Quantum computing holds immense potential, yet its practical success depends on multiple factors, including advances in quantum circuit design. In this paper, we introduce a generative approach based on denoising diffusion models (DMs) to synthesize parameterized quantum circuits (PQCs). Extending the recent diffusion model pipeline of [1], our model effectively conditions the synthesis process, enabling the simultaneous generation of circuit architectures and their continuous gate parameters. We demonstrate our approach in synthesizing PQCs optimized for generating high-fidelity Greenberger-Horne-Zeilinger (GHZ) states and achieving high accuracy in quantum machine learning (QML) classification tasks. Our Results indicate a strong generalization across varying gate sets and scaling qubit counts, highlighting the versatility and computational efficiency of diffusion-based methods. This work illustrates the potential of generative models as a powerful tool for accelerating and optimizing the design of PQCs, supporting the development of more practical and scalable quantum applications.
Quantum computing holds immense potential, yet its practical success depends on multiple factors, including advances in quantum circuit design. In this paper, we introduce a generative approach based on denoising diffusion models (DMs) to synthesize parameterized quantum circuits (PQCs). Extending the recent diffusion model pipeline of [1], our model effectively conditions the synthesis process, enabling the simultaneous generation of circuit architectures and their continuous gate parameters. We demonstrate our approach in synthesizing PQCs optimized for generating high-fidelity Greenberger-Horne-Zeilinger (GHZ) states and achieving high accuracy in quantum machine learning (QML) classification tasks. Our Results indicate a strong generalization across varying gate sets and scaling qubit counts, highlighting the versatility and computational efficiency of diffusion-based methods. This work illustrates the potential of generative models as a powerful tool for accelerating and optimizing the design of PQCs, supporting the development of more practical and scalable quantum applications.
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 .
Abstract Quantum circuit synthesis becomes increasingly challenging as system sizes grow and hardware-native gate sets diversify. Denoising diffusion models have recently been applied to quantum circuit synthesis as an alternative to expensive classical optimization. Existing diffusion-based approaches, however, either operate on discrete gate alphabets or separate gate identities and continuous parameters into different generative streams, which raises the question of whether a unified representation can more naturally encode structure–parameter dependencies. We propose a hybrid diffusion–optimization framework for quantum circuit synthesis with continuous native gates. Taking a trapped-ion-inspired native gate set as a representative example, our single-stream diffusion model operates directly on a continuous-parameter gate set { R X ( θ ), R Y ( θ ), R XX ( θ )} and produces fully parameterized circuits in a single diffusion sampling run. A lightweight gradient-based post-optimization of the continuous parameters, based on the process infidelity, then corrects residual stochastic errors. Trained and evaluated on random three-qubit unitaries, the model generates compact circuits that accurately approximate unseen targets. Under identical training conditions, the continuous-gate formulation achieves substantially lower process infidelity than both random-circuit and a discrete-gate diffusion baseline. Furthermore, applying gradient-based post-optimization to the continuous-gate diffusion output yields a significant additional improvement in fidelity compared with the same model without post-optimization, demonstrating that this refinement step is an effective strategy for correcting residual stochastic errors in the diffusion-generated parameters. These results point to a practical route toward continuous-parameter quantum circuit synthesis in native gate sets.
Abstract Parameterized Quantum Circuits (PQCs) have been acknowledged as a leading strategy to utilize near-term quantum advantages in multiple problems, including machine learning and combinatorial optimization. When applied to specific tasks, the parameters in the quantum circuits are trained to minimize the target function. Although there have been comprehensive studies to improve the performance of the PQCs on practical tasks, the errors caused by the quantum noise downgrade the performance when running on real quantum computers. In particular, when the quantum state is transformed through multiple quantum circuit layers, the effect of the quantum noise happens cumulatively and becomes closer to the maximally mixed state or complete noise. This paper studies the relationship between the quantum noise and the diffusion model. Then, we propose a novel diffusion-inspired learning approach to mitigate the quantum noise in the PQCs and reduce the error for specific tasks. Through our experiments, we illustrate the efficiency of the learning strategy and achieve state-of-the-art performance on classification tasks in the quantum noise scenarios.
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.
Designing effective quantum circuits remains a central challenge in quantum computing, as circuit structure strongly influences expressivity, trainability, and hardware feasibility. Current approaches, whether using manually designed circuit templates, fixed heuristics, or automated rules, face limitations in scalability, flexibility, and adaptability, often producing circuits that are poorly matched to the specific problem or quantum hardware. In this work, we propose the Evolutionary eXploration of Augmenting Quantum Circuits (EXAQC), an evolutionary approach to the automated design and training of parameterized quantum circuits (PQCs) which leverages and extends on strategies from neuroevolution and genetic programming. The proposed method jointly searches over gate types, qubit connectivity, parameterization, and circuit depth while respecting hardware and noise constraints. The method supports both Qiskit and Pennylane libraries, allowing the user to configure every aspect. This work highlights evolutionary search as a critical tool for advancing quantum machine learning and variational quantum algorithms, providing a principled pathway toward scalable, problem-aware, and hardware-efficient quantum circuit design. Preliminary results demonstrate that circuits evolved on classification tasks are able to achieve over 90% accuracy on most of the benchmark datasets with a limited computational budget, and are able to emulate target circuit quantum states with high fidelity scores.
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.