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\section{Optimal control}  Alberto In recent years, we have added to octopus some of the key results of quantum  optimal control theory (QOCT)~\cite{Brif2010,Werschnik2007}. In this section,  we will briefly summarize what this theory is about, overview the current  status of its implementation, and describe some of the results that have been  obtained with it to date.  ``Quantum control'' can be loosely defined as the manipulation of physical  processes at the quantum level. We are concerned here with the theoretical  branch of this discipline, whose most general formulation is precisely  QOCT. This is, in fact, a particular case of the general mathematical  ``optimal control'' field, that studies the optimization of dynamical  processes in general. The first applications of optimal control in the quantum  realm appeared in the 80s~\cite{Shi1988,Peirce1988,Kosloff1989a}, and the  field has rapidly evolved since then. Broadly speaking, QOCT attempts to  answer the following question: given a quantum process governed by a  Hamiltonian that depends on a set of parameters, what are the values of those  parameters that maximize a given observable that depends on the behaviour of  the system? In mathematical terms: let a set of parameters $u_1,\dots,u_M  \equiv u$ determine the Hamiltonian of a system $\hat{H}[u,t]$, so that the  evolution of the system also depends on the value taken by those parameters:  \begin{equation}  {\rm i}\frac{{\rm d}}{{\rm d}t}\vert\psi(t)\rangle =  \hat{H}[u]\vert\psi(t)\rangle\,,  \end{equation}  i.e. the solution of Schr{\"{o}}dinger's equation determines a map $u  \longrightarrow \psi[u]$ (QOCT can also be formulated in terms of von  Neumann's equation, Lindblad's equation, etc.). Suppose we wish to optimize a  functional of the system $F=F[\psi]$. QOCT is about finding the extrema of  $G(u)=F[\psi[u]]$. And, beyond this mere search, QOCT also studies topics such  as the robustness of the optimal solutions for those parameters, the number of  solutions, the construction of suitable algorithms for computing them, etc.  The previous formulation is very general; in our case the quantum systems are  obviously those that can be modeled with octopus (although the periodic ones  are still not compatible with the QOCT algorithms implemented so far), and the  handle that is used to control is a time-dependent electric field, such as the  ones that can be used to model a laser pulse. The parameters mentioned above  are used to define the shape of this electric field, i.e. they may be the  Fourier coefficients of the electric amplitude).