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Somewhere around the 3rd year of my physics PhD. program I came into this amazing subject of complexity theory. May be a motivating factor was that I was digging in my spare-time into this physics/complexity interface. Anyhow I took up courses in complexity theory and a few associated regions in the CS theory department in my university and I started attending one of the group meetings there and tried to contribute to a project (sadly the project turned out to be very hard and didn't move enough)

But how do I actually go about finding a career in this subject? Either in academia or industry?

I won't be taken seriously if I make a regular CS PhD. application because my background has no overlap with an usual CS grad student and neither am I interested in CS per se. (like I found the graduate "algorithms" course extremely boring though the mathematical algorithms part was fascinating where they did stuff like LP, SDP, entropy extraction, pseudorandomness etc.) My interest is complexity theory and its interface with physics : which I see as a fascinating branch of mathematics! (and I do have quite a strong background in mathematics)

  • Now why is there a downvote!? – PhysicsComplexity Jul 5 '15 at 21:14
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    My suggestion is to make your thesis topic in complexity theory and its interface with physics. – scaaahu Jul 6 '15 at 4:13
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    though the mathematical algorithms part was fascinating — All algorithms are "mathematical" algorithms, just not the kind of mathematics that you like. – JeffE Jul 6 '15 at 14:44
  • But how to find a way to pursue these subjects as a career? – PhysicsComplexity Jul 6 '15 at 18:10
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I would suggest you to continue studying in your physics Ph.D. program and successfully graduate. However, considering your interest in complexity theory (which I share with you, by the way, though, unfortunately, my math background is more limited than yours), I would advise to find a topic on the intersection of physics and complexity theory (aka complex systems) and write dissertation on that topic. That way will have a nice and flexible general physics education and, at the same time, you will stay motivated (which is extremely important for writing a dissertation) throughout the whole dissertation writing period. As for the complex systems field of study, please see my relevant question on Cross Validated site and references within. Good luck to both of us!

  • In my university there is no overlap between physics and these complexity subjects. No professor at the interface. May be you can show some examples of professors like this? Then I can get a better view of what kind of people you are talking of? – PhysicsComplexity Jul 6 '15 at 17:51
  • @PhysicsComplexity: I'm afraid that, if no single professor at your university will agree to chair your committee, you will have no choice, other than study complex systems on your own, as, AFAIK, most universities don't allow a foreign committee chair (advisor). As for examples of professors, working or having worked in this area, consider Grigoire Nicolis and Ilya Prigogine. They wrote book on the topic, called "Exploring Complexity: An Introduction". See it on Amazon and on GoodReads. – Aleksandr Blekh Jul 6 '15 at 18:13
  • @PhysicsComplexity: For more people, working in the domain of complex systems, see references on this Scholarpedia page. – Aleksandr Blekh Jul 6 '15 at 18:18
  • I wonder if you are confusing between "complexity theory" and "theory of complex systems". A priori I don't know of a relation between the two things. – PhysicsComplexity Jul 7 '15 at 0:18
  • @PhysicsComplexity: I don't think that I'm confusing anything, but the terminology in those fields of study is indeed confusing: en.wikipedia.org/wiki/Complexity_theory. Perhaps, what you are referring to is computational complexity theory, not just complexity theory. – Aleksandr Blekh Jul 7 '15 at 0:29
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The field of quantum information is very specifically a merger between physics and computer science. In particular, there is subfield called Hamiltonian complexity which is exactly what it sounds like you are looking for -- the interface of physics and computational complexity theory. See, for instance, arXiv:1106.5875 for a short introduction, or arXiv:1401.3916 for a longer more recent review article. You may find other subfields of theoretical quantum information congenial as well -- for instance, semidefinite programming is becoming a widely-used tool for analyzing quantum protocols. There are probably other connections between physics and complexity theory too, so this is definitely a viable career goal.

The easiest way to get into this is if you happen to have a professor in your university interested in this field. Even if it is someone in the CS or math department, not the physics department, you may be able to work something out, e.g., with a physics co-advisor.

An alternative route if there is no one suitable is to delay a bit getting into the field. Do some reading on your own and learn what topics are closely related. Then find an advisor in your department who is working on one of those related topics. Depending how closely related the subject is, you may be able to bring in the complexity-theoretic aspects as part of your thesis, or you may need to work on your advisor's subject but be prepared to switch as a postdoc. Your preparation in the related topic can provide a useful background when you do switch. Or you can finish your thesis on your current topic and work on Hamiltonian complexity (or whatever) on the side and then switch over completely as a postdoc.

A third possibility is to find someone in your department who is willing to either branch out a bit or supervise you for the topic even without working on it themselves. This is difficult, because you won't have anyone to guide you in the field and tell you what is already known, but I've seen it work before with highly-motivated students.

If none of those work, you can try to transfer schools. You may lose a little time on your Ph.D. in fulfilling requirements for the new university, but that way you may be able to find an advisor who is working on the right topic.

  • Inside my university I think the overlap is exactly zero. This subject simply doesn't seem to have arrived here. So inside the university my best option is probably to try to shift departments to say mathematics. But then shifting departments is incredibly difficult : professors are so suspicious of such things and for a senior student the skepticisms are even higher! Shifting institutes is an option but then I don't know which university gives a mid-year shift. I can't afford to lose an year waiting for the regular application cycle! – PhysicsComplexity Jul 7 '15 at 23:35
  • The question really is : should I go to a very low ranked university say CQT, Singapore which seems to have a very good quantum complexity group? (fortunately or unfortunately I am currently inside an extremely high-ranked place!) – PhysicsComplexity Jul 7 '15 at 23:36
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    Again, I suggest doing some reading and seeing if there are any related topics which sound interesting and are being done by someone in your department. For instance, entanglement in quantum field theory/string theory; or spin glasses or topological order in condensed matter. This will put you in a good position to make a lateral move later. A world-class group in a low-ranked university is a perfectly good option too, but a high-ranked school has plenty of benefits and may be worth sticking it out. – Daniel Gottesman Jul 8 '15 at 19:56

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