Lie Group Diffusion Models for Hardware-Aware Quantum Circuit Synthesis

2026-06-28 · Source: Takara TLDR - Daily AI Papers · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Emerging Technologies & Innovation, Mathematics & Computational Sciences · Depth: Expert, medium

Summary

Lie Group Diffusion Models for Hardware-Aware Quantum Circuit Synthesis introduces a novel generative approach for creating quantum circuits that adhere to physical hardware constraints. This method addresses the hybrid nature of quantum circuit synthesis, which involves continuous single-qubit gates on the Lie group SU(2) and discrete, hardware-dependent entangling structures. The model consists of two main components: a circuit skeleton selector that identifies an appropriate entangling circuit, and a diffusion model that generates quantum gates on the specified circuit template by performing diffusion directly on the curved manifold SU(2) ≅ S³. The approach was demonstrated through unitary compilation of physically motivated three-qubit Hamiltonian simulation targets, specifically the Transverse Field Ising Model and the Heisenberg-XXZ Model. Results indicate that Lie group diffusion outperforms comparable baselines, and the synthesized circuits can be customized, for instance, to produce circuits with varying gate rotation angles for the same target unitary evolution. Furthermore, the circuit selector effectively balances fidelity with complexity, avoiding collapse onto overly expansive templates.

Key takeaway

For quantum computing researchers developing hardware-aware circuit synthesis, this work suggests adopting Lie group diffusion models. You should consider integrating diffusion on curved manifolds like SU(2) for gate generation and a circuit skeleton selector for discrete structures. This approach can yield circuits that balance high fidelity with hardware constraints, outperforming traditional baselines and allowing customization of gate rotation angles.

Key insights

Lie group diffusion models effectively synthesize hardware-aware quantum circuits by integrating continuous gate generation with discrete structural selection.

Principles

• Quantum circuit synthesis has hybrid continuous/discrete structure.
• Diffusion on curved manifolds improves gate generation.
• Balancing fidelity and complexity is crucial for circuit selection.

Method

The method combines a circuit skeleton selector for discrete entangling structures with a diffusion model that generates continuous quantum gates on the SU(2) manifold.

In practice

• Compile three-qubit Hamiltonian simulation targets.
• Customize circuits for specific gate rotation angles.
• Balance circuit fidelity with complexity.

Topics

• Quantum Circuit Synthesis
• Lie Group Diffusion Models
• Hardware-Aware Quantum Computing
• SU(2) Manifold
• Hamiltonian Simulation
• Generative Models

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Editorial summary, takeaway, and curation by AIssential. Original article published by Takara TLDR - Daily AI Papers.