Quantum machine learning optimization using Koopman operator technique

Abstract

Quantum machine learning (QML) is a nascent field showing great potential in addressing complex problems. QML algorithms aim to combine the qubit’s properties, like entanglement, interference, and superposition, to perform better than any classical computation in specific tasks. This paper explores a new way of employing the Koopman operator to demonstrate its application to quantum optimization in quantum machine learning.

Koopman operator-based quantum optimization has applications in various dynamical systems, where it can optimally capture the full nonlinear behavior of a system [1]. This work investigates the Koopman operator approach for quantum optimization for quantum machine learning algorithms. To do so, we capitalize on recent breakthroughs in the field, such as data-driven methods for uncovering Koopman models and the application of the Koopman operator to investigate quantum machine learning optimal strategies. Specifically, we provide a strategy-driven approach with the full pipeline for encoding classical dynamical systems into quantum-accessible representation, thus employing beneficial properties of Koopman and transfer operators. This strategy enables us to represent the state space of classical systems in terms suitable for quantum computation. Here, we introduce a framework for using the Koopman operator to represent complex, high-dimensional classical dynamics on a quantum computer to enhance classical machine learning algorithms by transferring their capabilities onto quantum systems. Additionally, we provide a programmatical framework for using the Koopman operator in quantum machine learning frameworks on the IBM Qiskit framework.