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

Quantum generative models based on instantaneous quantum polynomial (IQP) circuits show great promise in learning complex distributions while maintaining classical train-ability. 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.