Quantum-enhanced bosonic learning machine

Abstract

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.

Sculpting bosonic states with arithmetic subtractions

“…For the concrete proposal, we refer to the experimental setup reported in [6,37,38]: a system of four ions in a linear Paul trap, with trap frequencies ω z ω x , ω y . We address the motional degree of freedom of the ions along the x direction and the internal spin state of the last (fourth) ion.…”

“…For instance, due to Coulomb interactions between ions, a beam-splitter-like coupling between the motional modes of two trapped ions has been experimentally demonstrated [30]. This has led to many applications, such as the implementation of the controlled-SWAP gate for machine learning algorithms [6,38] and the study of quantum walks using phonons [43].…”

Sculpting bosonic states with arithmetic subtractions

“…For the concrete proposal, we refer to the experimental setup reported in [6,42,43]: a system of four ions in a linear Paul trap, with trap frequencies ω z ω x , ω y . We address the motional degree of freedom of the ions along the x direction and the internal spin state of the last (fourth) ion.…”

“…For instance, due to Coulomb interactions between ions, a beam-splitter-like coupling between the motional modes of two trapped ions has been experimentally demonstrated [33]. This has led to many applications, such as the implementation of the controlled-SWAP gate for machine learning algorithms [6,43] and the study of quantum walks using phonons [48].…”

“…Alternatively, classical information can be encoded into the eigenstates of continuous-valued operators, such as the motion of trapped ions, the quadratures of an electromagnetic mode, and the spin variables of an atomic ensemble [4][5][6]. In such bosonic systems, a large dimension of the Hilbert space is typically available for the encoding.…”