No abstract

We examine a range of effects arising from ac magnetic fields in high precision metrology. These results are directly relevant to high precision measurements, and accuracy assessments for state-ofthe-art optical clocks. Strategies to characterize these effects are discussed and a simple technique to accurately determine trap-induced ac magnetic fields in a linear Paul trap is demonstrated using 171 Yb + .

Quantum processors enable computational speedups for machine learning through parallel manipulation of high-dimensional vectors [1]. Early demonstrations of quantum machine learning have focused on processing information with qubits [2][3][4][5][6][7][8]. 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 [9][10][11]. 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 highdimensional 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.