Paradise

The word dominates chapter one of Richard Holmes’s book The Age of WonderHolmes writes biographies of Romantic-Era writers: Mary Wollstonecraft, Percy Shelley, and Samuel Taylor Coleridge populate his bibliography. They have cameos in Age. But their scientific counterparts star.

“Their natural-philosopher” counterparts, I should say. The word “scientist” emerged as the Romantic Era closed. Romanticism, a literary and artistic movement, flourished between the 1700s and the 1800s. Romantics championed self-expression, individuality, and emotion over convention and artificiality. Romantics wondered at, and drew inspiration from, the natural world. So, Holmes argues, did Romantic-Era natural philosophers. They explored, searched, and innovated with Wollstonecraft’s, Shelley’s, and Coleridge’s zest.

Age of Wonder

Holmes depicts Wilhelm and Caroline Herschel, a German brother and sister, discovering the planet Uranus. Humphry Davy, an amateur poet from Penzance, inventing a lamp that saved miners’ lives. Michael Faraday, a working-class Londoner, inspired by Davy’s chemistry lectures.

Joseph Banks in paradise.

So Holmes entitled chapter one.

Banks studied natural history as a young English gentleman during the 1760s. He then sailed around the world, a botanist on exploratory expeditions. The second expedition brought Banks aboard the HMS Endeavor. Captain James Cook steered the ship to Brazil, Tahiti, Australia, and New Zealand. Banks brought a few colleagues onboard. They studied the native flora, fauna, skies, and tribes.

Banks, with fellow botanist Daniel Solander, accumulated over 30,000 plant samples. Artist Sydney Parkinson drew the plants during the voyage. Parkinson’s drawings underlay 743 copper engravings that Banks commissioned upon returning to England. Banks planned to publish the engravings as the book Florilegium. He never succeeded. Two institutions executed Banks’s plan more than 200 years later.

Banks’s Florilegium crowns an exhibition at the University of California at Santa Barbara (UCSB). UCSB’s Special Research Collections will host “Botanical Illustrations and Scientific Discovery—Joseph Banks and the Exploration of the South Pacific, 1768–1771” until May 2018. The exhibition features maps of Banks’s journeys, biographical sketches of Banks and Cook, contemporary art inspired by the engravings, and the Florilegium.

online poster

The exhibition spotlights “plants that have subsequently become important ornamental plants on the UCSB campus, throughout Santa Barbara, and beyond.” One sees, roaming Santa Barbara, slivers of Banks’s paradise.

2 bouganvilleas

In Santa Barbara resides the Kavli Institute for Theoretical Physics (KITP). The KITP is hosting a program about the physics of quantum information (QI). QI scientists are congregating from across the world. Everyone visits for a few weeks or months, meeting some participants and missing others (those who have left or will arrive later). Participants attend and present tutorials, explore beyond their areas of expertise, and initiate research collaborations.

A conference capstoned the program, one week this October. Several speakers had founded subfields of physics: quantum error correction (how to fix errors that dog quantum computers), quantum computational complexity (how quickly quantum computers can solve hard problems), topological quantum computation, AdS/CFT (a parallel between certain gravitational systems and certain quantum systems), and more. Swaths of science exist because of these thinkers.

KITP

One evening that week, I visited the Joseph Banks exhibition.

Joseph Banks in paradise.

I’d thought that, by “paradise,” Holmes had meant “physical attractions”: lush flowers, vibrant colors, fresh fish, and warm sand. Another meaning occurred to me, after the conference talks, as I stood before a glass case in the library.

Joseph Banks, disembarking from the Endeavour, didn’t disembark onto just an island. He disembarked onto terra incognita. Never had he or his colleagues seen the blossoms, seed pods, or sprouts before him. Swaths of science awaited. What could the natural philosopher have craved more?

QI scientists of a certain age reminisce about the 1990s, the cowboy days of QI. When impactful theorems, protocols, and experiments abounded. When they dangled, like ripe fruit, just above your head. All you had to do was look up, reach out, and prove a pineapple.

Cowboy

Typical 1990s quantum-information scientist

That generation left mine few simple theorems to prove. But QI hasn’t suffered extinction. Its frontiers have advanced into other fields of science. Researchers are gaining insight into thermodynamics, quantum gravity, condensed matter, and chemistry from QI. The KITP conference highlighted connections with quantum gravity.

…in paradise.

What could a natural philosopher crave more?

Contemporary

Artwork commissioned by the UCSB library: “Sprawling Neobiotic Chimera (After Banks’ Florilegium),” by Rose Briccetti

Most KITP talks are recorded and released online. You can access talks from the conference here. My talk, about quantum chaos and thermalization, appears here. 

With gratitude to the KITP, and to the program organizers and the conference organizers, for the opportunity to participate. 

A Few Words With Caltech Research Scientist, David Boyd

Twenty years ago, David Boyd began his career at Caltech as a Postdoctoral Scholar with Dave Goodwin, and since 2012 has held the position of Research Scientist in the Division of Physics, Mathematics and Astronomy.  A 20 year career at Caltech is in itself a significant achievement considering Caltech’s flair for amassing the very best scientists from around the world.  Throughout Boyd’s career he has secured 7 patents, and most recently discovered a revolutionary single-step method for growing graphene.  The method allows for unprecedented continuity in graphene growth essential to significantly scaling-up production capacity.  Boyd worked with a number of great scientists at the outset of his career.  Notably, he gained a passion for science from Professor Thomas Wdowiak (Mars’ Wdowiak Ridge is named in his honor) at the University of Alabama at Birmingham as an undergraduate, and worked as David Goodwin’s (best known for developing methods for growing thin film high-purity diamonds) postdoc at Caltech.  Currently, Boyd is formulating a way to apply Goodwin’s reaction modeling code to graphene.  Considering Boyd’s accomplishments and extensive scientific knowledge, I feel fortunate to have been afforded the opportunity to work in his lab the past six summers. I have learned much from Boyd, but I still have more questions (not all scientific), so I requested an interview and he graciously accepted.

On the day of the interview, I meet Boyd at his office on campus at Caltech.  We walk a ways down a sunlit hallway and out to a balcony through two glass doors.  There’s a slight breeze in the air, a smell of nearby roses, and the temperature is perfect.  It’s a picturesque day in Pasadena.  We sit at a table and I ask my first question.

How many patents do you own?

I have seven patents.  The graphene patent was really hard to get, but we got it.  We just got it executed in China, so they are allowed to use it.  This is particularly exciting because of all the manufacturing in China.  The patent system has changed a bit, so it’s getting harder and harder.  You can come up with the idea, but if disparate components have already been patented, then you can’t get the patent for combining them in a unique way.  The invention has to provide a result that is unexpected or not obvious, and the patent for growing graphene with a one step process was just that.  The one step process refers to cleaning the copper substrate and growing graphene under the same chemistry in a continuous manner.  What used to be a two step process can be done in one.

You don’t have to anneal the substrate to 1000 degrees before growing.

Exactly.  Annealing the copper first and then growing doesn’t allow for a nice continuous process.  Removing the annealing step means the graphene is growing in an environment with significantly lower temperatures, which is important for CMOS or computer chip manufacturing.

Which patents do you hold most dear?

Usually in the research areas that are really cutting edge.  I have three patents in plasmonics, and that was a fun area 10 years ago.  It was a new area and we were doing something really exciting.  When you patent something, an application may never be realized, sometimes they get used and sometimes they don’t.  The graphene patent has already been licensed, so we’ve received quite a bit of traction.  As far as commercial success, the graphene has been much more successful than the other ones, but plasmonics were a lot of fun.  Water desalinization may be one application, and now there is a whole field of plasmonic chemistry.  A company has not yet licensed it, so it may have been too far ahead of its time for application anytime soon.

When did you realize you wanted to be a scientist?

I liked Physics in high school, and then I had a great mentor in college, Thomas Wdowiak.  Wdowiak showed me how to work in the lab.  Science is one of those things where an initial spark of interest drives you into action.  I became hooked, because of my love for science, the challenge it offers, and the simple fact I have fun with it.  I feel it’s very important to get into the lab and start learning science as early as possible in your education.

Were you identified as a gifted student?

I don’t think that’s a good marker.  I went to a private school early on, but no, I don’t think I was good at what they were looking for, no I wasn’t.  It comes down to what you want to do.  If you want to do something and you’re motivated to do it, you’ll find ways to make it happen.  If you want to code, you start coding, and that’s how you get good at it.  If you want to play music and have a passion for it, at first it may be your parents saying you have to go practice, but in the end it’s the passion that drives everything else.

Did you like high school?

I went to high school in Alabama and I had a good Physics teacher.  It was not the most academic of places, and if you were into academics the big thing there was to go to medical school.  I just hated memorizing things so I didn’t go that route.

Were AP classes offered at your high school, and if so, were you an AP student?

Yeah, I did take AP classes.  My high school only had AP English and AP Math, but it was just coming onboard at that time.  I took AP English because I liked the challenge and I love reading.

Were you involved in any extracurricular activities in school?

I earned the rank of Eagle Scout in the Boy Scouts.  I also raced bicycles in high school, and I was a several time state champion.  I finished high school (in America) and wanted to be a professional cyclist.  So, I got involved in the American Field Service (AFS), and did an extra year of high school in Italy as an exchange student where I ended up racing with some of the best cyclists in the world all through Italy.  It was a fantastic experience.

Did you have a college in mind for your undergraduate studies?  

No, I didn’t have a school in mind.  I had thought about the medical school path, so I considered taking pre-med courses at the local college, University of Alabama at Birmingham (UAB), because they have a good medical school.  Then UAB called me and said I earned an academic scholarship.  My father advised me that it would be a good idea to go there since it’s paid for.  I could take pre-med courses and then go to medical school afterwards if I wanted.  Well, I was in an honors program at the university and met an astronomer by the name Thomas Wdowiak.  I definitely learned from him how to be a scientist.  He also gave me a passion for being a scientist.  So, after working with Wdowiak for a while, I decided I didn’t want to go to medical school, I wanted to study Physics.  They just named a ridge on Mars after him, Wdowiak Ridge.  He was a very smart guy, and a great experimentalist who really grew my interest in science… he was great.

Did you do research while earning your undergraduate degree?  

Yes, Wdowiak had me in the lab working all the time.  We were doing real stuff in the lab.  I did a lot of undergraduate research in Astronomy, and the whole point was to get in the lab and work on science.  Because I worked with Wdowiak I had one or two papers published by the time I graduated.  Wdowiak taught me how to do science.   And that’s the thing, you have to want to do science, have a lab or a place to practice, and then start working.  

So, he was professor and experimentalist.

He was a very hands-on lab guy.  I was in the lab breaking things and fixing things. Astronomers are fun to work with.  He was an experimental astronomer who taught me, among other things, spectroscopy, vacuum technology, and much about the history of science.  In fact, it was Professor Wdowiak who told me about Millikan’s famous “Machine Shop in a Vacuum” experiment that inspired the graphene discovery… it all comes back to Caltech!

Name another scientist, other than Wdowiak, who has influenced you.

Richard Feynman also had a big influence on me.  I did not know him, but I love his books.

Were you focused solely on academics in college, or did you have a social life as well?

I was part of a concert committee that brought bands to the college.  We had some great bands like R.E.M. and the Red Hot Chili Peppers play, and I would work as a stagehand and a roadie for the shows.

So, you weren’t doing keg stands at fraternity parties?

No, it wasn’t like that.  I liked to go out and socialize, but no keg stands.  Though, I have had friends that were very successful that did do keg stands.

What’s your least favorite part of your job?

You’re always having to raise funds for salaries, equipment, and supplies.  It can be difficult, but once you get the funding it is a relief for the moment.  As a scientist, your focus isn’t always on just the science.

What are your responsibilities related to generating revenue for the university?

I raise funds for my projects via grants.  Part of the money goes to Caltech as overhead to pay for the facilities, lab space, and to keep the lights on.

What do you wish you could do more of in your job?

Less raising money.  I like working in the lab, which is fun.  Now that I have worked out the technique to grow graphene, I’m looking for applications.  I’m searching for the next impactful thing, and then I’ll figure out the necessary steps that need to be taken to get there.

Is there an aspect of your job that you believe would surprise people?

You have to be entrepreneurial, you have to sell your ideas to raise money for these projects.  You have to go with what’s hot in research.  There are certain things that get funded and things that don’t.

There may be some things you’re interested in, but other people aren’t, so there’s no funding.

Yeah, there may not be a need, therefore, no funding.  Right now, graphene is a big thing, because there are many applications and problems to be solved.  For example, diamonds were huge back in the ‘80’s.  But once they solved all the problems, research cooled off and industrial application took over.

Is there something else you’d really rather be researching, or are the trending ideas right now in line with your interests?

There is nothing else I’d rather be researching.  I’m in a good place right now.  We’re trying to commercialize the graphene research.  You try to do research projects that are complementary to one another.  For example, there’s a project underway, where graphene is being used for hydrogen storage in cars, that really interests me.  I do like the graphene work, it’s exciting, we’ll see where that goes.

What are the two most important personality traits essential to being a good scientist?

Creativity.  You have to think outside the box.  Perseverance.  I’m always reading and trying to understand something better.  Curiosity is, of course, a huge part of it as well. You gotta be obsessive too, I guess.  That’s more than two, sorry.

What does it take for someone to become a scientist?

You must have the desire to be a scientist, otherwise you’ll go be a stockbroker or something else.  It’s more of a passion thing, your personality.  You do have to have an aptitude for it though.  If you’re getting D’s in math, physics is probably not the place for you.  There’s an old joke, the medical student in physics class asks the professor, “Why do we have to take physics?  We’ll never use it.”  The Physics professor answers, “Physics saves lives, because it keeps idiots out of medical school.”  If you like science, but you’re not so good at math, then look at less quantitative areas of science where math is not as essential.  Computational physics and experimental physics will require you to be very good at math.  It takes a different temperament, a different set of skills.  Same curiosity, same drive and intelligence, but different temperament.

Do you ever doubt your own abilities?  Do you have insecurities about not being smart enough?

Sure, but there’s always going to be someone out there smarter.  Although, you really don’t want to ask yourself these types of questions.  If you do, you’re looking down the wrong end of the telescope.  Everyone has their doubts, but you need to listen to the feedback from the universe.  If you’re doing something for a long time and not getting results, then that’s telling you something.  Like I said, you must have a passion for what you’re doing.  If people are in doubt they should read biographies of scientists and explore their mindset to discover if science seems to be a good fit for them.  For a lot of people, it’s not the most fun job, it’s not the most social job, and certainly not the most glamorous type of job.  Some people need more social interaction, researchers are usually a little more introverted.  Again, it really depends on the person’s temperament. There are some very brilliant people in business, and it’s definitely not the case that only the brilliant people in a society go into science.  It doesn’t mean you can’t be doing amazing things just because you’re not in a scientific field.  If you like science and building things, then follow that path.  It’s also important not to force yourself to study something you don’t enjoy.

Scientists are often thought to work with giant math problems that are far above the intellectual capabilities of mere mortals.  Have you ever been in a particular situation where the lack of a solution to a math problem was impeding progress in the lab?  If so, what was the problem and did you discover the solution?

I’m attempting to model the process of graphene growth, so I’m facing this situation right now.  That’s why I have this book here.  I’m trying to adapt Professor Dave Goodwin’s Cantera reactor modeling code to model the reaction kinetics in graphene (Goodwin originally developed and wrote the modeling software called Cantera).  Dave was a big pioneer in diamond and he died almost 5 years ago here in Pasadena.  He developed a reaction modeling code for diamond, and I’m trying to apply that to graphene.  So, yeah, it’s a big math problem that I’ve been spending weeks on trying to figure out.  It’s not that I’m worried about the algebra or the coding, it’s trying to figure things out conceptually.

Do you love your job?

I do, I’ve done it for awhile, it’s fun, and I really enjoy it.  When it works, it’s great. Discovering stuff is fun and possesses a great sense of satisfaction.  But it’s not always that way, it can be very frustrating.  Like any good love affair, it has its peaks and valleys.  Sometimes you hate it, but that’s part of the relationship, it’s like… aaarrgghh!!

 

Standing back at Stanford

T-shirt 1

This T-shirt came to mind last September. I was standing in front of a large silver-colored table littered with wires, cylinders, and tubes. Greg Bentsen was pointing at components and explaining their functions. He works in Monika Schleier-Smith’s lab, as a PhD student, at Stanford.

Monika’s group manipulates rubidium atoms. A few thousand atoms sit in one of the cylinders. That cylinder contains another cylinder, an optical cavity, that contains the atoms. A mirror caps each of the cavity’s ends. Light in the cavity bounces off the mirrors.

Light bounces off your bathroom mirror similarly. But we can describe your bathroom’s light accurately with Maxwellian electrodynamics, a theory developed during the 1800s. We describe the cavity’s light with quantum electrodynamics (QED). Hence we call the lab’s set-up cavity QED.

The light interacts with the atoms, entangling with them. The entanglement imprints information about the atoms on the light. Suppose that light escaped from the cavity. Greg and friends could measure the light, then infer about the atoms’ quantum state.

A little light leaks through the mirrors, though most light bounces off. From leaked light, you can infer about the ensemble of atoms. You can’t infer about individual atoms. For example, consider an atom’s electrons. Each electron has a quantum property called a spin. We sometimes imagine the spin as an arrow that points upward or downward. Together, the electrons’ spins form the atom’s joint spin. You can tell, from leaked light, whether one atom’s spin points upward. But you can’t tell which atom’s spin points upward. You can’t see the atoms for the ensemble.

Monika’s team can. They’ve cut a hole in their cylinder. Light escapes the cavity through the hole. The light from the hole’s left-hand edge carries information about the leftmost atom, and so on. The team develops a photograph of the line of atoms. Imagine holding a photograph of a line of people. You can point to one person, and say, “Aha! She’s the xkcd fan.” Similarly, Greg and friends can point to one atom in their photograph and say, “Aha! That atom has an upward-pointing spin.” Monika’s team is developing single-site imaging.

Solvay

Aha! She’s the xkcd fan.

Monika’s team plans to image atoms in such detail, they won’t need for light to leak through the mirrors. Light leakage creates problems, including by entangling the atoms with the world outside the cavity. Suppose you had to diminish the amount of light that leaks from a rubidium cavity. How should you proceed?

Tell the mirrors,

T-shirt 2

You should lengthen the cavity. Why? Imagine a photon, a particle of light, in the cavity. It zooms down the cavity’s length, hits a mirror, bounces off, retreats up the cavity’s length, hits the other mirror, and bounces off. The photon repeats this process until a mirror hit fails to generate a bounce. The mirror transmits the photon to the exterior; the photon leaks out. How can you reduce leaks? By preventing photons from hitting mirrors so often, by forcing the photons to zoom longer, by lengthening the cavity, by shifting the mirrors outward.

So Greg hinted, beside that silver-colored table in Monika’s lab. The hint struck a chord: I recognized the impulse to

T-shirt 3

The impulse had led me to Stanford.

Weeks earlier, I’d written my first paper about quantum chaos and information scrambling. I’d sat and read and calculated and read and sat and emailed and written. I needed to stand up, leave my cavity, and image my work from other perspectives.

Stanford physicists had written quantum-chaos papers I admired. So I visited, presented about my work, and talked. Patrick Hayden introduced me to a result that might help me apply my result to another problem. His group helped me simplify a mathematical expression. Monika reflected that a measurement scheme I’d proposed sounded not unreasonable for cavity QED.

And Greg led me to recognize the principle behind my visit: Sometimes, you have to

T-shirt 4

to move forward.

With gratitude to Greg, Monika, Patrick, and the rest of Monika’s and Patrick’s groups for their time, consideration, explanations, and feedback. With thanks to Patrick and Stanford’s Institute for Theoretical Physics for their hospitality.

What Clocks have to do with Quantum Computation

Have you ever played the game “telephone”? You might remember it from your nursery days, blissfully oblivious to the fact that quantum mechanics governs your existence, and not yet wondering why Fox canceled Firefly. For everyone who forgot, here is the gist of the game: sit in a circle with your friends. Now you think of a story (prompt: a spherical weapon that can destroy planets). Once you have the story laid out in your head, tell it to your neighbor on your left. She takes the story and tells it to her friend on her left. It is important to master the art of whispering for this game: you don’t want to be overheard when the story is passed on. After one round, the friend on your right tells you what he heard from his friend on his right. Does the story match your masterpiece?

If your story is generic, it probably survived without alterations. Tolstoy’s War and Peace, on the other hand, might turn into a version of Game of Thrones. Passing along complex stories seems to be more difficult than passing on easy ones, and it also becomes more prone to errors the more friends join your circle—which makes intuitive sense.

So what does this have to do with physics or quantum computation?

Let’s add maths to this game, because why not. Take a difficult calculation that follows a certain procedure, such as long division of two integer numbers.

long-division

Now you perform one step of the division and pass the piece of paper on to your left. Your friend there is honest and trusts you: she doesn’t check what you did, but happily performs the next step in the division. Once she’s done, she passes the piece of paper on to her left, and so on. By the time the paper reaches you again, you hopefully have the result of the calculation, given you have enough friends to divide your favorite numbers, and given that everyone performed their steps accurately.

I’m not sure if Feynman thought about telephone when he, in 1986, proposed a method of embedding computation into eigenstates (e.g. the ground state) of a Hamiltonian, but the fact remains that the similarity is striking. Remember that writing down a Hamiltonian is a way of describing a quantum-mechanical system, for instance how the constituents of a multi-body system are coupled with each other. The ground state of such a Hamiltonian describes the lowest energy state that a system assumes when it is cooled down as far as possible. Before we dive into how the Hamiltonian looks, let’s try to understand how, in Feynman’s construction, a game of telephone can be represented as a quantum state of a physical system.

telephone-history-state

In this picture, | \psi_t \rangle represents a snapshot of the story or calculation at time t—in the division example, this would be the current divisor and remainder terms; so e.g. the snapshot | \psi_1 \rangle represents the initial dividend and divisor, and the person next to you is thinking of | \psi_2 \rangle, one step into the calculation. The label |t\rangle in front of the tensor sign \otimes is like a tag that you put on files on your computer, and uniquely associates the snapshot | \psi_t \rangle with the t-th time step. We say that the story snapshot is entangled with its label.

This is also an example of quantum superposition: all the |t\rangle\otimes|\psi_t\rangle are distinct states (the time labels, if not the story snapshots, are all unique), and by adding these states up we put them into superposition. So if we were to measure the time label, we would obtain one of the snapshots uniformly at random—it’s as if you had a cloth bag full of cards, and you blindly pick one. One side of the card will have the time label on it, while the other side contains the story snapshot. But don’t be fooled—you cannot access all story snapshots by successive measurements! Quantum states collapse; whatever measurement outcome you have dictates what the quantum state will look like after the measurement. In our example, this means that we burn the cloth bag after you pick your card; in this sense, the quantum state behaves differently than a simple juxtaposition of scraps of paper.

Nonetheless, this is the reason why we call such a quantum state a history state: it preserves the history of the computation, where every step that is performed is appropriately tagged. If we manage to compare all pairs of successively-labeled snapshots (without measuring them!), one can verify that the end result does, in fact, stem from a valid computation—and not just a random guess. In the division example, this would correspond to checking that each of your friends performs a correct division step.

So history states are clearly useful. But how do you design a Hamiltonian with a history state as the ground state? Is it even possible? The answer is yes, and it all boils down to verifying that two successive snapshots | \psi_t \rangle and | \psi_{t+1} \rangle are related to each other in the correct manner, e.g. that your friend on seat t+1 performs a valid division step from the snapshot prepared by the person on seat t. In fancy physics speak (aka Bra-Ket notation), we can for example write

local-check

The actual Hamiltonian will then be a sum of such terms, and one can verify that its ground state is indeed the one representing the history state we introduced above.

I’m glossing over a few details here: there is a minus sign in front of this term, and we have to add its Hermitian conjugate (flip the labels and snapshots around). But this is not essential for the argument, so let’s not go there for now. However, you’re totally right with one thing: it wouldn’t make sense to write down all snapshots themselves into the Hamiltonian! After all, if we had to calculate every snapshot transition like | \psi_2 \rangle \langle \psi_1 | in advance, there would be no use to this construction. So instead, we can write

local-check-2.png

Perfect. We now have a Hamiltonian which, in its ground state, can encode the history of a computation, and if we replace the transition operator \mathbf U_\text{DIVISION} with another desired transition operator (a unitary matrix), we can perform any computation we want (more precisely, any computation that can be written as a unitary matrix; this includes anything your laptop can do). However, this is only half of the story, since we need to have a way of reading out the final answer. So let’s step back for a moment, and go back to the telephone game.

Can you motivate your friends to cheat?

Your friends playing telephone make mistakes.

no-mistakes

Ok, let’s assume we give them a little incentive: offer $1 to the person on your right in case the result is an even number. Will he cheat? With so much at stake?

no-mistakes-bribe.png

In fact, maybe your friend is not only greedy but also dishonest: he wants to hide the fact that he miscalculates on purpose, and sometimes tells his friend on his right to make a mistake instead (maybe giving him a share of the money). So for a few of your friends close to the person at the end of the chain, there is a real incentive to cheat!

local-check-3.png

Can we motivate spins to cheat?

We already discussed how to write down a Hamiltonian that verifies valid computational steps. But can we do the same thing as bribing your friends to procure a certain outcome? Can we give an energy bonus to certain outcomes of the computation?

In fact, we can. Alexei Kitaev proposed adding a term to Feynman’s Hamiltonian which raises the energy of an unwanted outcome, relative to a desirable outcome. How? Again in fancy physics language,

local-check-4.png

What this term does is that it takes the history state and yields a negative energy contribution (signaled by the minus sign in front) if the last snapshot | \psi_T \rangle is an even number. If it isn’t, no bonus is felt; this would correspond to you keeping the dollar you promised to your friend. This simply means that in case the computation has a desirable outcome—i.e. an even number—the Hamiltonian allows a lower energy ground state than for any other output. Et voilà, we can distinguish between different outputs of the computation.

The true picture is, of course, a tad more complicated; generally, we give penalty terms to unwanted states instead of bonus terms to desirable ones. The reason for this is somewhat subtle, but can potentially be explained with an analogy: humans fear loss much more than they value gains of the same magnitude. Quantum systems behave in a completely opposite manner: the promise of a bonus at the end of the computation is such a great incentive that most of the weight of the history state will flock to the bonus term (for the physicists: the system now has a bound state, meaning that the wave function is localized around a specific site, and drops off exponentially quickly away from it). This makes it difficult to verify the computation far away from the bonus term.

So the Feynman-Kitaev Hamiltonian consists of three parts: one which checks each step of the computation, one which penalizes invalid outcomes—and obviously we also need to make sure the input of the computation is valid. Why? Well, are you saying you are more honest than your friends?

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Physical Implications of History State Hamiltonians

If there is one thing I’ve learned throughout my PhD it is that we should always ask what use a theory is. So what can we learn from this construction? Almost 20 years ago, Alexei Kitaev used Feynman’s idea to prove that estimating the ground state energy of a physical system with local interactions is hard, even on a quantum computer (for the experts: QMA-hard under the assumption of a 1/\text{poly} promise gap splitting the embedded YES and NO instances). Why is estimating the ground state energy hard? The energy shift induced by the output penalty depends on the outcome of the computation that we embed (e.g. even or odd outcome). And as fun as long division is, there are much more difficult tasks we can write down as a history state Hamiltonian—in fact, it is this very freedom which makes estimating the ground state energy difficult: if we can embed any computation we want, estimating the induced energy shift should be at least as hard as actually performing the computation on a quantum computer. This has one curious implication: if we don’t expect that we can estimate the ground state energy efficiently, the physical system will take a long time to actually assume its ground state when cooled down, and potentially behave like a spin glass!

Feynman’s history state construction and the QMA-hardness proof of Kitaev were a big part of the research I did for my PhD. I formalized the case where the message is not passed on along a unique path from neighbor to neighbor, but can take an arbitrary path between beginning and end in a more complicated graph; in this way, computation can in some sense be parallelized.

Well, to be honest, the last statement is not entirely true: while there can be parallel tracks of computation from A to B, these tracks have to perform the same computation (albeit in potentially different steps); otherwise the system becomes much more complicated to analyze. The reason why this admittedly quite restricted form of branching might still be an advantage is somewhat subtle: if your computation has a lot of classical if-else cases, but you don’t have enough space on your piece of paper to store all the variables to check the conditions, it might be worth just taking a gamble: pass your message down one branch, in the hope that the condition is met. The only thing that you have to be careful about is that in case the condition isn’t met, you don’t produce invalid results. What use is that in physics? If you don’t have to store a lot of information locally, it means you can get away using a much lower local spin dimension for the system you describe.

Such small and physically realistic models have as of late been proposed as actual computational devices (called Hamiltonian quantum computers), where a prepared initial state is evolved under such a history state Hamiltonian for a specific time, in contrast to the static property of a history ground state we discussed above. Yet whether or not this is something one could actually build in a lab remains an open question.

Last year, Thomas Vidick invited me to visit Caltech, and I worked with IQIM postdoc Elizabeth Crosson to improve the analysis of the energy penalty that is assigned to any history state that cheats the constraints in the Feynman-Kitaev Hamiltonian. We identified some open problems and also proved limitations on the extent of the energetic penalty that these kinds of Hamiltonians can have. This summer I went back to Caltech to further develop these ideas and make progress towards a complete understanding of such “clock” Hamiltonians, which Elizabeth and I are putting together in a follow-up work that should appear soon.

It is striking how such simple idea can have so profound an implication across fields, and remain relevant, even 30 years after its first proposal.

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Feynman concludes his 1986 Foundations of Physics paper with the following words.

At any rate, it seems that the laws of physics present no barrier to reducing the size of computers until bits are the size of atoms, and quantum behavior holds dominant sway.

For my part, I hope that he was right and that history state constructions will play a part in this future.

Decoding (the allure of) the apparent horizon

I took 32 hours to unravel why Netta Engelhardt’s talk had struck me.

We were participating in Quantum Information in Quantum Gravity III, a workshop hosted by the University of British Columbia (UBC) in Vancouver. Netta studies quantum gravity as a Princeton postdoc. She discussed a feature of black holes—an apparent horizon—I’d not heard of. After hearing of it, I had to grasp it. I peppered Netta with questions three times in the following day. I didn’t understand why, for 32 hours.

After 26 hours, I understood apparent horizons like so.

Imagine standing beside a glass sphere, an empty round shell. Imagine light radiating from a point source in the sphere’s center. Think of the point source as a minuscule flash light. Light rays spill from the point source.

Which paths do the rays follow through space? They fan outward from the sphere’s center, hit the glass, and fan out more. Imagine turning your back to the sphere and looking outward. Light rays diverge as they pass you.

At least, rays diverge in flat space-time. We live in nearly flat space-time. We wouldn’t if we neighbored a supermassive object, like a black hole. Mass curves space-time, as described by Einstein’s theory of general relativity.

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Imagine standing beside the sphere near a black hole. Let the sphere have roughly the black hole’s diameter—around 10 kilometers, according to astrophysical observations. You can’t see much of the sphere. So—imagine—you recruit your high-school-physics classmates. You array yourselves around the sphere, planning to observe light and compare observations. Imagine turning your back to the sphere. Light rays would converge, or flow toward each other. You’d know yourself to be far from Kansas.

Picture you, your classmates, and the sphere falling into the black hole. When would everyone agree that the rays switch from diverging to converging? Sometime after you passed the event horizon, the point of no return.1 Before you reached the singularity, the black hole’s center, where space-time warps infinitely. The rays would switch when you reached an in-between region, the apparent horizon.

Imagine pausing at the apparent horizon with your sphere, facing away from the sphere. Light rays would neither diverge nor converge; they’d point straight. Continue toward the singularity, and the rays would converge. Reverse away from the singularity, and the rays would diverge.

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UBC near twilight

Rays diverged from the horizon beyond UBC at twilight. Twilight suits UBC as marble suits the Parthenon; and UBC’s twilight suits musing. You can reflect while gazing on reflections in glass buildings, or reflections in a pool by a rose garden. Your mind can roam as you roam paths lined by elms, oaks, and willows. I wandered while wondering why the sphere intrigued me.

Science thrives on instrumentation. Galileo improved the telescope, which unveiled Jupiter’s moons. Alexander von Humboldt measured temperatures and pressures with thermometers and barometers, charting South America during the 1700s. The Large Hadron Collider revealed the Higgs particle’s mass in 2012.

The sphere reminded me of a thermometer. As thermometers register temperature, so does the sphere register space-time curvature. Not that you’d need a sphere to distinguish a black hole from Kansas. Nor do you need a thermometer to distinguish Vancouver from a Brazilian jungle. But thermometers quantify the distinction. A sphere would sharpen your observations’ precision.

A sphere and a light source—free of supercolliders, superconductors, and superfridges. The instrument boasts not only profundity, but also simplicity.

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Alexander von Humboldt

Netta proved a profound theorem about apparent horizons, with coauthor Aron Wall. Jakob Bekenstein and Stephen Hawking had studied event horizons during the 1970s. An event horizon’s area, Bekenstein and Hawking showed, is proportional to the black hole’s thermodynamic entropy. Netta and Aron proved a proportionality between another area and another entropy.

They calculated an apparent horizon’s area, A. The math that represents their black hole represents also a quantum system, by a duality called AdS/CFT. The quantum system can occupy any of several states. Different states encode different information about the black hole. Consider the information needed to describe, fully and only, the region outside the apparent horizon. Some quantum state \rho encodes this information. \rho encodes no information about the region behind the apparent horizon, closer to the black hole. How would you quantify this lack of information? With the von Neumann entropy S(\rho). This entropy is proportional to the apparent horizon’s area: S( \rho )  \propto  A.

Netta and Aron entitled their paper “Decoding the apparent horizon.” Decoding the apparent horizon’s allure took me 32 hours and took me to an edge of campus. But I didn’t mind. Edges and horizons suited my visit as twilight suits UBC. Where can we learn, if not at edges, as where quantum information meets other fields?

 

With gratitude to Mark van Raamsdonk and UBC for hosting Quantum Information in Quantum Gravity III; to Mark, the other organizers, and the “It from Qubit” Simons Foundation collaboration for the opportunity to participate; and to Netta Engelhardt for sharing her expertise.

1Nothing that draws closer to a black hole than the event horizon can turn around and leave, according to general relativity. The black hole’s gravity pulls too strongly. Quantum mechanics implies that information leaves, though, in Hawking radiation.

Teacher Research at Caltech

The Yeh Lab group’s research activities at Caltech have been instrumental in studying semiconductors and making two-dimensional materials such as graphene, as highlighted on a BBC Horizons show.  

An emerging sub-field of semiconductor and two-dimensional research is that of Transition metal dichalcogenide (TDMC) monolayers. In particular, a monolayer of Tungsten disulfide, a TDMC, is believed to exhibit interesting semiconductor properties when exposed to circularly polarized light. My role in the Yeh Lab, as a visiting high school Physics Teacher intern,  for the Summer of 2017 has been to help research and set up a vacuum chamber to study Tungsten disulfide samples under circularly polarized light.

What makes semiconductors unique is that conductivity can be controlled by doping or changes in temperature. Higher temperatures or doping can bridge the energy gap between the valence and conduction bands; in other words, electrons can start moving from one side of the material to the other. Like graphene, Tungsten disulfide has a hexagonal, symmetric crystal structure. Monolayers of transition metal dichalcogenides in such a honeycomb structure have two valleys of energy. One valley can interact with another valley. Circularly polarized light is used to populate one valley versus another. This gives a degree of control over the population of electrons by polarized light.

The Yeh Lab Group prides itself on making in-house the materials and devices needed for research. For example, in order to study high temperature superconductors, the Yeh Group designed and built their own scanning tunneling microscope. When they began researching graphene, instead of buying vast quantities of graphene, they pioneered new ways of fabricating it. This research topic has been no different: Wei-hsiang Lin, a Caltech graduate student, has been busy fabricating Tungsten disulfide samples via chemical vapor deposition (CVD) using Tungsten oxide and sulfur powder.  

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Wei-hsiang Lin’s area for using PLD to form the TDMC samples

The first portion of my assignment was spent learning more about vacuum chambers and researching what to order to confine our sample into the chamber. One must determine how the electronic feeds should be attached, how many are necessary, which vacuum pump will be used, how many flanges and gaskets of each size must be purchased in order to prepare the vacuum chamber.

There were also a number of flanges and parts already in the lab that needed to be examined for possible use. After triple checking the details the order was set with Kurt J. Lesker. Following a sufficient amount of anti-seize lubricant and numerous nuts, washers, and bolts, we assembled the vacuum chamber that will hold the TDMC sample.

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The original vacuum chamber


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Fun in the lab


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The prepped vacuum chamber

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The second part of my assignment was spent researching how to set up the optics for our experiment and ordering the necessary equipment. Once the experiment is up and running we will be using a milliWatt broad spectrum light source that is directed into a monochromator to narrow down the light to specific wavelengths for testing. Ultimately we will be evaluating the giant wavelength range of 300 nm through 1800 nm. Following the monochromator, light will be refocused by a planoconvex lens. Next, light will pass through a linear polarizer and then a circular polarizer (quarter wave plate). Lastly, the light will be refocused by a biconvex lens into the vacuum chamber and onto a 1 mm by 1 mm area of the sample.  

Soon, we are excited to verify how tungsten disulfide responds to circularly polarized light.  Does our sample resonate at the exact same wavelengths as the first labs found? Why or why not?  What other unique properties are observed?  How can they be explained?  How is the Hall Effect observed?  What does this mean for the possible applications of semiconductors? How can the transfer of information from one valley to another be used in advanced electronics for communication?  Then, similar exciting experimentation will take place with graphene under circularly polarized light.

I love the sharp contrast of the high-energy, adolescent classroom to the quiet, calm of the lab.  I am grateful for getting to learn a different and new-to-me area of Physics during the summer.  Yes, I remember studying polarization and semiconductors in high school and as an undergraduate.  But it is completely different to set up an experiment from scratch, to be a part of groundbreaking research in these areas.  And it is just fun to get to work with your hands and build research equipment at a world leading research university.  Sometimes Science teachers can get bogged down with all the paperwork and meetings.  I am grateful to have had this fabulous opportunity during the summer to work on applied Science and to be re-energized in my love for Physics.  I look forward to meeting my new batch of students in a few short weeks to share my curiosity and joy for learning how the world works with them.

Two Views of the Eclipse

I am sure many of us are thinking about the eclipse.

It all starts with how far are we going to drive in order to see totality. My family and I are currently in Colorado, so we are relatively close to the path of darkness in Wyoming. I thought about trying to book a hotel room. But if you’d like to see the dusk in Lusk, here is what you get:

Let us just say that I became quite acquainted with small-town WY and any-ville NE before giving up. Driving in the same day for 10 hours with my two children, ages 4 and 5, was not an option. So I will have to be content with 90% coverage.

90% coverage sounds like it is good enough… But when you think about the sun and its output, you realize that it won’t actually be very dark. The sun gives out about 1kW of light and heat per square meter. 90% of that still leaves us with 100W per meter squared. Imagine a room lit by a square array of 100W incandescent bulbs at one meter apart from each other. Not so dark. Luckily, we have really dark eclipse glasses.

All things considered, it is a huge coincidence that the moon is just about the right size and distance from the earth to block the sun exactly, \frac{\mbox{sun radius}}{\mbox{sun-Earth distance}}=\frac{0.7\cdot 10^6 km}{150\cdot 10^6 km}\approx \frac{\mbox{luna radius}}{\mbox{luna-Earth distance}}=\frac{1.7\cdot 10^3 km}{385\cdot 10^3 km}.

On a more personal note, another coincidence of a lesser cosmic meaning is that my wife, Jocelyn Holland, a professor of comparative literature at UCSB and Caltech, has also done research on eclipses. She has recently published an essay that shows how, for nineteenth-century observers, and astronomers in particular, the unique darkness associated with the eclipse during totality shook their subjective experience of time. Readers might want to share their own personal experiences at the end of this blog so that we can see how a twenty-first century perspective compares.

As for Jocelyn’s paper, here is a redacted ‘poetry for scientists’ excerpt from it.

Eclipses are well-known objects of scientific study but it is just as true that, throughout history, they have been perceived as the most supernatural of events, permitting superstition and fear to intrude. As a result, eclipses have frequently been used across cultures, in particular, by the community of scientists and scholars, as an index of “enlightenment.” Astronomers in the nineteenth century – an epoch that witnessed several mathematical advances in the calculation of solar and lunar eclipses, as exemplified in the work of Friedrich Bessel – looked back at prior centuries with scorn, mocking the irrational fears of times past. The German astronomer Ludwig August Busch, in text published shortly before a total eclipse in 1851, points out with some smugness that scarcely 200 years before then, in Germany, “the majority of the population threw itself upon its knees in desperation during a total eclipse,” and that the composure with which the next eclipse will be greeted is “the most certain proof how only science is able to conquer prejudices and superstition which prior centuries have gone through.”

Two solar eclipses were witnessed by Europeans in the mid-nineteenth century, on July 8th, 1842 and July 28th, 1851, when the first photographic image of an eclipse was made by Julius Berkowski (see below).

What Berkowski’s daguerreotype cannot convey, however, is a particular perception shared by both professional astronomers and amateur observers of these eclipses: that the darkness of the eclipse’s totality is unlike any darkness they had experienced before. As it turns out, this perception posed a challenge to their self-proclaimed enlightenment.

There was already a historical record in place describing the strange darkness of a total eclipse. As another nineteenth-century astronomer, Jacob Lehmann, phrased it, “How is it now to be explained, namely what several observers report during the eclipse of 1706, that the darkness at the time of the total occultation of the sun compares neither to night nor to dusk, but rather is of a particular kind. What is this particular kind?” The strange darkness of the eclipse presents a problem that one can state quite simply in temporal terms: it corresponds to no prior experience of natural light or time of day.

It might strike us as odd that August Ludwig Busch, the same astronomer who derided the superstition of prior generations, writes the following with reference to eclipses past, and in anticipation of the eclipse of 1851:

You will all remember the inexplicable melancholic frame of mind which one already experiences during large if not even total eclipses, when all objects appear in a dull, unusual light, there lies namely in the sight of great plains and far-spread drifts, upon which trees and rocks, although still illuminated by sunlight, still seem to cast no shadow, such a thing which causes mourning, that one is involuntarily overcome by horror. This feeling should occur more intensely in people when, during the total eclipse, a very peculiar darkness arrives which can be named neither night nor dusk.

August Ludwig Busch.

One can say that the perceived relationship between the quality of light and time of day is based on expectations that are so innate as to be taken as infallible until experience teaches otherwise. It is natural for us to use the available light in the sky as the basis for a measure of time when no time-keeping piece is on hand. The cyclical predictability of a steady increase and decrease in available light during the course of the day, however, in addition to all the nuances of how the midday light differs from dawn and twilight, is less than helpful in the rare event of an eclipse. The quality of light does not correspond to any experience of lived time. As a consequence, not only August Ludwig Busch, but also numerous other observers, attributed it to death, as if for lack of an alternative.

For all their claims of rationality, nineteenth-century observers were troubled by this darkness that conformed to no experienced time of day. It signaled to them, among other things, that time and light are out of joint. In short, as natural and as it may be, a full solar eclipse has, historically, posed a real challenge: not to the predictability of mechanical time-keeping, but rather to a very human experience of time.