Quantum computing is a transformative technology with wide-ranging applications, and efficient quantum circuit generation is crucial for unlocking its full potential. Current diffusion model approaches based on U-Net architectures, while promising, encounter challenges related to computational efficiency and modeling global context. To address these issues, we propose UDiT,a novel U-Net-style Diffusion Transformer architecture, which combines U-Net's strengths in multi-scale feature extraction with the Transformer's ability to model global context. We demonstrate the framework's effectiveness on two tasks: entanglement generation and unitary compilation, where UDiTQC consistently outperforms existing methods. Additionally, our framework supports tasks such as masking and editing circuits to meet specific physical property requirements. This dual advancement, improving quantum circuit synthesis and refining generative model architectures, marks a significant milestone in the convergence of quantum computing and machine learning research.
Quantum computing is a transformative technology with wide-ranging applications, and efficient quantum circuit generation is crucial for unlocking its full potential. Current diffusion model approaches based on U-Net architectures, while promising, encounter challenges related to computational efficiency and modeling global context. To address these issues, we propose UDiT,a novel U-Net-style Diffusion Transformer architecture, which combines U-Net's strengths in multi-scale feature extraction with the Transformer's ability to model global context. We demonstrate the framework's effectiveness on two tasks: entanglement generation and unitary compilation, where UDiTQC consistently outperforms existing methods. Additionally, our framework supports tasks such as masking and editing circuits to meet specific physical property requirements. This dual advancement, improving quantum circuit synthesis and refining generative model architectures, marks a significant milestone in the convergence of quantum computing and machine learning research.
Abstract Efficiently compiling quantum operations remains a major bottleneck in scaling quantum computing. Today’s state-of-the-art methods achieve low compilation error by combining search algorithms with gradient-based parameter optimization, but they incur long runtimes and require multiple calls to quantum hardware or expensive classical simulations, making their scaling prohibitive. Recently, machine-learning models have emerged as an alternative, though they are currently restricted to discrete gate sets. Here, we introduce a multimodal denoising diffusion model that simultaneously generates a circuit’s structure and its continuous parameters for compiling a target unitary. It leverages two independent diffusion processes, one for discrete gate selection and one for parameter prediction. We benchmark the model over different experiments, analyzing the method’s accuracy across varying qubit counts and circuit depths, showcasing the ability of the method to outperform existing approaches in gate counts and under noisy conditions. Additionally, we show that a simple post-optimization scheme allows us to significantly improve the generated ansätze. Finally, by exploiting its rapid circuit generation, we create large datasets of circuits for particular operations and use these to extract valuable heuristics that can help us discover new insights into quantum circuit synthesis. Code and models are publicly available at https://github.com/FlorianFuerrutter/genQC .
In recent years, machine learning models like DALL-E, Craiyon, and Stable Diffusion have gained significant attention for their ability to generate high-resolution images from concise descriptions. Concurrently, quantum computing is showing promising advances, especially with quantum machine learning which capitalizes on quantum mechanics to meet the increasing computational requirements of traditional machine learning algorithms. This paper explores the integration of quantum machine learning and variational quantum circuits to augment the efficacy of diffusion-based image generation models. Specifically, we address two challenges of classical diffusion models: their low sampling speed and the extensive parameter requirements. We introduce two quantum diffusion models and benchmark their capabilities against their classical counterparts using MNIST digits, Fashion MNIST, and CIFAR-10. Our models surpass the classical models with similar parameter counts in terms of performance metrics FID, SSIM, and PSNR. Moreover, we introduce a consistency model unitary single sampling architecture that combines the diffusion procedure into a single step, enabling a fast one-step image generation.
Quantum computing holds great potential for solving socially relevant and computationally complex problems. Furthermore, quantum machine learning (QML) promises to rapidly improve our current machine learning capabilities. However, current noisy intermediate-scale quantum (NISQ) devices are constrained by limitations in the number of qubits and gate counts, which hinder their full capabilities. Furthermore, the design of quantum algorithms remains a laborious task, requiring significant domain expertise and time. Quantum Architecture Search (QAS) aims to streamline this process by automatically generating novel quantum circuits, reducing the need for manual intervention. In this paper, we propose a diffusion-based algorithm leveraging the LayerDAG framework [1] to generate new quantum circuits. This method contrasts with other approaches that utilize large language models (LLMs), reinforcement learning (RL), variational autoencoders (VAE), and similar techniques. Our results demonstrate that the proposed model consistently generates 100% valid quantum circuit outputs.
Generative models have achieved remarkable success in data synthesis, though recent advances driven by increasing model scale have introduced challenges in computational cost and efficiency. Quantum machine learning offers a promising alternative, representing complex data distributions using compact, highly expressive models. Here, we propose QDiffusion-TS, the first quantum generative diffusion model for time series synthesis, and validate it on the IQM quantum processor. The framework extends a classical diffusion architecture by replacing feed-forward components within the denoising transformer with quantum neural networks, yielding a hybrid quantum transformer that reduces the number of trainable parameters in each replaced component by nearly three orders of magnitude. Evaluated on financial time series from Apple and Amazon, the model generates synthetic data that more accurately reproduces the real distributions, reducing Wasserstein distance by approximately 44% relative to its classical counterpart across both datasets. In a downstream forecasting task, augmentation with the generated data improves predictive performance by up to 71% in RMSE over a baseline trained solely on real data. These results show that quantum enhanced architectures can consistently match and frequently surpass classical performance with substantially fewer parameters, establishing a practical framework towards more efficient and scalable data-driven generative modelling.
Machine Learning (ML) has been widely applied across numerous domains due to its ability to automatically identify informative patterns from data for various tasks. The availability of large-scale data and advanced computational power enables the development of sophisticated models and training strategies, leading to state-of-the-art performance, but it also introduces substantial challenges. Quantum Computing (QC), which exploits quantum mechanisms for computation, has attracted growing attention and significant global investment as it may address these challenges. Consequently, Quantum Machine Learning (QML), the integration of these two fields, has received increasing interest, with a notable rise in related studies in recent years. We are motivated to review these existing contributions regarding quantum circuit-based learning models for classical data analysis and highlight the identified potentials and challenges of this technique. Specifically, we focus not only on QML models, both kernel-based and neural network-based, but also on recent explorations of their integration with classical machine learning layers within hybrid frameworks. Moreover, we examine both theoretical analysis and empirical findings to better understand their capabilities, and we also discuss the efforts on noise-resilient and hardware-efficient QML that could enhance its practicality under current hardware limitations. In addition, we cover several emerging paradigms for advanced quantum circuit design and highlight the adaptability of QML across representative application domains. This study aims to provide an overview of the contributions made to bridge quantum computing and machine learning, offering insights and guidance to support its future development and pave the way for broader adoption in the coming years.
An important task in quantum computing is unitary circuit synthesis compatible with physical hardware constraints. This problem has a natural hybrid structure as local single-qubit gates are continuous variables on the Lie group SU(2) while the entangling circuit structure is discrete and hardware-dependent. In this work, we use generative models to perform quantum circuit synthesis incorporating both the natural SU(2) manifold geometry of quantum gates and hardware constraints that determine the overall circuit structure. Our model comprises two components: a circuit skeleton selector that chooses an entangling circuit and a diffusion model that generates quantum gates on the given circuit template by performing diffusion on the curved manifold SU(2)≃S3 itself. We demonstrate this approach with unitary compilation of physically motivated three-qubit Hamiltonian simulation targets such as the Transverse Field Ising Model and the Heisenberg-XXZ Model and show that Lie group diffusion outperforms comparable baselines. The synthesised circuits can also be customised subject to constraints, which we demonstrate by producing circuits with large and small gate rotation angles for the same target unitary evolution. We also investigate the fidelity-complexity frontier of the synthesised gates to demonstrate that the circuit selector learns to select circuits that balance fidelity with complexity rather than collapsing onto the most expansive entangling template. These results demonstrate that Lie group diffusion provides a natural generative framework for hardware-aware quantum circuit synthesis.