Statistical Physics vs QFT for quantum information processing

[Verdict]

Good day,

I'm starting my master in physics, and it's time for me to choose my courses. I've decided that I probably want to pursue the direction of quantum information processing, and I'm trying to pick my courses with that in mind. For my first semester I'll be taking four courses: Quantum Optics, Quantum Information Theory, a mandatory social science course and the fourth course, which will either be Statistical Physics or QFT I. Now, I'm finding it very hard to decide as both have parts that will probably be very valuable, as well as topics that I don't really need to learn about, for now.

As for the actual contents of the courses:
Statistical Physics

Spoiler

Basics of phenomenological thermodynamics, three laws of thermodynamics.
Basics of kinetic gas theory: conservation laws, H-theorem, Boltzmann-Equations, Maxwell distribution.
Classical statistical physics: microcanonical ensembles, canonical ensembles and grandcanonical ensembles, applications to simple systems.
Quantum statistical physics: single particle, ideal quantum gases, fermions and bosons.
Bose-Einstein condensation: Bogolyubov theory, superfluidity.
Mean field and Landau theory: Ising model, Heisenberg model, Landau theory of phase transitions, fluctuations.
Critical phenomena: mean field, series expansions, scaling behavior, universality.
Renormalization group: fixed points, simple models.
Linear response theory: general formulation, response in mean field, sum rules, collective modes, fluctuation dissipation theorem.

QFT I:

Spoiler

This course discusses the quantisation of fields in order to introduce a coherent formalism for the combination of quantum mechanics and special relativity.
Topics include:
- Relativistic quantum mechanics
- Quantisation of bosonic and fermionic fields
- Interactions in perturbation theory
- Scattering processes and decays
- Radiative corrections

Now I've already done some StatMech in my Bachelors degree, but definitely not as advanced as will be treated here. I know about Fermi Dirac and Bose Einstein, and the different canonical ensembles, but that's about it. When it comes to QFT, I guess I don't know anything about that really, only that a lot of people say it's only useful if I want to do theory, but I feel like that does not do it justice.

Note that taking both simultaneously does not work out schedule wise. I might be able to take the other course a year from now, although I'm not sure if that'll work out. If I left out anything important, please let me know!

 

[atyy]

In a way the statistical mechanics course has field theory. There's a close formal analogy between statistical mechanics of fields and quantum field theory. Historically, critical phenomena in statistical physics was figured out by Wilson, a quantum field theorist. However, he brought new concepts in, and those concepts migrated back to quantum field theory. After Wilson, people understood that renormalization was conceptually ok from a physics point of view.

 

[nonequilibrium]

I find this a hard one, it seems neither is particularly relevant for quantum information.

Statistical physics doesn't really enter into quantum information, since the latter is about preserving exact quantum mechanical evolution, hence the usual statistical approximations are not that useful. However I see that stat phys course also addresses some condensed matter, which is definitely more relevant to quantum information when it comes to finding physical systems which could be used for quantum computing.

The reason QFT doesn't seem that relevant is because quantum information usually addresses systems with finite degrees of freedom (bits!). Again QFT plays an important role in condensed matter physics, but for the type of condensed matter systems that are useful from a quantum info POV (at least the branch I'm familiar with: topological quantum computing) QFT doesn't play such a central role (topological quantum field theory can, but that's quite different from what you'd learn in a QFT course).

If I were you, I'd probably choose for QFT, mostly motivated by a well-rounded education: the things you'd learn in the stat mech course could probably be picked up along the way, but I doubt you'd ever properly learn QFT if you didn't take a course in it (and honestly it seems a bit weird to have had a grad education in physics without knowing some QFT, but that's perhaps personal!). But yeah maybe it's just best to follow your personal preference on this one? I've only had experience with Q info, stat mech and QFT at the level of grad level courses, so maybe others can give better advice, but as far as I can see there's not a compelling reason to choose one course over the other. (Is there no condensed matter course?)

 

[Verdict]

Thanks for the comments, very insightful! To answer your question about the condensed matter, there is indeed an advanced condensed matter course. However, it violently clashes with the quantum information theory course, timetable wise. I might be able to take it the year after though. If I can, I definitely will. But for now, your argument for QFT sounds sensible, and many of my peers have also suggested taking the course. Some even say that you can't call yourself a physicist until you've learned QFT, but that's a story for a different topic..