Generative IQP Circuit Learning with Physics-Informed Latent Initialization

Instantaneous quantum polynomial-time (IQP) generative models can reuse a shared circuit across related scientific-data instances by adapting only a low-dimensional latent parameter block. Existing latent-adaptation schemes initialize the reference latent randomly, although this choice can strongly affect the shared core learned around it. We introduce a physics-informed initialization that transfers a latent representation from a classical physics-informed neural network (PINN) surrogate into the IQP model. On parameterized Burgers' equation solution families, the PINN is trained on lower-resolution grids whereas the IQP generator models a $64\times64$ solution domain. Across three initial-condition families and unseen viscosities, transferred initialization consistently reduces reconstruction error relative to random initialization, including when the PINN uses grids as coarse as $12\times12$. Pairwise latent similarities remain strongly rank-correlated between the classical and quantum representations, supporting the view that the transfer supplies a structured warm start rather than an arbitrary initial vector.