OVERLAP MEASUREMENT OF INFINITE DIMENSIONAL QUANTUM STATES AND BOSONIC LEARNING MACHINE WITH TRAPPED IONS

Abstract

We describe the implementation of the controlled beam splitter (CBS) gate to create entanglement between the spins and motional modes of trapped 171Yb+ ions. We combine two CBS gates to demonstrate the SWAP test between two infinitely dimensional states encoded in the motional modes. To characterise the SWAP test , we measure the overlap between the Fock states, superposition of Fock states, coherent states, squeezed vacuum states and cat states, with a constant-depth circuit. With the SWAP test and ability to prepare arbitrary state of a harmonic oscillator based on the Eberly-Law method, we successfully implement two quantum machine learning algorithms: the supervised k-NN and unsupervised K-means cluster algorithm. We first correctly group the 15 unlabeled quantum states into three clusters in three iterations of the K-means cluster algorithm. Next, the k-NN algorithm uses the previously described 15 quantum states as the training states to identify patterns in five trial states.