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 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.
High-fidelity circuit execution on noisy intermediate-scale quantum devices is bottlenecked by compilation pipelines that disregard complex, correlated noise. To address this, this methodology article proposes a quantum machine learning control (QMLC) framework for generative quantum circuit synthesis from gate-set tomography (GST) data that bypasses the traditional two-step pipeline of characterizing native quantum gates via GST followed by unitary decomposition algorithms. Instead, a generative concept space is directly learnt from GST data, enabling conditional synthesis of quantum circuits on a desired output distribution. Our approach tokenizes GST germ circuits and embeds them into a structured latent space using a curriculum-learning-motivated strategy, starting with short circuits and progressively incorporating longer ones with diverse output statistics. The embedded sequences are processed by a set-vision transformer with permutation-invariant pooling, producing k-seed vectors that represent the learned concept space of the quantum device. Aggregating data across multiple circuits makes this latent representation inherently context-aware, capturing the shared physical noise environment (e.g., crosstalk, drift) that isolated gate metrics miss. We propose an unconditional diffusion model to sample from the concept space. During inference, a user provides a target measurement distribution, and the model generates a corresponding circuit. To ensure fidelity and robustness, the output is denoised using a diffusion model that operates on the target conditional covariance matrix. This end-to-end framework is a step towards context-aware, hardware-native circuit synthesis directly from raw GST data, which offers a new paradigm for integrating quantum control and compilation. The QMLC framework is particularly suited for near-term quantum devices with complex calibration procedures.
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.
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.
Quantum algorithms will likely play a key role in future high-performance-computing (HPC) environments. These algorithms are typically expressed as quantum circuits composed of arbitrary gates or as unitary matrices. Executing these on physical devices, however, requires translation to device-compatible circuits, in a process called quantum compilation or circuit synthesis, since these devices support a limited number of native gates. Moreover, these devices typically have specific qubit topologies, which constrain how and where gates can be applied. Consequently, logical qubits in input circuits and unitaries may need to be mapped to and routed between physical qubits. Furthermore, current Noisy Intermediate-Scale Quantum (NISQ) devices present additional constraints. They are vulnerable to errors during gate application and their short decoherence times lead to qubits rapidly succumbing to accumulated noise and possibly corrupting computations. Therefore, circuits synthesized for NISQ devices need to minimize gates and execution times. The problem of synthesizing device-compatible circuits, while optimizing for low gate count and short execution times, can be shown to be computationally intractable using analytical methods. Therefore, interest has grown towards heuristics-based synthesis techniques, which are able to produce approximations of the desired algorithm, while optimizing depth and gate-count. In this work, we investigate using genetic algorithms (GA)—a proven gradient-free optimization technique based on natural selection—for circuit synthesis. In particular, we formulate the quantum synthesis problem as a multi-objective optimization (MOO) problem, with the objectives of minimizing the approximation error, number of multi-qubit gates, and circuit depth. We also employ fuzzy logic for runtime parameter adaptation of GA to enhance search efficiency and solution quality in our proposed method.
Quantum computing emerges as a promising direction for high-performance computing in the post-Moore era. Leveraging quantum mechanical properties, quantum devices can theoretically provide significant speedup over classical computers in certain problem domains. Quantum algorithms are typically expressed as quantum circuits composed of quantum gates, or as unitary matrices. Execution of quantum algorithms on physical devices requires translation to machine-compatible circuits -- a process referred to as quantum compilation or synthesis. Quantum synthesis is a challenging problem. Physical quantum devices support a limited number of native basis gates, requiring synthesized circuits to be composed of only these gates. Moreover, quantum devices typically have specific qubit topologies, which constrain how and where gates can be applied. Consequently, logical qubits in input circuits and unitaries may need to be mapped to and routed between physical qubits on the device. Current Noisy Intermediate-Scale Quantum (NISQ) devices present additional constraints, through their gate errors and high susceptibility to noise. NISQ devices are vulnerable to errors during gate application and their short decoherence times leads to qubits rapidly succumbing to accumulated noise and possibly corrupting computations. Therefore, circuits synthesized for NISQ devices need to have a low number of gates to reduce gate errors, and short execution times to avoid qubit decoherence. The problem of synthesizing device-compatible quantum circuits, while optimizing for low gate count and short execution times, can be shown to be computationally intractable using analytical methods. Therefore, interest has grown towards heuristics-based compilation techniques, which are able to produce approximations of the desired algorithm to a required degree of precision. In this work, we investigate using Genetic Algorithms (GAs) -- a proven gradient-free optimization technique based on natural selection -- for circuit synthesis. In particular, we formulate the quantum synthesis problem as a multi-objective optimization (MOO) problem, with the objectives of minimizing the approximation error, number of multi-qubit gates, and circuit depth. We also employ fuzzy logic for runtime parameter adaptation of GA to enhance search efficiency and solution quality of our proposed quantum synthesis method.