Quantum-enhanced bosonic learning machine

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.