Project Description

Anand Natarajan

“I am interested in the connections between the rigorous math of quantum mechanics and computer science, and I enjoy thinking about the way that the deep ideas of physics and the deep ideas of computer science come together. When I was studying physics, I observed how brilliant physicists like Richard Feynman and John Preskill were proposing prescient ideas about quantum computing, and I was intrigued by the apparent possibilities in the field. Since I really enjoy math, I found that this intersection of the fields of theoretical computer science and physics was a great fit for me.”

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I am a theorist broadly considering the role that computational complexity has in entanglement. Foundational questions of how the Hilbert space should be defined were previously though to be purely mathematical details, but it seems that they might have different computational powers. This probably would have been surprising to people like von Neumann when they were writing down the axioms of quantum mechanics because they would not have thought that thinking about computer programs would have anything to do with this. The unexpected connection between quantum mechanics with all this deep math and then computer science is one thing that I find really cool about this area.

In computer science people care a lot about proof systems. One topic that I work on is multi-proofer entracted (MPE) proofs and how they are related to quantum computing. In these systems, two people or systems are spatially separated which raises some interesting questions. What does it mean to have two systems that are separated? And in what way does entanglement makes it possible for them to prove more computational problems, particularly problems that come from the quantum realm?

My current work is thinking of protocols in the MPE model for computational problems, and then proving that these protocols actually work so the provers cannot falsely prove something that is not true. I do a lot of math with pencil and paper to understand what sorts of things two parties sharing an entangled state can do. If they have measurements and you know something about the properties of their measurements, what can you deduce from that? It’s a lot of working with matrixes. The MPE is not really realistic, but classical research has ways to take results from this model and import them over to a more realistic use. In the quantum world, this is yet to be done, but that is something that I want to investigate over the course of my post doc.

I grew up listening to pop science lectures about black holes and participating in the Physics Olympiad, and I was inspired by the ideas of physics. When I began studying physics in undergrad, I imagined that I would end up working in particle physics or string theory, but as I studied and took computer science classes for fun, I discovered that I enjoyed the way that the deep ideas of physics and the deep ideas of computer science come together. I observed how brilliant physicists like Feynman and John Preskell were proposing prescient ideas about quantum computing, and I was intrigued by the apparent possibilities in the field. While physics is dependent on experiments, in quantum information a lot of what we do is rigorous math. We can provide mathematically rigorous proofs of things, and that is a way to make progress without experiments. Since I really enjoy rigorous math, I found that this intersection of the fields of theoretical computer science and physics was a great fit for me.
I enjoy learning new languages. I have learned Spanish and French, and as a child I learned both Sanskrit and Tamil. I credit my experiences in the Linguistic Olympiad in high school with fostering my love of language. In the Olympiad, we had to derive linguistic solutions based on foreign language information, and I enjoyed the intellectual puzzle. I also like listening to Indian classical music, and before my life as a researcher, I played the piano. Cooking is another hobby, and I am always looking for more vegetarian culinary possibilities.