An IQP Born Machine for Calorimeter Image Generation at 64 Qubits with Compiled-IQP Deployment

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: a Mixture-of-IQP moiqp{} architecture, whose Walsh-diagonal MMD² loss is classically trainable by Van den Nest Fourier Monte Carlo; 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; and an exact deferred-measurement compilation of \moiqp{} into a single IQP circuit on nfeat + lceil log₂ Lcomp rceil qubits ciqp{}. Across five seeds at Lcomp = 8, 1500 epochs, the model reaches maerho = 0.069 pm 0.008 against a 0.052 encoding-fidelity floor on the training split and 0.071 pm 0.008 on a held-out test split, versus a Liu--Wang baseline at maerho = 0.100. The compiled \ciqp{} reproduces the \moiqp{} marginal to 0.591 pm 0.012 times the Monte Carlo noise floor.