Stochastic learning control of inhomogeneous quantum ensembles

Gabriel Turinici (1, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 IUF - Institut universitaire de France

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.

Mots clés: quantum control; Stochastic gradient descent; number(s): 0367a; 0230Yy; 0367Pp

Domaines: Analyse numérique [math.NA]; Physique Quantique [quant-ph]; Intelligence artificielle [cs.AI]; Machine Learning [stat.ML]; Analyse numérique [cs.NA]; Systèmes et contrôle [cs.SY]

Gabriel Turinici. Stochastic learning control of inhomogeneous quantum ensembles. 2019. ⟨hal-02149374v2⟩