ConQuER: Modular Conditional Control of Frozen IQP Generators

Pretrained instantaneous quantum polynomial (IQP) generators learn data distributions but lack direct control over the generated samples when trained unconditionally. Practical applications often require generation conditioned on a specific mode or class. We study how to add this capability without updating the pretrained backbone or departing from the IQP circuit family. We propose ConQuER, a modular post-training framework that equips frozen IQP generators with a reusable conditional generation interface. Its controller adopts the same IQP structure and composes directly with the backbone to steer generation toward requested conditions. On Binary Blobs, a 784-support controller achieves mean conditional squared maximum mean discrepancy (${\mathrm{MMD}}^2$) of $0.0105$ and a mean requested-mode hit rate of $78.49\%$. On $4\times 4$ binarized MNIST-3/5, a controller with 1,380 trainable parameters serves both classes and reduces mean conditional ${\mathrm{MMD}}^2$ by $94.1\%$ relative to the frozen unconditional backbone. Further evaluations on these tasks and Shapes20 characterize the trade-off between conditional distribution quality and parameter budget and demonstrate parameter savings through shared control across conditions.