A classical Hamiltonian description of the quantum brachistochrone problem

The quantum brachistochrone plays an important role in quantum control since it sets fundamental limits on the resources required to realize a quantum operation.

Although its generality, the solution to the problem is complicated, since one has to deal with a system of coupled nonlinear ODEs.

In this talk, we show how one can rewrite the problem in the Hamiltonian formulation. This way insight can be acquired and integrable points can be identified.

Moreover, in the general/ chaotic regime, more credible claims can be made about the trade-off between the cost and the fidelity of the target unitary operation.