Mastroserio, Ivana (2022) Realizing quantum protocols with an atom-chip for quantum embedding and reversed quantum dynamics. [Tesi di dottorato]

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A quantum protocol is a set of rules or procedures, that exploit Quantum Mechanics, to realize a specific task. In this thesis, I explore two different quantum protocols realized by the coherent manipulation of the internal dynamics of a Bose-Einstein condensate (BEC) of Rubidium 87 produced on an atom-chip. In the first quantum protocol I experimentally investigate the possibility to successfully implement quantum embedding of a large amount of classical data, to be classified, into the evolution parameters of the BEC quantum state. A quantum embedding is, indeed, the mapping of a set of data input into new data clusters in a larger Hilbert space where their subsequent classification can be more feasible by well-trained artificial neural networks. The high degree of control and isolation of the atomic system from the external environment makes it the ideal candidate, among the other explored platforms, for implementing such algorithms, as further confirmed by the high fidelities achieved exceeding 97%. The potential advantages of representing classical data on quantum systems include not only the possibility to simplify a classification problem as experimentally demonstrated in this work, but also the ability to speed up any processing of classical data, such as quantum parallelism to search through a database exploitation, feature extraction, image segmentation and edge detection. The second quantum protocol I report concerns the experimental realization of a time-inversion evolution of our BEC dynamics. In the context of gate-based quantum computers applications, this procedure allows one to time-reverse the last performed operation on a quantum computer so as to perfectly restore a condition in which an arbitrary new operation can be realized. In this regard, our work explores several time-reversal experiments letting the BEC evolve through different paths in the Hilbert space. I detail how the optimal backward evolution is achieved by means of a radio-frequency pulse modulation designed with a dressed Chopped Random Basis (dCRAB) algorithm. I show how this technique successfully works in bringing the system back to its initial conditions with an average accuracy of 92%. Furthermore, I demonstrate how the proposed procedure can be interpreted, from a thermodynamic point of view, as an entropy rectification method. The final results can be applied for the practical realization of a quantum undo operation encoded in a sub-part of a quantum processor. The undo command is indeed a logical operation reverse, which in some platforms, like the gate-based one presented in this thesis, can be related to the time-reversal of the last performed operation. All the presented experiments of time-inversion constitute the proof-of-principle of a wide class of quantum undo operations to be implemented in several quantum technology contexts.

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