Stochastic learning control of inhomogeneous quantum ensembles

Stochastic learning control of inhomogeneous quantum ensembles Gabriel Turinici IUF - Institut Universitaire de France CEREMADE, Universit e Paris Dauphine - PSL Research University Oct 2019 Abstract In quantum control, the robustness with respect to uncertainties in the system's parameters or driving field characteristics is of paramount importance and has been studied theoretically, numerically and experimentally. We test in this paper stochastic search procedures (Stochastic gradient descent and the Adam algorithm) that sample, at each iteration, from the distribution of the parameter uncertainty, as opposed to previous approaches that use a fixed grid. We show that both algorithms behave well with respect to benchmarks and discuss their relative merits. In addition the methodology allows to address high dimensional parameter uncertainty; we implement numerically, with good results, a 3D and a 6D case. 1 Introduction Quantum control is a promising technology with many applications ranging from NMR [12] to quantum computing [15] and laser control of quantum dynamics [7]. The controlling field encounters many molecules which although identical in nature may interact differently with the incoming field because of e.g., different Larmor frequencies or rf attenuation factors (in NMR spin control or quantum computing, see [19, 29, 35, 22, 13, 17]), different spatial profile (see [24]) or other parameters (see [36, 8, 10]). For obvious practical reasons, it is of paramount importance to ensure that the control quality is 1 arXiv:1906.02991v3