The lack of enough labeled data is a great issue when designing a real-life scheme.Data labeling is timeconsuming as well as costly.Semi-supervised learning (SSL) is a way to solve the issues of data labeling.SSL uses a tiny quantity of labeled data to find labels of massive quantities of unlabeled data.This paper presents a quantum-classical SSL mechanism named "Iterative Labels Finding (ILF)" by combining the Quantum Support Vector Machine algorithm (QSVM) and Ising Models Based Binary Clustering algorithm.The proposed method performs a matching and iteration process to discover the labels of unlabeled data.ILF is designed for binary classification purposes.We have illustrated the experimental result of ILF with a real-time dataset and with a practical example.From experimental results, we have found ILF as a highly efficient approach for quantum SSL.
The lack of enough labeled data is a great issue when designing a real-life scheme.Data labeling is timeconsuming as well as costly.Semi-supervised learning (SSL) is a way to solve the issues of data labeling.SSL uses a tiny quantity of labeled data to find labels of massive quantities of unlabeled data.This paper presents a quantum-classical SSL mechanism named "Iterative Labels Finding (ILF)" by combining the Quantum Support Vector Machine algorithm (QSVM) and Ising Models Based Binary Clustering algorithm.The proposed method performs a matching and iteration process to discover the labels of unlabeled data.ILF is designed for binary classification purposes.We have illustrated the experimental result of ILF with a real-time dataset and with a practical example.From experimental results, we have found ILF as a highly efficient approach for quantum SSL.
Recent advances in quantum technology have led to the development and the manufacturing of programmable quantum annealers that promise to solve certain combinatorial optimization problems faster than their classical counterparts. Semi-supervised learning is a machine learning technique that makes use of both labeled and unlabeled data for training, which enables a good classifier with only a small amount of labeled data. In this paper, we propose and theoretically analyze a graph-based semi-supervised learning method with the aid of the quantum annealing technique, which efficiently utilizes the quantum resources while maintaining good accuracy. We illustrate two classification examples, suggesting the feasibility of this method even with a small portion (30%) of labeled data involved.
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. In the meantime, we show that naive quantum matrix product estimation algorithm outperforms the best known classical matrix multiplication algorithm. 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.
This paper develops a hybrid quantum approach for graph-based semi-supervised learning to enhance performance in scenarios where labeled data is scarce. We introduce two enhanced quantum models, the Improved Laplacian Quantum Semi-Supervised Learning (ILQSSL) and the Improved Poisson Quantum Semi-Supervised Learning (IPQSSL), that incorporate advanced label propagation strategies within variational quantum circuits. These models utilize QR decomposition to embed graph structure directly into quantum states, thereby enabling more effective learning in low-label settings. We validate our methods across four benchmark datasets like Iris, Wine, Heart Disease, and German Credit Card -- and show that both ILQSSL and IPQSSL consistently outperform leading classical semi-supervised learning algorithms, particularly under limited supervision. Beyond standard performance metrics, we examine the effect of circuit depth and qubit count on learning quality by analyzing entanglement entropy and Randomized Benchmarking (RB). Our results suggest that while some level of entanglement improves the model's ability to generalize, increased circuit complexity may introduce noise that undermines performance on current quantum hardware. Overall, the study highlights the potential of quantum-enhanced models for semi-supervised learning, offering practical insights into how quantum circuits can be designed to balance expressivity and stability. These findings support the role of quantum machine learning in advancing data-efficient classification, especially in applications constrained by label availability and hardware limitations.
Label propagation is an essential semi-supervised learning method based on graphs, which has a broad spectrum of applications in pattern recognition and data mining. This paper proposes a quantum semi-supervised classifier based on label propagation. Considering the difficulty of graph construction, we develop a variational quantum label propagation (VQLP) method. In this method, a locally parameterized quantum circuit is created to reduce the parameters required in the optimization. Furthermore, we design a quantum semi-supervised binary classifier based on hybrid Bell and Z bases measurement, which has a shallower circuit depth and is more suitable for implementation on near-term quantum devices. We demonstrate the performance of the quantum semi-supervised classifier on the Iris data set, and the simulation results show that the quantum semi-supervised classifier has higher classification accuracy than the swap test classifier. This work opens a new path to quantum machine learning based on graphs.
Semi-supervised learning (SSL) has emerged as a critical paradigm for leveraging abundant unlabeled data alongside scarce labeled samples, yet classical approaches often struggle in sparse label regimes where the ratio of labeled to unlabeled data is extremely low. Meanwhile, quantum machine learning (QML) has demonstrated that quantum feature spaces can induce rich kernel structures with provable representational advantages, but these methods typically require quantum hardware that remains inaccessible for practical deployment. In this work, we propose a quantum-inspired semi-supervised learning framework that harnesses the geometric properties of quantum Hilbert space embeddings while remaining entirely classical and hardware-independent. Our approach, which we term Quantum-Inspired SemiSupervised Learning (QISSL), constructs feature maps that mimic the action of quantum encoding circuits via classically simulable kernel functions derived from randomized trigonometric expansions. We provide rigorous theoretical analysis establishing: (1) a bounded approximation guarantee between our classical embeddings and their quantum counterparts; (2) a generalization bound for QISSL under low-label regimes via Rademacher complexity analysis; and (3) a convergence proof for the alternating optimization procedure that jointly trains the embedding and classifier modules. Extensive experiments on benchmark datasets demonstrate that QISSL achieves state-of-the-art performance in extreme low-label settings (0.1%–1% labeled data), outperforming strong baselines including FixMatch, MixMatch, and FlexMatch by margins of 2–7% in accuracy. Our results suggest that the inductive biases of quantum feature spaces—when properly classically approximated—offer a powerful and practical tool for semi-supervised learning without quantum hardware.
Quantum computing is an interdisciplinary field at the intersection of computer science, mathematics, and physics that studies information processing tasks on a quantum computer. A quantum computer is a device whose operations are governed by the laws of quantum mechanics. As building quantum computers is nearing the era of commercialization and quantum supremacy, it is essential to think of potential applications that we might benefit from. Among many applications of quantum computation, one of the emerging fields is quantum machine learning. We focus on predictive models for binary classification and variants of Support Vector Machines that we expect to be especially important when training data becomes so large that a quantum algorithm with a guaranteed speedup becomes useful. We present a quantum machine learning algorithm for training Sparse Support Vector Machine for problems with large datasets that require a sparse solution. We also present the first quantum semi-supervised algorithm, where we still have a large dataset, but only a small fraction is provided with labels. While the availability of data for training machine learning models is steadily increasing, oftentimes it is much easier to collect feature vectors to obtain the corresponding labels. Here, we present a quantum machine learning algorithm for training Semi-Supervised Kernel Support Vector Machines. The algorithm uses recent advances in quantum sample-based Hamiltonian simulation to extend the existing Quantum LS-SVM algorithm to handle the semi-supervised term in the loss while maintaining the same quantum speedup as the Quantum LS-SVM.