The convergence of quantum and classical computing, particularly in the realm of quantum machine learning, has gained substantial attention. Hybrid quantum algorithms, merging the strengths of both computing paradigms, offer a promising avenue, especially in the era of NISQ (noisy intermediate-scale quantum) computing. Leveraging these hybrid approaches allows researchers to employ quantum algorithms on existing quantum processors while harnessing classical methods to handle complex computational challenges. A core component of these hybrid systems is the Parameterized Quantum Circuit Element (PQCE). These circuits, defined by parameterized unitary operations, possess exceptional expressiveness, effectively modeling intricate distributions. This study introduces a novel application of Parameterized Quantum Circuits in Generative Flow Networks for object generation tasks. This model demonstrates efficiency and quality on par with classical deep neural network-based approaches. Despite longer training times, the quantum model achieves comparable results with significantly fewer parameters (151), emphasizing its potential in scenarios prioritizing parameter efficiency.
The convergence of quantum and classical computing, particularly in the realm of quantum machine learning, has gained substantial attention. Hybrid quantum algorithms, merging the strengths of both computing paradigms, offer a promising avenue, especially in the era of NISQ (noisy intermediate-scale quantum) computing. Leveraging these hybrid approaches allows researchers to employ quantum algorithms on existing quantum processors while harnessing classical methods to handle complex computational challenges. A core component of these hybrid systems is the Parameterized Quantum Circuit Element (PQCE). These circuits, defined by parameterized unitary operations, possess exceptional expressiveness, effectively modeling intricate distributions. This study introduces a novel application of Parameterized Quantum Circuits in Generative Flow Networks for object generation tasks. This model demonstrates efficiency and quality on par with classical deep neural network-based approaches. Despite longer training times, the quantum model achieves comparable results with significantly fewer parameters (151), emphasizing its potential in scenarios prioritizing parameter efficiency.
With the rapid development of quantum computing technology, we have entered the era of noisy intermediate-scale quantum (NISQ) computers. Therefore, designing quantum algorithms that adapt to the hardware conditions of current NISQ devices and can preliminarily solve some practical problems has become the focus of researchers. In this paper, we focus on quantum generative models in the field of quantum machine learning, and propose a hybrid quantum-classical normalizing flow (HQCNF) model based on parameterized quantum circuits. Based on the ideas of classical normalizing flow models and the characteristics of parameterized quantum circuits, we cleverly design the form of the ansatz and the hybrid method of quantum and classical computing, and derive the form of the loss function in the case that quantum computing is involved. We test our model on the image generation problem. Experimental results show that our model is capable of generating images of good quality. Compared with other quantum generative models, such as quantum generative adversarial networks (QGAN), our model achieves lower (better) Fréchet inception distance (FID) score, and compared with classical generative models, we can complete the image generation task with significantly fewer parameters. These results prove the advantage of our proposed model.
Parameterized quantum circuits (PQC) have emerged as a quantum analogue of deep neural networks and can be trained for discriminative or generative tasks and can be trained with gradient-based optimization on near-term quantum devices [1], [2], [3]. In the current era of quantum computing, known as the noisy intermediate scale quantum (NISQ) era [4], these devices contain a moderate number of qubits (< 100), and algorithmic performance is strongly impacted by hardware noise. Additionally, the training of PQCs are hybrid algorithms, in which the computational workflow is split between quantum and classical computing platforms.
Quantum computing has emerged as one of the most influential paradigms capable of transforming computational processes that struggle under classical limitations. In recent years, hybrid quantum–classical algorithms have gained significant attention for their ability to leverage the strengths of both architectures, especially within the Noisy Intermediate-Scale Quantum (NISQ) era. This research paper explores a quantum-enhanced optimization framework designed to improve machine learning model performance through parameterized quantum circuits (PQCs). The goal of this study is to provide a practical, scalable approach that can be integrated into existing machine learning workflows without requiring fully developed fault-tolerant quantum hardware. The proposed framework uses classical preprocessing to encode data into quantum states, followed by quantum transformations that explore richer feature spaces due to quantum superposition and entanglement. A classical optimizer then updates the quantum circuit parameters based on measurement results, forming an end-to-end feedback loop. This hybrid model aims to demonstrate improved optimization efficiency, reduction in loss-function plateaus, and better generalization for specific ML tasks involving small to medium-sized datasets. This paper provides a comprehensive investigation of methodology, literature background, and experimental reasoning with statistical analysis, along with conceptual diagrams illustrating system architecture and circuit layouts. The outcomes further strengthen the viability of hybrid quantum–classical computation as a promising direction for advanced machine learning systems.
Despite the advantage quantum computers are expected to deliver when performing simulations compared to their classical counterparts, the current noisy intermediate-scale quantum (NISQ) devices remain limited in their capabilities. The training of parameterized quantum circuits (PQCs) remains a significant practical challenge, exacerbated by the requirement of shallow circuit depth necessary for their hardware implementation. Hybrid methods employing classical computers alongside quantum devices, such as the Variational Quantum Eigensolver (VQE), have proven useful for analyzing the capabilities of NISQ devices to solve relevant optimization problems. Still, in the simulation of complex structures involving the many-body problem in quantum mechanics, major issues remain about the representation of the system and obtaining results which clearly outperform classical computational devices. In this research contribution we propose the use of parameterized Tensor Networks (TNs) to attempt an improved performance of the VQE algorithm. A joint approach is presented where the Hamiltonian of a system is encapsulated into a Matrix Product Operator (MPO) within a parameterized unitary TN hereby splitting up the optimization task between the TN and the VQE. We show that the hybrid TN-VQE implementation improves the convergence of the algorithm in comparison to optimizing randomly-initialized quantum circuits via VQE.
Quantum Generative Adversarial Networks (QGANs), as a rising paradigm in Quantum Machine Learning, have shown promising potential in image generation and processing. However, their output quality remains suboptimal, and existing research is largely limited to small-scale, proof-of-concept studies. In this work, we propose a hybrid quantum-classical GAN architecture, where the generator integrates parameterized quantum circuits (PQCs) and classical neural networks. This integration significantly enhances the visual quality of generated images. Our model leverages the complementary strengths of quantum and classical components and outperforms existing methods (Tsang et al. in IEEE Trans. Quantum Eng. 4:1–19, 2023 ; Gulrajani et al. in Proceedings of the 31st international conference on neural information processing systems. NIPS’17, Red Hook, pp. 5769–5779, 2017 ), particularly in terms of image fidelity. Experiments conducted on the MNIST family of datasets show that our hybrid approach achieves a 20.26% average reduction in Fréchet Inception Distance. Furthermore, it improves the Structural Similarity Index Measure, Cosine Similarity, and Peak Signal-to-Noise Ratio by 26.04%, 2.22%, and 7.62%, respectively. These results highlight the effectiveness of combining quantum computing with machine learning, and underscore the potential of hybrid quantum-classical models in advancing generative tasks.
In recent years, many generation-based machine learning algorithms such as generative adversarial networks, Boltzmann machine, auto-encoder, etc. are widely used in data generation and probability distribution simulation. On the other hand, the combined algorithms of quantum computation and classical machine learning algorithms are proposed in various styles. Especially, there exist many relevant researches about quantum generative models, which are regarded as the branch of quantum machine learning. Quantum generative models are hybrid quantum-classical algorithms, in which parameterized quantum circuits are introduced to obtain the cost function of the task as well as its gradient, and then classical optimization algorithms are used to find the optima. Compared with its classical counterpart, quantum generative models map the data stream to high-dimensional Hilbert space with parameterized quantum circuits. In the mapping space, data features are easier to learn, which can surpass classical generative models in some tasks. Besides, quantum generative models are potential to realize the quantum advantage in noisy intermediate-scale quantum devices.