  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 are unable to carry out complex tasks due
to scalability issues on input and output which is currently the biggest hurdle
in QML. Therefore, the purpose of this paper is to overcome the problem of
scalability. Motivated by this challenge, we focus on projection-valued
measurements (PVM) which utilize the nature of probability amplitude in quantum
statistical mechanics. By leveraging PVM, the output dimension is expanded from
$q$, which is the number of qubits, to $2^q$. We propose a novel QML framework
that utilizes PVM for multi-class classification. Our framework is proven to
outperform the state-of-the-art (SOTA) methodologies with various datasets,
assuming no more than 6 qubits are used. Furthermore, our PVM-based QML shows
about $42.2\%$ better performance than the SOTA framework.
