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

arXiv: https://arxiv.org/abs/2210.16731 · HTML: https://mlsanity.com/paper/2210.16731/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 34 references that are in the map.
- First posted on arXiv 30 Oct 2022.

## Builds on (most cited first, 16 of 16)

- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [Federated Quantum Machine Learning](https://mlsanity.com/paper/2103.12010/) (2021)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [Communication-Efficient and Distributed Learning Over Wireless Networks: Principles and Applications](https://mlsanity.com/paper/2008.02608/) (2020)
- [Quantum Federated Learning with Quantum Data](https://mlsanity.com/paper/2106.00005/) (2021)
- [Quantum Multi-Agent Reinforcement Learning via Variational Quantum Circuit Design](https://mlsanity.com/paper/2203.10443/) (2022)
- [Slimmable Quantum Federated Learning](https://mlsanity.com/paper/2207.10221/) (2022)
- [Quantum Multi-Agent Meta Reinforcement Learning](https://mlsanity.com/paper/2208.11510/) (2022)
- [Quantum Neural Networks: Concepts, Applications, and Challenges](https://mlsanity.com/paper/2108.01468/) (2021)
- [Classical-to-quantum convolutional neural network transfer learning](https://mlsanity.com/paper/2208.14708/) (2022)
- [Scalable Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2209.12372/) (2022)
- [Dual-Frequency Quantum Phase Estimation Mitigates the Spectral Leakage of Quantum Algorithms](https://mlsanity.com/paper/2201.09323/) (2022)
- [3D Scalable Quantum Convolutional Neural Networks for Point Cloud Data Processing in Classification Applications](https://mlsanity.com/paper/2210.09728/) (2022)
- [Training Hybrid Classical-Quantum Classifiers via Stochastic Variational Optimization](https://mlsanity.com/paper/2201.08629/) (2022)

## Built on by (most cited first, 4 of 4)

- [Quantum Multi-Agent Reinforcement Learning for Autonomous Mobility Cooperation](https://mlsanity.com/paper/2308.01519/) (2023)
- [Quantum Split Neural Network Learning using Cross-Channel Pooling](https://mlsanity.com/paper/2211.06524/) (2022)
- [MORE: Measurement and Correlation Based Variational Quantum Circuit for Multi-classification](https://mlsanity.com/paper/2307.11875/) (2023)
- [Empirical Study of Observable Sets in Multiclass Quantum Classification](https://mlsanity.com/paper/2602.08485/) (2026)

## Abstract (arXiv)

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 2q. 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.