Browsing by Subject "Quantum Kernel Methods"

For machine learning, quantum computing provides effective new computation methods. The number of states a quantum register may express is exponential compared to the classical register of the same size, and this expressivity may be used in machine learning. It has been shown that in less than exponential time, a theoretical fault-tolerant quantum computer may perform computations that cannot be run on a classical computer in a feasible time. In machine learning, however, it has been shown that a classical machine learning method may learn a target model defined by an arbitrary quantum circuit if given a sufficient number of training data. In other words, a machine learning method that utilizes quantum computing may gain a quantum prediction advantage over its classical counterpart if the number of training data is low. However, this result does not address the noise of contemporary quantum computers. In this thesis, we use a simulation of a quantum circuit to test how a gradually increased noise affects the ability of a hybrid quantum-classical machine learning system to retain the quantum prediction advantage. With a simulated quantum circuit, we embed classical data rows into the quantum Hilbert space that acts as a feature space known from classical kernel theory. We project the data back to classical space, yielding a projected dataset that differs from the original. Using kernel matrices of the original and projected datasets, we then create adversarial binary labeling. With few training data, this adversarial labeling is easy for a classical neural network to learn using the projected features but impossible for using the original data. We show that this quantum prediction advantage diminishes as a function of the error rate introduced in the simulation of the data-embedding quantum circuit. Our results suggest the noise threshold for a feasible system lies slightly above the ones of contemporary hardware, indicating our experiment should be tested on actual quantum hardware. We derive a parameter optimization scheme for an arbitrary hardware implementation such that it may be concluded whether the quantum hardware in question may produce a quantum advantage dataset beyond the simulation capability of classical computers.