Quantum Kernel Learning for Bosonic Modes AIP2024

Abstract

Kernel methods are of current interest in quantum machine learning due to similarities shared with quantum computing in how information is processed in high-dimensional feature (Hilbert) spaces. Kernels are believed to offer particular advantages when they are hard to simulate classically, so a kernel with the right kind of complexity, or nonclassicality, is considered important. Kerr nonlinearities, already a known route to universal continuous variable quantum computation, are also a strong source of nonclassicality for machine learning.

We propose a scheme which implements a kernel on quantum hardware, such as superconducting quantum circuits, and exploits the analogue features of Kerr-coupled modes. The kernel is sampled via displaced parity measurements related to those used in Wigner state tomography. We first focus here on deriving analytically the relevant fiducial state for embedding data, and then on testing the scheme on a common machine learning algorithm—a support vector machine (SVM). We discuss the analytical form of the Kerr kernel for two modes, as well as the measurements that would be made via displaced parity operators in a physical system. We use four examples of such measurements, which effectively produce four different Wigner functions each with different labels for the same synthetic data set. We then implement the SVM algorithm using our Kerr kernel, and test its ability to learn each of the four encodings and classify unseen data. We then compare the accuracy of this model to a classical radial basis function SVM. We find that the SVM displays excellent learning with the Kerr kernel, regardless of which displacement operators are used for the labelling, without requiring hyperparameter tuning. The radial basis function, on the other hand, also displays good learning, but requires hyperparameter tuning to approach the benchmarks attained by the Kerr kernel.

Carolyn Wood

Postdoctoral Scientist

Carolyn Wood is a postdoctoral researcher at the University of Queensland, in Brisbane, Australia focusing on quantum machine learning and physics at the interface between quantum mechanics and general relativity.