# Quantum circuit synthesis with diffusion models

arXiv: https://arxiv.org/abs/2311.02041 · HTML: https://mlsanity.com/paper/2311.02041/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 27 of its 59 references that are in the map.
- First posted on arXiv 3 Nov 2023.

## Placed in

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

## Builds on (most cited first, 27 of 27)

- [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)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Make-A-Video: Text-to-Video Generation without Text-Video Data](https://mlsanity.com/paper/2209.14792/) (2022)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [CrossViT: Cross-Attention Multi-Scale Vision Transformer for Image Classification](https://mlsanity.com/paper/2103.14899/) (2021)
- [Attention is not not Explanation](https://mlsanity.com/paper/1908.04626/) (2019)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://mlsanity.com/paper/2305.08891/) (2023)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Input Perturbation Reduces Exposure Bias in Diffusion Models](https://mlsanity.com/paper/2301.11706/) (2023)
- [Divide & Bind Your Attention for Improved Generative Semantic Nursing](https://mlsanity.com/paper/2307.10864/) (2023)
- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)
- [Active learning machine learns to create new quantum experiments](https://mlsanity.com/paper/1706.00868/) (2017)
- [Topological Quantum Compiling with Reinforcement Learning](https://mlsanity.com/paper/2004.04743/) (2020)
- [Improving Quantum Circuit Synthesis with Machine Learning](https://mlsanity.com/paper/2306.05622/) (2023)

## Built on by (most cited first, 30 of 33)

- [Accelerating Diffusion Models with Parallel Sampling: Inference at Sub-Linear Time Complexity](https://mlsanity.com/paper/2405.15986/) (2024)
- [QCircuitBench: A Large-Scale Dataset for Benchmarking Quantum Algorithm Design](https://mlsanity.com/paper/2410.07961/) (2024)
- [Artificial intelligence for representing and characterizing quantum systems](https://mlsanity.com/paper/2509.04923/) (2025)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [Hybrid Diffusion for Simultaneous Symbolic and Continuous Planning](https://mlsanity.com/paper/2509.21983/) (2025)
- [DiffBatt: A Diffusion Model for Battery Degradation Prediction and Synthesis](https://mlsanity.com/paper/2410.23893/) (2024)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Synthesis of discrete-continuous quantum circuits with multimodal diffusion models](https://mlsanity.com/paper/2506.01666/) (2025)
- [Interpretable representation learning of quantum data enabled by probabilistic variational autoencoders](https://mlsanity.com/paper/2506.11982/) (2025)
- [Optimizing the non-Clifford-count in unitary synthesis using Reinforcement Learning](https://mlsanity.com/paper/2509.21709/) (2025)
- [FairDiffusion: Enhancing Equity in Latent Diffusion Models via Fair Bayesian Perturbation](https://mlsanity.com/paper/2412.20374/) (2024)
- [Leveraging Diffusion Models for Parameterized Quantum Circuit Generation](https://mlsanity.com/paper/2505.20863/) (2025)
- [Optimal Quantum Circuit Design via Unitary Neural Networks](https://mlsanity.com/paper/2408.13211/) (2024)
- [Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning](https://mlsanity.com/paper/2505.05151/) (2025)
- [BenchRL-QAS: Benchmarking reinforcement learning algorithms for quantum architecture search](https://mlsanity.com/paper/2507.12189/) (2025)
- [Beyond Reinforcement Learning: Fast and Scalable Quantum Circuit Synthesis](https://mlsanity.com/paper/2602.15146/) (2026)
- [Stochastic Reconstruction of Gappy Lagrangian Turbulent Signals by Conditional Diffusion Models](https://mlsanity.com/paper/2410.23971/) (2024)
- [Scalable Parameter Design for Superconducting Quantum Circuits with Graph Neural Networks](https://mlsanity.com/paper/2411.16354/) (2024)
- [Quantum Circuit Generation via test-time learning with large language models](https://mlsanity.com/paper/2602.03466/) (2026)
- [QFlowNet: Fast, Diverse, and Efficient Unitary Synthesis with Generative Flow Networks](https://mlsanity.com/paper/2603.03045/) (2026)
- [Aligning Quantum Operators with Large Language Models](https://mlsanity.com/paper/2606.13811/) (2026)
- [Lie Group Diffusion Models for Hardware-Aware Quantum Circuit Synthesis](https://mlsanity.com/paper/2606.29636/) (2026)
- [When Close Enough Is Not Enough: Autoregressive Drift in Quantum Circuit Synthesis](https://mlsanity.com/paper/2607.12780/) (2026)
- [Diffusion Models to Enhance the Resolution of Microscopy Images: A Tutorial](https://mlsanity.com/paper/2409.16488/) (2024)
- [VQEzy: An Open-Source Dataset for Parameter Initialization in Variational Quantum Eigensolvers](https://mlsanity.com/paper/2509.17322/) (2025)
- [DiffQ: Unified Parameter Initialization for Variational Quantum Algorithms via Diffusion Models](https://mlsanity.com/paper/2509.17324/) (2025)
- [SMILES-Inspired Transfer Learning for Quantum Operators in Generative Quantum Eigensolver](https://mlsanity.com/paper/2509.19715/) (2025)
- [Q-Tag: Watermarking Quantum Circuit Generative Models](https://mlsanity.com/paper/2602.23085/) (2026)
- [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)

## Abstract (arXiv)

Quantum computing has recently emerged as a transformative technology. Yet, its promised advantages rely on efficiently translating quantum operations into viable physical realizations. In this work, we use generative machine learning models, specifically denoising diffusion models (DMs), to facilitate this transformation. Leveraging text-conditioning, we steer the model to produce desired quantum operations within gate-based quantum circuits. Notably, DMs allow to sidestep during training the exponential overhead inherent in the classical simulation of quantum dynamics -- a consistent bottleneck in preceding ML techniques. We demonstrate the model's capabilities across two tasks: entanglement generation and unitary compilation. The model excels at generating new circuits and supports typical DM extensions such as masking and editing to, for instance, align the circuit generation to the constraints of the targeted quantum device. Given their flexibility and generalization abilities, we envision DMs as pivotal in quantum circuit synthesis, enhancing both practical applications but also insights into theoretical quantum computation.