Welcome to Carlos Mochon's publications page!

Over the years I have written a number of scientific articles in the field of quantum computation, information and cryptography. Most of my research has focused on the areas of quantum computation with non-abelian anyons and quantum protocols for coin flipping by telephone. Links to my publications can be found below.

Having completed a postdoc at the Perimeter Institute, I have decided that it is time for me to settle down and find a permanent job. Sadly, this means that I must depart academia. My new job is at the D. E. Shaw group and so far it seems like a wonderful place filled with interesting people. Nevertheless, I will always miss the world of quantum computing and its peculiar inhabitants.

Though I am no longer looking for a job, here are my old resume and CV (which someday will get updated with my current job):
Carlos' resume: PDF, LaTeX.
Carlos' CV: PDF, LaTeX.

Graduate+Postdoc Work

My work has focused on

Quantum coin flipping,
Hamiltonian oracles,
Quantum computation with anyons,
Quantum teleportation (You know, for kids!)

Quantum coin flipping papers

Quantum weak coin flipping with arbitrarily small bias (PDF, LaTeX).
Also available as arXiv:0711.4114. See http://lightlike.com/zerocoin/ for updates.

A large family of quantum weak coin-flipping protocols (PDF, LaTeX).
Published as Phys. Rev. A 72, 022341, also available as quant-ph/0502068.

Quantum weak coin flipping with bias of 0.192 (PDF, LaTeX).
In proceedings of FOCS 2004, pages 2-11, also available as quant-ph/0403193.

Serial composition of quantum coin flipping, and bounds on cheat detection for bit-commitment (PDF, LaTeX).
Published as Phys. Rev. A 70, 032312, also available as quant-ph/0311165.

Flipping a coin is a natural way to determine turn order in games and sports. When it is done in the presence of both teams it is reasonably trustworthy. But what if the teams wanted to flip the coin in advance, say over the telephone? How would you guarantee that neither side can cheat?

If you think about it for a while, you will realize that it is a hard problem unless both teams trust some third neutral party. Clever solutions such as using a videophone can be defeated with clever tricks such as prerecording coin tosses. In fact, it turns out that classically, if you don't want to assume any limitation to the equipment your opponent can use to cheat, the problem is impossible.

Surprisingly, if the two people involved are allowed to use quantum computers, and chat over a quantum phone, then it does become possible to prevent any cheating. The result is the conclusion of a four and a half year quest of mine to find good protocols for quantum coin flipping.

Of course, many other people have also worked on this problem. In fact, a crucial step in the proof of quantum coin flipping (probably the most difficult and important step of the construction) was carried out not by me but by Alexei Kitaev, a very very smart researcher that I met at Caltech. It is humbling to realize that without Kitaev's step I probably could have worked on this problem for my entire life without finding an answer.

By now you should be wondering if it was all worth it? And whether all this is useful for anything? I don't seriously expect any Vegas casinos to start using our protocol any time soon. However, for those of you already familiar with the mysteries of the quantum, my latest paper lists a number of reasons why you might find this result interesting.

Here are some slides on the latest paper: PDF, LaTeX.

Some of the ideas from the second paper (now seriously outdated) were presented at FOCS 2004, a conference in Rome, Italy. Here are the slides that were used for the talk: PDF, LaTeX.

Hamiltonian oracles

Hamiltonian Oracles (PDF, LaTeX).
Published as Phys. Rev. A 75, 042313, also available as quant-ph/0602032.

A lot of interesting things happen when you study the continuum limit of quantum computing problems. In particular, the problems often get mapped into geometrical problems of length minimization. Such problem arise in physics in the context of General Relativity. Though the geometric problems are often as hard as the original computer science problem, a new perspective can sometimes be useful in solving difficult problems.

The above paper discusses three examples of the continuum limit of quantum oracle problems. Oracle problems are like a game of twenty questions, where the oracle has some hidden information and you have to ask it questions in order to guess this hidden information. In the continuum limit you are allowed arbitrarily many questions, and in each case the oracle responds with an arbitrarily small answer. Surprisingly, there is very little difference between the discrete and continuous cases for the three problems that were studied.

Some of the above ideas are also available as a talk: PDF, LaTeX. A shortened version of this talk was presented at the Asian Conference on Quantum Information Science (AQIS'06) in Beijing, China.

Computing with anyons papers

Anyons from non-solvable finite groups are sufficient for universal quantum computation (PDF, LaTeX).
Published as Phys. Rev. A 67, 022315, also available as quant-ph/0206128.

Anyon computers with smaller groups (PDF, LaTeX).
Published as Phys. Rev. A 69, 032306, also available as quant-ph/0306063.

A fun piece of theoretical work combining group theory, particle physics and computer science. The papers show how to construct a quantum computer out of a class of rare particles called non-abelian anyons. These particles are the exotic cousins of bosons and fermions. In the anyon model I use, which involves electric and magnetic charges, the charges of the particles will change when one particle goes around another even if they are arbitrarily far apart.

While nobody has ever found these particular particles, I'm still keeping my fingers crossed. Clearly only a true theorist would try to design a (thus far) theoretical machine such as a quantum computer, out of a class of particles that has yet to be discovered.

The above work (mostly the first paper) has also been translated into:
Talk Format: PDF, LaTeX.
Poster format: PDF, LaTeX.

The talk was presented at the AMS Special Session on Topological Quantum Computation (May 3, 2003).

Quantum teleportation

The Perimeter Institute, in addition to promoting research, is involved in outreach activities designed to explain ideas of modern physics to a wide audience. I've been involved in a couple of such activities, which includes a talk I gave on Quantum Teleportation to our physics "summer-camp" for high-school students at the International Summer School for Young Physicists.

My notes on Quantum Teleportation are available on the web, and in printable format as PDF and LaTeX.

Graduate Thesis

"From non-abelian anyons to quantum computation to coin flipping by telephone."
Ph.D. Thesis by Carlos Mochon. California Institute of Technology, Department of Physics, 2005.
Available as PDF, LaTeX, or formatted for two-sided printing: PDF (two-sided).

The product of six years at Caltech, mostly it is a collection of my graduate papers, stapled together. However, the introduction, which is supposed to tie together the different chapters, is new. How I managed to relate quantum computation with non-abelian anyons to coin flipping by telephone remains a source of wonder to me. A priori most people wouldn't think that high-energy particle physics would have applications to online gambling.

Though I generally recommend reading the original papers (available above) rather then their double-spaced thesis version, I quite like the way the thesis introduction reads. In particular, the section on quantum coin flipping contains lots of history, including its relation to classical secure computation.

The unofficial subtitle of the thesis "How I learned to stop worrying about Physics and love Computer Science," reflects my slow evolution from a string theorist, via the study of non-abelian anions, to someone who works mainly on computer science problems such as coin flipping by telephone. Deep down, though, I still consider myself a physicist, even if only to justify my sloppy proofs.

Undergraduate Work

My undergraduate thesis involved computer simulations of the 2-D Heisenberg model antiferromagnet. While not necessarily earth shattering research, it allowed me to graduate and therefore served its purpose. I still have a copy:

Low Energy Parameters of Quantum Antiferromagnets: Simulation versus Spin-Wave Theory.
Available as PS, Source (.tar.gz, LaTeX).

I also spent three summers at Xerox PARC, which produced a bunch of papers. The quantum computing one is a good paper. The other two I've actually never read, but got my name added because of the work I did implementing some of their ideas.

Distributed Allocation Using Analog Market Wire Computation And Communication, from Mechatronics'2000

Tools for Quantum Algorithms (quant-ph/9811073, also published as Int.J.Mod.Phys. C10 1347-1362).

Squeeze Me, Hold Me, Tilt Me! An Exploration of Manipulative User Interfaces, from CHI 1998

In fact, the latter paper led to two patents: Handedness detection for a physical manipulatory grammar (number 6,243,074) and Graspable device manipulation for controlling a computer display (number 6,243,075). Of course, the patents themselves are owned by Xerox, but I am proud to call myself one of the fathers of squeezable computing.

Though I might make fun of such great title as "Squeeze Me, Hold Me, Tilt Me!," I am really grateful to Xerox PARC, and to my hosts over the years, for the wonderful research opportunities that they provided.