Abstract
We train an instantaneous quantum polynomial-time (IQP) Born machine on real high-energy-physics calorimeter shower images at 64 qubits and compile the trained model into a single sampling-hard IQP circuit for quantum deployment. The pipeline has three components. The first is a Mixture-of-IQP (MoIQP) architecture, whose Walsh-diagonal MMD² loss is classically trainable by Van den Nest Fourier Monte Carlo. The second is the Pearson-Stabilized Correlation Kernel (PSCK), a positive-definite MMD kernel that biases descent toward correlation-sensitive directions through a data-evaluated Jacobian of the empirical Pearson matrix. The third is an exact deferred-measurement compilation of MoIQP into a single IQP circuit on n + log₂ L qubits (cIQP). Across five seeds at L = 8, 1500 epochs, the model reaches MAE_ρ = 0.069 ± 0.008 against a 0.052 encoding-fidelity floor on the training split and 0.071 ± 0.008 on a held-out test split, versus a Liu-Wang baseline at MAE_ρ = 0.100. The compiled cIQP reproduces the MoIQP marginal to 0.591 ± 0.012 times the Monte Carlo noise floor.