Nowadays the need of processing large amount of data is considerably increasing, and the development of supercomputers has further encouraged the advancement of Quantum Technologies and the study of algorithms in that direction. In particular, the introduction of Quantum Machine Learning algorithms has provided a remarkable speedup over their classical counterparts. However, the natural structure of the original data can be very complex and an intensive preprocessing is often necessary for Machine Learning algorithms to perform efficiently. In the case of binary classification problems, one would aim at achieving a geometrical representation of the data in which they are easier to be identified into distinct categories later to be analyzed.
In this context, we have developed an extensive experimental study of Quantum Embedding implementing the ideas proposed by Lloyd et al on two different experimental platforms based on ultracold atoms and quantum optics respectively. We perform also a similar analysis on the Rigetti superconducting quantum computer. The embedding protocol concerns a novel approach to perform classification in the context of Quantum Metric Learning used in Machine Learning. We have implemented a quantum feature map that can be trained, via optimization, to separate and embed classical data points, coming from two different classes, into a much larger Hilbert space. Quantum Mechanics suggests that the natural representation of a quantum bit is the Bloch sphere, therefore the embedding we want to train will be composed of a sequence of rotations on noncommuting axes to be applied to an input qubit. The training and the parameters of the embedding are flexible and can be manipulated in order to account for the specific needs of the different experimental platforms.
The atomic platform in which we realize the embedding is a BoseEinstein Condensate (BEC) of ^{87}Rb realized with an Atomchip. We illustrate how the performance of Quantum Embedding depend on the degree of control on the actual system, thus on the level of experimental imperfections specific to the solutions adopted.
The aim of our study is to prove that this kind of approach is robust to experimental errors and that can be applied in practice, hence supporting the promising idea of hybrid quantum technologies for future Quantum Machine Learning applications.
I. Gianani, et al., Experimental Quantum Embedding for Machine Learning Adv. Quantum Technol. 5, 2100140 (2022)
