Quantum Semi-Supervised Learning with Quantum Supremacy

Quantum machine learning promises to efficiently solve important problems. There are two persistent challenges in classical machine learning: the lack of labeled data, and the limit of computational power. We propose a novel framework that resolves both issues: quantum semi-supervised learning. Moreover, we provide a protocol in systematically designing quantum machine learning algorithms with quantum supremacy, which can be extended beyond quantum semi-supervised learning. We showcase two concrete quantum semi-supervised learning algorithms: a quantum self-training algorithm named the propagating nearest-neighbor classifier, and the quantum semi-supervised K-means clustering algorithm. By doing time complexity analysis, we conclude that they indeed possess quantum supremacy.

Quantum Data Compression and Quantum Cross Entropy

Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. A central quantity for the theoretical foundation of quantum machine learning is the quantum cross entropy. In this paper, we present one operational interpretation of this quantity, that the quantum cross entropy is the compression rate for sub-optimal quantum source coding. To do so, we give a simple, universal quantum data compression protocol, which is developed based on quantum generalization of variable-length coding, as well as quantum strong typicality.

Quantum Cross Entropy and Maximum Likelihood Principle

Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. Classical cross entropy plays a central role in machine learning. We define its quantum generalization, the quantum cross entropy, and investigate its relations with the quantum fidelity and the maximum likelihood principle. We also discuss its physical implications on quantum measurements.