# Synthesis of discrete-continuous quantum circuits with multimodal diffusion models

arXiv: https://arxiv.org/abs/2506.01666 · HTML: https://mlsanity.com/paper/2506.01666/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 36 of its 83 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://mlsanity.com/paper/2305.08891/) (2023)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Efficient Diffusion Training via Min-SNR Weighting Strategy](https://mlsanity.com/paper/2303.09556/) (2023)
- [MM-Diffusion: Learning Multi-Modal Diffusion Models for Joint Audio and Video Generation](https://mlsanity.com/paper/2212.09478/) (2022)
- [One Transformer Fits All Distributions in Multi-Modal Diffusion at Scale](https://mlsanity.com/paper/2303.06555/) (2023)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [Lumina-Next: Making Lumina-T2X Stronger and Faster with Next-DiT](https://mlsanity.com/paper/2406.18583/) (2024)
- [Round and Round We Go! What makes Rotary Positional Encodings useful?](https://mlsanity.com/paper/2410.06205/) (2024)
- [DiffiT: Diffusion Vision Transformers for Image Generation](https://mlsanity.com/paper/2312.02139/) (2023)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)
- [Simpler Diffusion (SiD2): 1.5 FID on ImageNet512 with pixel-space diffusion](https://mlsanity.com/paper/2410.19324/) (2024)
- [Active learning machine learns to create new quantum experiments](https://mlsanity.com/paper/1706.00868/) (2017)

## Built on by (most cited first, 6 of 6)

- [Generative flow-based warm start of the variational quantum eigensolver](https://mlsanity.com/paper/2507.01726/) (2025)
- [Generative AI for Quantum Circuits and Quantum Code: A Technical Review and Taxonomy](https://mlsanity.com/paper/2603.16216/) (2026)
- [From Characterization To Construction: Generative Quantum Circuit Synthesis from Gate Set Tomography Data](https://mlsanity.com/paper/2605.01367/) (2026)
- [Physics Guided Generative Optimization for Trotter Suzuki Decomposition](https://mlsanity.com/paper/2605.13268/) (2026)
- [Generative Quantum Data Embeddings for Supervised Learning](https://mlsanity.com/paper/2605.30866/) (2026)
- [Bridge of Psi's: Quantum Circuit Optimization with Schr"odinger Bridges](https://mlsanity.com/paper/2609.25947/) (2026)

## Abstract (arXiv)

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 ans"atze. 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.