  Quantum processors enable computational speedups for machine learning through
parallel manipulation of high-dimensional vectors. Early demonstrations of
quantum machine learning have focused on processing information with qubits. In
such systems, a larger computational space is provided by the collective space
of multiple physical qubits. Alternatively, we can encode and process
information in the infinite-dimensional Hilbert space of bosonic systems such
as quantum harmonic oscillators. This approach offers a hardware-efficient
solution with potential quantum speedups to practical machine learning
problems. Here we demonstrate a quantum-enhanced bosonic learning machine
operating on quantum data with a system of trapped ions. Core elements of the
learning processor are the universal feature-embedding circuit that encodes
data into the motional states of ions, and the constant-depth circuit that
estimates overlap between two quantum states. We implement the unsupervised
K-means algorithm to recognize a pattern in a set of high-dimensional quantum
states and use the discovered knowledge to classify unknown quantum states with
the supervised k-NN algorithm. These results provide building blocks for
exploring machine learning with bosonic processors.
