# From Characterization To Construction: Generative Quantum Circuit Synthesis from Gate Set Tomography Data

arXiv: https://arxiv.org/abs/2605.01367 · HTML: https://mlsanity.com/paper/2605.01367/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 67 references that are in the map.
- First posted on arXiv 2 May 2026.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
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- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [Curriculum Learning: A Survey](https://mlsanity.com/paper/2101.10382/) (2021)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [Memory and information processing in neuromorphic systems](https://mlsanity.com/paper/1506.03264/) (2015)
- [Quantum circuit synthesis with diffusion models](https://mlsanity.com/paper/2311.02041/) (2023)
- [Colloquium: Advances in automation of quantum dot devices control](https://mlsanity.com/paper/2112.09362/) (2021)
- [CCDM: Continuous Conditional Diffusion Models for Image Generation](https://mlsanity.com/paper/2405.03546/) (2024)
- [Efficient decomposition of unitary matrices in quantum circuit compilers](https://mlsanity.com/paper/2101.02993/) (2021)
- [Improving Quantum Circuit Synthesis with Machine Learning](https://mlsanity.com/paper/2306.05622/) (2023)
- [Synthesis of discrete-continuous quantum circuits with multimodal diffusion models](https://mlsanity.com/paper/2506.01666/) (2025)
- [UDiTQC: U-Net-Style Diffusion Transformer for Quantum Circuit Synthesis](https://mlsanity.com/paper/2501.16380/) (2025)
- [Leveraging Diffusion Models for Parameterized Quantum Circuit Generation](https://mlsanity.com/paper/2505.20863/) (2025)
- [QKSA: Quantum Knowledge Seeking Agent](https://mlsanity.com/paper/2107.01429/) (2021)
- [Expressing and Analyzing Quantum Algorithms with Qualtran](https://mlsanity.com/paper/2409.04643/) (2024)
- [Neuromorphic Electronic Systems for Reservoir Computing](https://mlsanity.com/paper/1908.09572/) (2019)
- [Optimal Quantum Circuit Design via Unitary Neural Networks](https://mlsanity.com/paper/2408.13211/) (2024)
- [Quantum Computation with Machine-Learning-Controlled Quantum Stuff](https://mlsanity.com/paper/1911.13282/) (2019)
- [DeQompile: quantum circuit decompilation using genetic programming for explainable quantum architecture search](https://mlsanity.com/paper/2504.08310/) (2025)

## Abstract (arXiv)

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.