# ConQuER: Modular Architectures for Control and Bias Mitigation in IQP Quantum Generative Models

arXiv: https://arxiv.org/abs/2509.22551 · HTML: https://mlsanity.com/paper/2509.22551/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 6 of 6)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Trainability barriers and opportunities in quantum generative modeling](https://mlsanity.com/paper/2305.02881/) (2023)
- [QuantumNAT: Quantum Noise-Aware Training with Noise Injection, Quantization and Normalization](https://mlsanity.com/paper/2110.11331/) (2021)

## Built on by (most cited first, 1 of 1)

- [MolPaQ: Modular Quantum-Classical Patch Learning for Interpretable Molecular Generation](https://mlsanity.com/paper/2604.08575/) (2026)

## Abstract (arXiv)

Quantum generative models based on instantaneous quantum polynomial (IQP) circuits show great promise in learning complex distributions while maintaining classical trainability. However, current implementations suffer from two key limitations: lack of controllability over generated outputs and severe generation bias towards certain expected patterns. We present a Controllable Quantum Generative Framework, ConQuER, which addresses both challenges through a modular circuit architecture. ConQuER embeds a lightweight controller circuit that can be directly combined with pre-trained IQP circuits to precisely control the output distribution without full retraining. Leveraging the advantages of IQP, our scheme enables precise control over properties such as the Hamming Weight distribution with minimal parameter and gate overhead. In addition, inspired by the controller design, we extend this modular approach through data-driven optimization to embed implicit control paths in the underlying IQP architecture, significantly reducing generation bias on structured datasets. ConQuER retains efficient classical training properties and high scalability. We experimentally validate ConQuER on multiple quantum state datasets, demonstrating its superior control accuracy and balanced generation performance, only with very low overhead cost over original IQP circuits. Our framework bridges the gap between the advantages of quantum computing and the practical needs of controllable generation modeling.