Experimental quantum-enhanced bosonic learning machine with trapped ions

The infinite-dimensional Hilbert space of bosonic systems can be utilized as the feature space for quantum machine learning. This approach offers a hardware-efficient solution with potential quantum speedups to the classification of both classical and quantum data. Here we demonstrate a quantum-enhanced bosonic learning machine with a system of trapped Yb171 ions. We encode information into the motional states of ions using a universal embedding circuit and apply a constant-dept SWAP test to measure the overlap of the states. We highlight the application of the bosonic learning machine by implementing the unsupervised K-mean algorithm to recognize a pattern in a set of high-dimensional quantum states. Using the discovered clusters as a training data set for the supervised k-NN algorithm, we demonstrate the classification of unknown quantum states with high accuracy.