Lately I’ve been getting emails from undergrads with stellar-looking résumés who want to be my summer students. My initial reaction was: “who, me? I’m barely more than a summer student myself!” But today a light bulb went off: “hey, if these ambitious whippersnappers really want to do my research for me, why shouldn’t I let them do it — thereby freeing up my own time for more important priorities like blogging?”
I’ve therefore decided to list three project ideas. If you’re an undergrad or grad student who wants to tackle one of them this summer at the University of Waterloo, email me (scott at scottaaronson dot com). Tell me about yourself and what you want to do, and attach a CV. I’ll pick up to two students. Deadline: Feb. 21 or until positions are filled.
Scott Aaronson is an equal opportunity employer. He doesn’t have his own funding, so if you can bring your own, great; if not, he’ll try to scrounge some from under Mike Lazaridis’s couch. If the projects listed below don’t interest you — or if you’re more interested in physics, engineering, or information theory than in quantum complexity — there are many, many potential supervisors at both the Institute for Quantum Computing and the Perimeter Institute who’d probably be a better match for you.
Project #1: The Learnability of Quantum States. For this project, you’d first read and understand my paper of the same name, ideally before the summer started. You’d then implement my quantum state reconstruction algorithm in Matlab, Mathematica, or any other environment of your choice, and study its performance with realistic physical systems. This is a crucial first step if experimentalists are ever going to be convinced to try my quantum state learning approach. (The fact that I proved it works is completely irrelevant to them…) There’s also plenty of scope for new theoretical ideas if you swing that way. The eventual goal would be to publish the results somewhere like Physical Review Letters. This project is highly recommended.
Project #2: Multiple Quantum Proofs. Today we believe that there are mathematical truths that you could efficiently verify if given a small quantum state, but that you couldn’t efficiently verify if given a short classical string. But what if you were given two quantum states, which were guaranteed to be unentangled with each other? Would that let you verify even more truths than you could with a single quantum state? The answer is, we have no idea! Nor do we know whether three quantum proofs are more powerful than two, etc. When it comes to the power of multiple quantum proofs, even the most embarrassingly simple questions are open. In this project, you’d work with me to try and sort out the mess. This project is only for students who are confident of their ability to do original research in theoretical computer science.
Project #3: Insert Your Own Project. Wow me. Dazzle me. Give me a specific, detailed idea for a research project in quantum complexity theory or a related area, and convince me that you’re ferocious enough to get somewhere with it in one summer. I’ll try to help where I can.