research level - Quantum computing and quantum control

In 2009, Bernard Chazelle published a famous algorithms paper, "Natural Algorithms," in which he applied computational complexity techniques to a control theory model of bird flocking. Control theory methods (like Lyapunov functions) had been able to show that the models eventually converged to equilibrium, but could say nothing about the rate of convergence. Chazelle obtained tight bounds on the rate of convergence.

Inspired by this, I had the idea of seeing how to apply quantum computing to quantum control, or vice versa. However, I got nowhere with this, because the situations did not seem to be analogous. Further, QComp seemed to have expressive power in finite dimensional Hilbert spaces, while QControl seemed fundamentally infinite-dimensional to me. So I could not see how to make progress.

So my question: does this seem like a reasonable research direction, and I just didn't understand the technicalities well enough? Or are control theory and quantum control fundamentally different fields, which just happen to have similar names in English? Or some third possibility?

EDIT: I have not thought about this for a few years, and I just started Googling. I found this quantum control survey paper, which, at a glance, seems to answer one of my questions: that quantum control and traditional control theory are indeed allied fields and use some similar techniques. Whether there is a research question like Chazelle's analysis of the BOIDS model that would be amenable to quantum computing techniques, I have no idea.

Answer

Well, obviously I don't know exactly what you were trying, but it's not an unreasonable direction. There is certainly a bit of interplay between the two areas. Many of the open loop techniques which have become standard practice in spin resonance (for example decoupling pulses such as WAHUHA [Waugh, J.S., Huber, L.M., Haeberlen, U. (1968) Phys. Rev. Lett., 20, 180.] etc.) are based on exactly the same Suzuki-Trotter tricks that are now used in quantum simulation algorithms.

Additionally, there have been some nice results from Steffen Glaser and others on optimal control for the basic building blocks of quantum computation, including some pretty high level operations like generating cluster states (see arXiv:0903.4066) and state transfer (see arXiv:0705.0378).

There is also a huge literature on trying to make stuff into quantum computers even when you don't have all the control knobs you might wish for (see for example Seth Lloyd's papers on Universal quantum interfaces, all of the stuff on global control, and recent papers by Daniel Burgarth and Alistair Kay on Lie algebraic control techniques).

Lastly, the two areas are very closely linked via the adiabatic model, where the efficiency is directly linked to how quickly you can adiabticly transition between two Hamiltonians.