Maxim Gorlach

Lecture 1. Introduction to quantum brachistochrone method
Ancient brachistochrone problem posed in XVII century by J. Bernoulli aimed to find a curve of the quickest descent between the two points and gave birth to the variational calculus. Nowadays analogous problems arise in many other contexts including quantum physics. Recently emerged quantum brachistochrone method addresses a similar question: how one should vary the Hamiltonian of a quantum system in order to transfer it from the given initial to the desired final state within the minimal possible time given the prescribed constraints on the Hamiltonian. This lecture will introduce the methodology, derive the governing equations and present several simple but instructive examples.
 
Lecture 2. Applications of quantum brachistochrone to quantum optimal control problems
This lecture will introduce further applications of quantum brachistochrone technique to the multi-qubit systems. Despite the large number of degrees of freedom involved, we will demonstrate that numerical solutions are available unlocking routes to time-optimal manipulation of large-scale quantum systems.

Frank Wilczek