Projection Valued Measure-based Quantum Machine Learning for Multi-Class Classification

In recent years, quantum machine learning (QML) has been actively used for various tasks, e.g., classification, reinforcement learning, and adversarial learning. However, these QML studies do not achieve complex tasks due to scalability issues on input and output are the biggest hurdle in QML. To cope with this problem, we aim to solve the output scalability issue. Motivated by this challenge, we focus on projection-valued measure (PVM) which utilizes the nature of probability amplitude in quantum statistical mechanics. By leveraging PVM, the output dimension is expanded from the number of qubits $q$ to $\mathcal{O}(2^q)$. We propose a novel QML framework for multi-class classification. We corroborate that our framework outperforms the state-of-theart (SOTA) with various datasets using no more than 6 qubits. Furthermore, our PVM-based QML outperforms 42.2% SOTA.