Fall teaching

Caltech’s academic year started this week, with Monday being the first day of instruction for the Fall quarter (Caltech’s quarter-based division, as opposed to the more usual division in semesters, explains why we’re starting a month later than many others). So even though I moved to Pasadena in early June, it’s only now that I’m getting to experience the buzzing of a surprisingly lively campus (given the small – less than 1k -undergraduate population), as opposed to the relative quietness of the summer. Having moved in the early summer helped a lot with the settling down, and I now have a functional office (got the last piece – the chair – today), studio (one of the perks of being at Caltech!), and stream of students coming in to ask for signatures ūüôā

Now, first week of the quarter means, well, let’s get back to business! A lot happened since the last post I wrote on this blog (including many many aborted drafts: when I saw what was the last thing I wrote, I couldn’t believe I hadn’t brought myself to posting¬†anything in the meantime), but I’ll have to settle for the status quo and look forwards, rather than backwards, for regular postings. Caltech’s IQIM alread maintains an excellent blog, to which I’ll attempt to contribute. But this blog will continue to live on for less scientific, or less directly quantum-related posts, so stay tuned! Here’s some brief news on the start of the quarter:

If only I could get inspiration from my predecessors!

So, first week of instruction means, well, first week of instruction. Someone has to teach something to the hungry crowds, and this quarter I’ll bring my own modest contribution by teaching CS286: Topics in Computer Science, that I bravely (foolishly?) decided to entitle “Around the Quantum PCP Conjecture”. The goal of the class is to use the conjecture as a backdrop, a motivating theme; not one to be approached directly but one to suggest interesting questions that can be studied for their own sake.

My plan is to start by reviewing the classical PCP theorem, in enough depth to give a reasonable idea of the kind of ingredients that go into both known proofs of the theorem, though clearly without having the time to cover any of them completely. This week we (almost) covered NP in PCP(poly,1). Next week we’ll see a few of the ideas that go into Dinur’s proof. The next step will be to¬†give an introduction to the area of quantum Hamiltonian complexity, including Kitaev’s QMA-completeness result. We’ll then be in a position to state the conjecture and discuss some of its implications.

Once the background is properly set, I’d like to spend the six remaining weeks of the quarter to dive deep into two or three current topics of research, associated to the conjecture but that we’ll study independently. The three I have in mind are quantum multiprover interactive proofs, area laws, and de Finetti theorems in quantum information theory. Each of these topics would be well worth spending a full semester course on by itself. But instead, I’d like¬†to pick just one particular aspect, one result, and describe the simplest possible non-trivial instantiation of that component or result. The hope is that such a¬†depth-first, rather than breadth-first, exploration, will still give the students some interesting insight into the area and motivate them to continue the exploration on their own.

We’ll have to see how this plays. The first two lectures had a very mixed audience: from the first-year undergraduate (courageous!) to the full professor, going through undergraduate, graduate and postdocs in CS and physics, not a single one of them has a matching background. This was a reason for choosing the “quantum PCP” topic in the first place: my hope is that both CS and Physics students can find some angle of interest on that theme, drawing both crowds around the same preoccupation. It’s going to be challenging to keep everyone together, but it could also be a very fun and rewarding experience…I’m looking forward to it!

About Thomas

I am a professor in the department of Computing and Mathematical Sciences (CMS) at the California Institute of Technology, where I am also a member of the Institute for Quantum Information and Matter (IQIM). My research is in quantum complexity theory and cryptography.
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