Good news everyone! Flatland is non-contextual!











What about quantum mechanics?







Contextuality of quantum mechanics








on the outcomes.





Peres-Mermin proof of contextuality







Quantum braiding: It’s all in (and on) your head.

Morning sunlight illuminated John Preskill’s lecture notes. The notes concern Caltech’s quantum-computation course, Ph 219. I’m TAing (the teaching assistant for) Ph 219. I previewed lecture material one sun-kissed Sunday.

Pasadena sunlight spilled through my window. So did the howling of a dog that’s deepened my appreciation for Billy Collins’s poem “Another reason why I don’t keep a gun in the house.” My desk space warmed up, and I unbuttoned my jacket. I underlined a phrase, braided my hair so my neck could cool, and flipped a page.

I flipped back. The phrase concerned a mathematical statement called “the Yang-Baxter relation.” A sunbeam had winked on in my mind: The Yang-Baxter relation described my hair.

The Yang-Baxter relation belongs to a branch of math called “topology.” Topology resembles geometry in its focus on shapes. Topologists study spheres, doughnuts, knots, and braids.

Topology describes some quantum physics. Scientists are harnessing this physics to build quantum computers. Alexei Kitaev largely dreamed up the harness. Alexei, a Caltech professor, is teaching Ph 219 this spring.1 His computational scheme works like this.

We can encode information in radio signals, in letters printed on a page, in the pursing of one’s lips as one passes a howling dog’s owner, and in quantum particles. Imagine three particles on a tabletop.

Peas 1

Consider pushing the particles around like peas on a dinner plate. You could push peas 1 and 2 until they swapped places. The swap represents a computation, in Alexei’s scheme.2

The diagram below shows how the peas move. Imagine slicing the figure into horizontal strips. Each strip would show one instant in time. Letting time run amounts to following the diagram from bottom to top.

Peas 2

Arrows copied from John Preskill’s lecture notes. Peas added by the author.

Imagine swapping peas 1 and 3.

Peas 3

Humor me with one more swap, an interchange of 2 and 3.

Peas 4

Congratulations! You’ve modeled a significant quantum computation. You’ve also braided particles.

2 braids

The author models a quantum computation.

Let’s recap: You began with peas 1, 2, and 3. You swapped 1 with 2, then 1 with 3, and then 2 with 3. The peas end up ordered oppositely the way they began—end up ordered as 3, 2, 1.

You could, instead, morph 1-2-3 into 3-2-1 via a different sequence of swaps. That sequence, or braid, appears below.

Peas 5

Congratulations! You’ve begun proving the Yang-Baxter relation. You’ve shown that  each braid turns 1-2-3 into 3-2-1.

The relation states also that 1-2-3 is topologically equivalent to 3-2-1: Imagine standing atop pea 2 during the 1-2-3 braiding. You’d see peas 1 and 3 circle around you counterclockwise. You’d see the same circling if you stood atop pea 2 during the 3-2-1 braiding.

That Sunday morning, I looked at John’s swap diagrams. I looked at the hair draped over my left shoulder. I looked at John’s swap diagrams.

“Yang-Baxter relation” might sound, to nonspecialists, like a mouthful of tweed. It might sound like a sneeze in a musty library. But an eight-year-old could grasp the half the relation. When I braid my hair, I pass my left hand over the back of my neck. Then, I pass my right hand over. But I could have passed the right hand first, then the left. The braid would have ended the same way. The braidings would look identical to a beetle hiding atop what had begun as the middle hunk of hair.


The Yang-Baxter relation.

I tried to keep reading John’s lecture notes, but the analogy mushroomed. Imagine spinning one pea atop the table.

Pea 6

A 360° rotation returns the pea to its initial orientation. You can’t distinguish the pea’s final state from its first. But a quantum particle’s state can change during a 360° rotation. Physicists illustrate such rotations with corkscrews.


Pachos corkscrew 2

A quantum corkscrew (“twisted worldribbon,” in technical jargon)

Like the corkscrews formed as I twirled my hair around a finger. I hadn’t realized that I was fidgeting till I found John’s analysis.

Version 2

I gave up on his lecture notes as the analogy sprouted legs.

I’ve never mastered the fishtail braid. What computation might it represent? What about the French braid? You begin French-braiding by selecting a clump of hair. You add strands to the clump while braiding. The addition brings to mind particles created (and annihilated) during a topological quantum computation.

Ancient Greek statues wear elaborate hairstyles, replete with braids and twists.  Could you decode a Greek hairdo? Might it represent the first 18 digits in pi? How long an algorithm could you run on Rapunzel’s hair?

Call me one bobby pin short of a bun. But shouldn’t a scientist find inspiration in every fiber of nature? The sunlight spilling through a window illuminates no less than the hair spilling over a shoulder. What grows on a quantum physicist’s head informs what grows in it.


1Alexei and John trade off on teaching Ph 219. Alexei recommends the notes that John wrote while teaching in previous years.

2When your mother ordered you to quit playing with your food, you could have objected, “I’m modeling computations!”

A detective with a quantum helper

Have you ever wanted to be incredibly perceptive and make far-reaching deductions about people? I have always been fascinated by spy stories, and how the main character in them notices tiny details of his surroundings to navigate life-or-death situations. This skill seems out of reach for us normal people; you have to be “a high-functioning sociopath” to memorize all existing data on behavior, clothes choices and forensic science. Of course I’m referring to:
Small details help Sherlock figure out what did the woman do to meet such a sad end
Yet in the not too distant future, a computer may help you become a brilliant detective (or a scheming villain) yourself! The first step is noticing the details, which is known in machine learning as the classification task. Here is a pioneering work that somewhat resembles the above picture, only it’s done by a computer:
A computer spits out a sentence (read down) describing what's in the picture. Work by Stanford group.

The task for the computer here was to produce a verbal description of the image. There are thousands of words in the vocabulary, and a computer has to try them in different combinations to make a sensible sentence. There is no way a computer can be given an exhaustive list of correct sentences with examples of images for each. That kind of list would be a database bigger than the earth (as one can see just by counting the number of combinations). So to train the computer to use language like in a picture above, one only possesses a limited set of examples – maybe a few thousand pictures with descriptions. Yet we as humans are capable of learning from just seeing a few examples, by noticing the repeating patterns. So the computer can do the same! The score next to each word above is an estimate based on those few thousand examples of how relevant is the word “tennis” or “woman” to what’s in the box on the image. The algorithm produces possible sentences, scores them, and then selects the sentence with the highest total score.

Once the classification task is done, one needs to use all the collected information to make a prediction – as Sherlock is able to point out the most probable motive in the first picture, we also want to predict a piece of very personal information: we’d like to know how to start up a conversation with that tennis player.

Humans are actually good at classification tasks: with luck, we can notice and type in our cellphone all the details the predictor will need, like brand of clothing, hair color, height… though computers recently became better than humans at facial expression recognition, so we don’t have to trust ourselves on that anymore. Finally, when all the data is collected, most humans will still say only generic advice to you on conversation starters. Which means we are very bad at prediction tasks. We don’t notice the hidden dependencies between brand of clothes and sense of humor. But such information may not hide from the all-seeing eye of the machine learning algorithm! So expect your cellphones to give you dating advice within 10 years… 

Now how do quantum computers come into play? Well if you look at your search results, they are still pretty irrelevant most of the time. Imagine you used them as conversation starters – you’ll embarrass yourself 9 out of 10 times! To make this better, a certain company needs more memory and processing power. Yet most advanced deep learning routines remain out of reach, just because there are exponentially many hidden dependencies one would need to try and reject before the algorithm finds the right predictor. So a certain company turns to us, quantum computing people, as we deal with exponentially hard problems notoriously well! And indeed, quantum algorithms make some of the machine learning routines exponentially faster – see this Quantum Machine Learning article, as well as a talk by Seth Lloyd for technical details. Some anonymous stock trader is already trying to intimidate their fellow quants (quantitative analysts) by calling the top trading system “Quantum machine learning”. I think we should appreciate his sense of humor and invest into his algorithm as soon as opens such functionality. Or we could invest in Teagan from Caltech – her code recently won the futures contest on the same website.

Apply to join IQIM!

Editor’s Note: Dr. Chandni Usha is an IQIM postdoctoral scholar working with Prof. Eisenstein. We asked her to describe her experience as an IQIM fellow.

Just another day at work!

Just another day at work!

When I look back at how I ended up here, I find myself in a couple of metastable states. Every state pushed me to newer avenues of knowledge. Interestingly, growing up I never really knew what it was like to be a scientist. I had not watched any of those sci-fi movies or related TV series as a kid. No outreach program ever reached me in my years of schooling! My first career choice was to be a lawyer. But a casual comment by a friend that lawyers are ‘liars’ was strong enough to change my mind. Strangely enough, now the quest is for the truth, in a lab down at the sub-basement of one of the world’s best research institutes.

I did my masters in Physics at this beautiful place called the Indian Institute of Science in Bangalore. I realized that I like doing things with my hands. Fixing broken instruments seemed fun. Every new data point on a plot amused me. It was more than obvious that experimental physics is where my heart was and hence I went on to do a Ph.D. in condensed matter physics. When I decided to apply for postdoctoral positions, an old friend of mine, Debaleena Nandi, told me to look up the IQIM website. That was in November 2012, and I applied for the IQIM postdoctoral fellowship. My stars were probably aligned to be here. Coincidentally, Jim Eisenstein, my adviser, was in India on a sabbatical and I happened to hear him give a talk. It left such a strong impression in my mind that I was willing to give up on a trip to Europe for an interview the next day had he offered me a position. We spoke about possible problems, but no offer was in sight and hence I did travel to Europe with my mind already at Caltech. IQIM saved me from my dilemma when they offered me the fellowship a few days later.

Now, why choose IQIM! Reason number one was Jim. And reason number two was this blog which brought in this feeling that there exists a community here; where experimentalists and theorists could share their ideas and grow together in a symbiotic manner. My first project was with an earlier postdoc, Erik Henriksen, who is now a faculty at Washington University in St. Louis. It was based on a proposal by fellow IQIM professor Jason Alicea which involved decorating a film of graphene with a certain heavy metal adatom. Jason’s prediction was that if you choose the right adatom, it could endow some of its unique properties such as strong spin-orbit coupling to the underlying graphene sheet. One can thus engineer graphene to what is called a topological insulator where only the edges of the graphene sheet conduct. Erik had taken on this task and I tagged along. Working in a very small campus with a close-knit community helps bounce your ideas around others and that’s how this experiment came into being. I found it particularly interesting that Jason and his colleagues often ask us, the experimentalists, whether some of the ideas they have are actually feasible to be performed in a lab!

The IQIM fellowship allows you to work on a variety of fields that come under the common theme of quantum information and matter. In addition to providing an independent funding and research grant, the fellowship offers the flexibility to work with any mentor and even multiple mentors, especially in the theory group. In experimental groups however, that flexibility is limited but not impossible. The fellowship gives you a lot of freedom and encourages collaborations. IQIM theory folks have a very strong and friendly group with a lot of collaborations, to the extent that it is often hard to distinguish the faculty from the postdocs and students.

Apart from a yearly retreat to a beautiful resort in Lake Arrowhead, the social life at IQIM is further enhanced through the Friday seminars where you get to hear about the work from postdocs and graduate students from IQIM, as well as other universities. IQIM’s outreach activities have been outstanding. A quick look at this blog will take you from the PhD Comics animations, to teaching kids quantum mechanics through Miinecraft, to hosting middle school students at the InnoWorks academy and a host of other activities. This note will not be complete without mentioning about our repeated efforts to attract women candidates. My husband lives in India, and I live right across the globe, all for the love of science. I am not alone in this respect as we have two more women postdocs at IQIM who have similar stories to tell. So, if you are a woman and wish to pursue a quality research program, this is the place to be, for together we can bring change.

Now that I have convinced you that IQIM is something not to be missed, kindly spread the word. And if you are looking for an awesome opportunity to work at Caltech, get your CV and research statement and apply for the fellowships before Dec 5, 2014!

John Preskill and the dawn of the entanglement frontier















-D. Gottesman

A Public Lecture on Quantum Information

Sooner or later, most scientists are asked to deliver a public lecture about their research specialties. When successful, lecturing about science to the lay public can give one a feeling of deep satisfaction. But preparing the lecture is a lot of work!

Caltech sponsors the Earnest C. Watson lecture series (named after the same Earnest Watson mentioned in my post about Jane Werner Watson), which attracts very enthusiastic audiences to Beckman Auditorium nine times a year. I gave a Watson lecture on April 3 about Quantum Entanglement and Quantum Computing, which is now available from iTunes U and also on YouTube:

I did a Watson lecture once before, in 1997. That occasion precipitated some big changes in my presentation style. To prepare for the lecture, I acquired my first laptop computer and learned to use PowerPoint. This was still the era when a typical physics talk was handwritten on transparencies and displayed using an overhead projector, so I was sort of a pioneer. And I had many anxious moments in the late 1990s worrying about whether my laptop would be able to communicate with the projector — that can still be a problem even today, but was a more common problem then.

I invested an enormous amount of time in preparing that 1997 lecture, an investment still yielding dividends today. Aside from figuring out what computer to buy (an IBM ThinkPad) and how to do animation in PowerPoint, I also learned to draw using Adobe Illustrator under the tutelage of Caltech’s digital media expert Wayne Waller. And apart from all that technical preparation, I had to figure out the content of the lecture!

That was when I first decided to represent a qubit as a box with two doors, which contains a ball that can be either red or green, and I still use some of the drawings I made then.

Entanglement, illustrated with balls in boxes.

Entanglement, illustrated with balls in boxes.

This choice of colors was unfortunate, because people with red-green color blindness cannot tell the difference. I still feel bad about that, but I don’t have editable versions of the drawings anymore, so fixing it would be a big job …

I also asked my nephew Ben Preskill (then 10 years old, now a math PhD candidate at UC Berkeley), to make a drawing for me illustrating weirdness.

The desire to put weirdness to work has driven the emergence of quantum information science.


I still use that, for sentimental reasons, even though it would be easier to update.

The turnout at the lecture was gratifying (you can’t really see the audience with the spotlight shining in your eyes, but I sensed that the main floor of the Auditorium was mostly full), and I have gotten a lot of positive feedback (including from the people who came up to ask questions afterward — we might have been there all night if the audio-visual staff had not forced us to go home).

I did make a few decisions about which I have had second thoughts. I was told I had the option of giving a 45 minute talk with a public question period following, or a 55 minute talk with only a private question period, and I opted for the longer talk. Maybe I should have pushed back and insisted on allowing some public questions even after the longer talk — I like answering questions. And I was told that I should stay in the spotlight, to ensure good video quality, so I decided to stand behind the podium the whole time to curb my tendency to pace across the stage. But maybe I would have seemed more dynamic if I had done some pacing.

I got some gentle criticism from my wife, Roberta, who suggested I could modulate my voice more. I have heard that before, particularly in teaching evaluations that complain about my “soporific” tone. I recall that Mike Freedman once commented after watching a video of a public lecture I did at the KITP in Santa Barbara — he praised its professionalism and “newscaster quality”. But that cuts two ways, doesn’t it? Paul Ginsparg listened to a podcast of that same lecture while doing yardwork, and then sent me a compliment by email, with a characteristic Ginspargian twist. Noting that my sentences were clear, precise, and grammatical, Paul asked: “is this something that just came naturally at some early age, or something that you were able to acquire at some later stage by conscious design (perhaps out of necessity, talks on quantum computing might not go over as well without the reassuring smoothness)?”

Another criticism stung more. To illustrate the monogamy of entanglement, I used a slide describing the frustration of Bob, who wants to entangle with both Alice and Carrie, but finds that he can increase his entanglement with Carrie only my sacrificing some of his entanglement with Alice.

Entanglement is monogamous. Bob is frustrated to find that he cannot be fully entangled with both Alice and Carrie.


This got a big laugh. But I used the same slide in a talk at the APS Denver meeting the following week (at a session celebrating the 100th anniversary of Niels Bohr’s atomic model), and a young woman came up to me after that talk to complain. She suggested that my monogamy metaphor was offensive and might discourage women from entering the field!

After discussing the issue with Roberta, I decided to address the problem by swapping the gender roles. The next day, during the question period following Stephen Hawking’s Public Lecture, I spoke about Betty’s frustration over her inability to entangle fully with both Adam and Charlie. But is that really an improvement, or does it reflect negatively on Betty’s morals? I would appreciate advice about this quandary in the comments.

In case you watch the video, there are a couple of things you should know. First, in his introduction, Tom Soifer quotes from a poem about me, but neglects to name the poet. It is former Caltech postdoc Patrick Hayden. And second, toward the end of the lecture I talk about some IQIM outreach activities, but neglect to name our Outreach Director Spiros Michalakis, without whose visionary leadership these things would not have happened.

The most touching feedback I received came from my Caltech colleague Oskar Painter. I joked in the lecture about how mild mannered IQIM scientists can unleash the superpower of quantum information at a moment’s notice.

Mild mannered professor unleashes the super power of quantum information.

Mild mannered professor unleashes the superpower of quantum information.

After watching the video, Oskar shot me an email:

“I sent a link to my son [Ewan, age 11] and daughter [Quinn, age 9], and they each watched it from beginning to end on their iPads, without interruption.  Afterwards, they had a huge number of questions for me, and were dreaming of all sorts of “quantum super powers” they imagined for the future.”