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 $\mathrm{SU(2)} \simeq S^3$ 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.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 $\mathrm{SU(2)} \simeq S^3$ 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.

quant-pharXiv:2606.29636Jun 30, 20260 citations

Studies on methods for the synthesis of quantum circuits

裕美中島

Jan 1, 20090 citations

Hybrid diffusion-optimization for quantum synthesis with continuous native gates

Dajun Guo, Chukun Hu, Xiaolu Su

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 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.

Physica ScriptaMay 7, 20260 citations

UDiTQC: U-Net-Style Diffusion Transformer for Quantum Circuit Synthesis

Zhiwei Chen, Hao Tang

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.

arXiv:2501.16380Jan 24, 20250 citations

Modeling quantum circuits

Margareta Vamos

Jan 1, 20111 citation

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

\mathrm{SU(2)} \simeq S^3

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.