In this work we experimentally demonstrate that the undo of an operation is possible also in quantum regimes. The last performed operation can be time-reversed via the undo command so as to perfectly restore a condition in which any new operation can be applied by an external user. We exploit the optimal control algorithm based on the dressed chopped random basis method, to perform several time-reversal transformations. We implement this algorithm by applying different levels of complexity, in terms of control, in order to manipulate the forward and backward internal state dynamics of a ^{87}Rb Bose–Einstein condensate within an atom chip. As well as providing a thermodynamic interpretation of our results, in this paper we demonstrate that the quantum undo command can be performed also by time-reversing an operation in a generic instant of the past. The concept of quantum undo can be thus generalized. An external user, indeed, will be able to restore not only the last but also any past step of his complex computational routine. We are confident that our successful results could be applied in the next future on a real gate-based quantum computer. I. Mastroserio, et al., |