of 2008. I was 22 years old, and it was my second week working in the crude oil and natural gas options pit at the New York Mercantile Exchange (NYMEX.) My head was throbbing after two consecutive weeks of disorientation. It was like being born into a new world, but without the neuroplasticity of a young human. And then the crowd erupted. “Yeeeehawwww. YeEEEeeHaaaWWWWW. Go get ’em cowboy.”

It seemed that everyone on the sprawling trading floor had started playing Wild Wild West and I had no idea why. After at least thirty seconds, the hollers started to move across the trading floor. They moved away 100 meters or so and then doubled back towards me. After a few meters, he finally got it, and I’m sure he learned a life lesson. Don’t be the biggest jerk in a room filled with traders, and especially, never wear triple-popped pastel-colored Lacoste shirts. This young aspiring trader had been “spurred.”

In other words, someone had made paper spurs out of trading receipts and taped them to his shoes. Go get ’em cowboy.

I was one academic quarter away from finishing a master’s degree in statistics at Stanford University and I had accepted a full time job working in the algorithmic trading group at DRW Trading. I was doing a summer internship before finishing my degree, and after three months of working in the algorithmic trading group in Chicago, I had volunteered to work at the NYMEX. Most ‘algo’ traders didn’t want this job, because it was far-removed from our mental mathematical monasteries, but I knew I would learn a tremendous amount, so I jumped at the opportunity. And by learn, I mean, get ripped calves and triceps, because my job was to stand in place for seven straight hours updating our mathematical models on a bulky tablet PC as trades occurred.

I have no vested interests in the world of high-frequency trading (HFT). I’m currently a PhD student in the quantum information group at Caltech and I have no intentions of returning to finance. I found the work enjoyable, but not as thrilling as thinking about the beginning of the universe (what else is?) However, I do feel like the current discussion about HFT is lop-sided and I’m hoping that I can broaden the perspective by telling a few short stories.

What are the main attacks against HFT? Three of them include the evilness of: front-running markets, making money out of nothing, and instability. It’s easy to point to extreme examples of algorithmic traders abusing markets, and they regularly do, but my argument is that HFT has simply computerized age-old tactics. In this process, these tactics have become more benign and markets more stable.

Front-running markets: large oil producing nations, such as Mexico, often want to hedge their exposure to changing market prices. They do this by purchasing options. This allows them to lock in a minimum sale price, for a fee of a few dollars per barrel. During my time at the NYMEX, I distinctly remember a broker shouting into the pit: “what’s the price on DEC9 puts.” A trader doesn’t want to give away whether they want to buy or sell, because if the other traders know, then they can artificially move the price. In this particular case, this broker was known to sometimes implement parts of Mexico’s oil hedge. The other traders in the pit suspected this was a trade for Mexico because of his anxious tone, some recent geopolitical news, and the expiration date of these options.

Some confident traders took a risk and faded the market. They ended up making between $1-2 million dollars from these trades, relative to what the fair price was at that moment. I mention relative to the fair price, because Mexico ultimately received the better end of this trade. The price of oil dropped in 2009, and Mexico executed its options enabling it to sell its oil at a higher than market price. Mexico spent $1.5 billion to hedge its oil exposure in 2009.

This was an example of humans anticipating the direction of a trade and capturing millions of dollars in profit as a result. It really is profit as long as the traders can redistribute their exposure at the ‘fair’ market price before markets move too far. The analogous strategy in HFT is called “front-running the market” which was highlighted in the New York Times’ recent article “the wolf hunters of Wall Street.” The HFT version involves analyzing the prices on dozens of exchanges simultaneously, and once an order is published in the order book of one exchange, then using this demand to adjust its orders on the other exchanges. This needs to be done within a few microseconds in order to be successful. This is the computerized version of anticipating demand and fading prices accordingly. These tactics as I described them are in a grey area, but they rapidly become illegal.

Making money from nothing: arbitrage opportunities have existed for as long as humans have been trading. I’m sure an ancient trader received quite the rush when he realized for the first time that he could buy gold in one marketplace and then sell it in another, for a profit. This is only worth the trader’s efforts if he makes a profit after all expenses have been taken into consideration. One of the simplest examples in modern terms is called triangle arbitrage, and it usually involves three pairs of currencies. Currency pairs are ratios; such as USD/AUD, which tells you, how many Australian dollars you receive for one US dollar. Imagine that there is a moment in time when the product of ratios is 1.01. Then, a trader can take her USD, buy AUD, then use her AUD to buy CAD, and then use her CAD to buy USD. As long as the underlying prices didn’t change while she carried out these three trades, she would capture one cent of profit per trade.

After a few trades like this, the prices will equilibrate and the ratio will be restored to one. This is an example of “making money out of nothing.” Clever people have been trading on arbitrage since ancient times and it is a fundamental source of liquidity. It guarantees that the price you pay in Sydney is the same as the price you pay in New York. It also means that if you’re willing to overpay by a penny per share, then you’re guaranteed a computer will find this opportunity and your order will be filled immediately. The main difference now is that once a computer has been programmed to look for a certain type of arbitrage, then the human mind can no longer compete. This is one of the original arenas where the term “high-frequency” was used. Whoever has the fastest machines, is the one who will capture the profit.

Instability: I believe that the arguments against HFT of this type have the most credibility. The concern here is that exceptional leverage creates opportunity for catastrophe. Imaginations ran wild after the Flash Crash of 2010, and even if imaginations outstripped reality, we learned much about the potential instabilities of HFT. A few questions were posed, and we are still debating the answers. What happens if market makers stop trading in unison? What happens if a programming error leads to billions of dollars in mistaken trades? Do feedback loops between algo strategies lead to artificial prices? These are reasonable questions, which are grounded in examples, and future regulation coupled with monitoring should add stability where it’s feasible.

The culture in wealth driven industries today is appalling. However, it’s no worse in HFT than in finance more broadly and many other industries. It’s important that we dissociate our disgust in a broad culture of greed from debates about the merit of HFT. Black boxes are easy targets for blame because they don’t defend themselves. But that doesn’t mean they aren’t useful when implemented properly.

Are we better off with HFT? I’d argue a resounding yes. The primary function of markets is to allocate capital efficiently. Three of the strongest measures of the efficacy of markets lie in “bid-ask” spreads, volume and volatility. If spreads are low and volume is high, then participants are essentially guaranteed access to capital at as close to the “fair price” as possible. There is huge academic literature on how HFT has impacted spreads and volume but the majority of it indicates that spreads have lowered and volume has increased. However, as alluded to above, all of these points are subtle–but in my opinion, it’s clear that HFT has increased the efficiency of markets (it turns out that computers can sometimes be helpful.) Estimates of HFT’s impact on volatility haven’t been nearly as favorable but I’d also argue these studies are more debatable. Basically, correlation is not causation, and it just so happens that our rapidly developing world is probably more volatile than the pre-HFT world of the last Millennia.

We could regulate away HFT, but we wouldn’t be able to get rid of the underlying problems people point to unless we got rid of markets altogether. As with any new industry, there are aspects of HFT that should be better monitored and regulated, but we should have level-heads and diverse data points as we continue this discussion. As with most important problems, I believe the ultimate solution here lies in educating the public. Or in other words, this is my plug for Python classes for all children!!

I promise that I’ll repent by writing something that involves actual quantum things within the next two weeks!

Evan Miyazono and I recently visited Navajo Preparatory High School in Farmington, New Mexico, the second half of the first exchange of visitors between Caltech and Navajo Prep. Two students and two teachers from the high school visited our campus last summer, spending time touring labs, working on small science and technology projects, and sharing their background and thoughts on science education in the Navajo Nation with us. Evan and I were happy to return the favor and take a trip out to Farmington.

We spent the school days giving lectures about light and solar power to the underclassmen and having discussions with the seniors about college applications, college life, and graduate school. We took over physics classes for the entire freshmen class, and spent an hour and a half with each class teaching them the basic E&M they needed to know to understand the wave nature of light and walking them through some simple experiments with lenses and diffraction gratings. When Evan put a piece of paper on which he had cut two very thin slits in front of a green laser-pointer, “oh”s and “ah”s bubbled up from the students as they saw the diffraction pattern appear on the other side of the room. During a math class where Evan was demonstrating how the area and circumference of a circle are related in an intuitive way by breaking up the area of the circle into a rectangle with sides r and pi*r, from where I stood to the side of the classroom, I could hear a student exclaim to his friend “Math is amazing!”.

The next day, after I gave a presentation to the freshmen physics classes on solar power and photovoltaic cells, four students asked for help or resources for their science projects. Two students were making a working model of a “modernized Hogan.” The school has a hogan in the middle of campus where important ceremonies and traditional Navajo gatherings take place. The students want to build a table-top model hogan with working solar water heating and photovoltaic panel to provide warm water and lighting. Another student is working on making a smart phone app for visitors to the Navajo Nation as her senior project. Her app will inform tourists about Navajo landmarks and the significance they hold to the Navajo people. She wants to inform visitors about her culture in an effort to replace the many stereotypes held about native people and Navajos in particular with factual information. These are just a few examples of how students are honoring the traditions of their culture while also taking advantage of new technology and empowering themselves through science education.

I shared with the students stories of friends of mine who had grown up on the Navajo Reservation and the unique issues they confronted in college and afterward. Students who come from tribal reservations often experience homesickness to a much greater degree than other groups when they go away to college. Many of these young adults are accustomed to a very tight community and strong sense of belonging and support that they feel in their hometown, so leaving that community to join a huge group of strangers with cultures foreign from their own can be a big challenge. I gave an informal seminar to the senior class where I discussed college in general as well as issues specific to native students. I gave them advice gleaned from my own experiences as well as the experiences of some of my Navajo friends. Evan and I also answered tons of questions that the students had about all aspects of college—getting in, financial aid, being successful, and finding balance. They asked how to approach a professor about doing research in their lab and how to budget their finances, what kind of summer job they should look for, and how to balance family life and ties with college life. The seniors had so many questions that together we spent more than two hours discussing these topics and answering general and specific questions. I was really happy we could provide so much useful and desired information for these young scholars.

In our free time Evan and I got to spend more time with teachers and students, sharing meals, information, and ideas. It was great to get to know the students and teachers better and learn more about their perspectives and experiences, and how education is fitting into their lives. I look forward to continuing to develop these relationships from afar. We already have plans to mentor a couple of students with their science and senior projects and hope to recruit more Caltech grad students to serve as mentors. Supporting and encouraging these native students in their participation in math and science fields, and higher education in general, as well as helping them to maintain a strong commitment and connection to their culture and families is something that I want to continue to foster as a mentor and ally of the school. I want to thank IQIM for providing the funding for this trip that made these connections possible.

by Jorge Cham

How do you make something that has never existed before?

I often get suggestions for comics I should draw, which I welcome because A) I like to think of PHD Comics as a global collaborative effort and B) after 17 years, I’m almost out of ideas. This particular suggestion came from Chen-Lung Hung, a postdoc in Physics at Caltech:

PANEL 1 – Ask a scientist: “What motivates you to do the research you do?”

PANEL 2 – What people expect them to answer: “This can lead to real-life applications such as A, B, C, D, etc.”

PANEL 3 – How a real scientist would answer: “Because it’s cool.”

Ok, granted, the punchline needs work. Chen-Lung also asked me to make it clear that his research has important real-life applications, should someone from NSF, who funds his work, happen to be reading this blog.

Chen-Lung’s work with Prof. Jeff Kimble of Caltech’s IQIM is the subject of the third installment in our animated series of explanations of Quantum concepts and devices.

“The problem with atoms,” Prof. Kimble said at one point during our 3-4 hour conversation, “is that they exist in three dimensional space.” I didn’t know that was a problem (unless you expect them to exist in more than 3 dimensions), but Jeff explained that it means it’s very hard to control Quantum systems because the world is wide open, and information can leak and be corrupted from any direction. After a entire academic career making breakthroughs with one type of Quantum System, he’s now directing his group towards a new, experimental type which they believe has more potential for building devices with many Quantum Objects. As Jeff says in the video, “It’s a privilege to be able to explore.”

Shaping light, trapping atoms, alligator waveguides… The goal, Jeff and Chen-lung explained, is to make systems that are “surprising.” Not surprisingly, it was really hard to draw this video. How do you depict something that has never existed before? And more importantly, do you draw alligators differently from crocodiles? (Did you know alligators only exist in two places in the world: the Southern part of the United States, and in China?).

Hopefully, those of you watching will get some understanding of some key Quantum concepts and what it takes to build and manipulate Quantum systems, but to be honest, I make these videos because I think the work is really cool.

Jeff and Chen-Lung: thanks for taking us along on this adventure of yours, the privilege is all ours.

Watch the third installment of this series:

Jorge Cham is the creator of Piled Higher and Deeper (www.phdcomics.com).

CREDITS:

Featuring: Jeff Kimble and Chen-Lung Hung
Animated by Jorge Cham

Produced in Partnership with the Institute for Quantum Information and Matter (http://iqim.caltech.edu) at Caltech with funding provided by the National Science Foundation and the Betty and Gordon Moore Foundation.

Making your way to the cutting edge of any field is a daunting challenge. But especially when the edge of the field is expanding; and even harder still when the rate of expansion is accelerating. John recently helped Physics World create a special 25th anniversary issue where they identified the five biggest breakthroughs in physics over the past 25 years, and also the five biggest open questions. In pure John fashion, at his group meeting on Wednesday night, he made us work before revealing the answers. The photo below shows our guesses, where the asterisks denote Physics World‘s selections. This is the blog post I wish I had when I was a fifteen year-old aspiring physicist–this is an attempt to survey and provide a tiny toehold on the edge (from my biased, incredibly naive, and still developing perspective.)

The biggest breakthroughs of the past 25 years:

*Neutrino Mass: surprisingly, neutrinos have a nonzero mass, which provides a window into particle physics beyond the standard model. THE STANDARD MODEL has been getting a lot of attention recently. This is well deserved in my opinion, considering that the vast majority of its predictions have come true, most of which were made by the end of the 1960s. Last year’s discovery of the Higgs Boson is the feather in its cap. However, it’s boring when things work too perfectly, because then we don’t know what path to continue on. That’s where the neutrino mass comes in. First, what are neutrinos? Neutrinos are a fundamental particle that have the special property that they barely interact with other particles. There are four fundamental forces in nature: electromagnetism, gravity, strong (holds quarks together to create neutrons and protons), and weak (responsible for radioactivity and nuclear fusion.) We can design experiments which allow us to observe neutrinos. We have learned that they are electrically neutral, so they aren’t affected by electromagnetism. They are barely affected by the strong force, if at all. They have an extremely small mass, so gravity acts on them only subtly. The main way in which they interact with their environment is through the weak force. Here’s the amazing thing: only really clunky versions of the standard model can allow for a nonzero neutrino mass! Hence, when a small but nonzero mass was experimentally established in 1998, we gained one of our first toeholds into particle physics beyond the standard model. This is particularly important today, because to the best of my knowledge, the LHC hasn’t yet discovered any other new physics beyond the standard model. The mechanism behind the neutrino mass is not yet understood. Moreover, neutrinos have a bunch of other bizarre properties which we understand empirically, but not their theoretical origins. The strangest of which goes by the name neutrino oscillations. In one sentence: there are three different kinds of neutrinos, and they can spontaneously transmute themselves from one type to another. This happens because physics is formulated in the language of mathematics, and the math says that the eigenstates corresponding to ‘flavors’ are not the same as the eigenstates corresponding to ‘mass.’ Words, words, words. Maybe the Caltech particle theory people should have a blog?

Shor’s Algorithm: a quantum computer can factor N=1433301577 into 37811*37907 exponentially faster than a classical computer. This result from Peter Shor in 1994 is near and dear to our quantum hearts. It opened the floodgates showing that there are tasks a quantum computer could perform exponentially faster than a classical computer, and therefore that we should get BIG$$$ from the world over in order to advance our field!! The task here is factoring large numbers into their prime factors; the difficulty of which has been the basis for many cryptographic protocols. In one sentence, Shor’s algorithm achieves this exponential speed-up because there is a step in the factoring algorithm (period finding) which can be performed in parallel via the quantum Fourier transform.
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The RSS subscriptions which populate my Google Reader mainly fall into two categories: scientific and other. Sometimes patterns emerge when superimposing these disparate fields onto the same photo-detection plate (my brain.) Today, it became abundantly clear that it’s been a tough week for hidden variable theories.

Let me explain. Hidden variable theories were proposed by physicists in an attempt to explain the ‘indeterminism’ which seems to arise in quantum mechanics, and especially in the double-slit experiment. This probably means nothing to many of you, so let me explain further: the hidden variables in Tuesday’s election weren’t enough to trump Nate Silver’s incredibly accurate predictions based upon statistics and data (hidden variables in Tuesday’s election include: “momentum,” “the opinions of undecided voters,” and “pundit’s hunches.”) This isn’t to say that there weren’t hidden variables at play — clearly the statistical models used weren’t fully complete and will someday be improved upon — but hidden variables alone weren’t the dominant influence. Indeed, Barack Obama was re-elected for a second term. However, happy as I was to see statistics trump hunches, the point of this post is not to wax political, but rather to describe the recent failure of hidden variable theories in an arena more appropriate for this blog: quantum experiments.

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