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

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 MMD$^2$ 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 + $log_2 L$ qubits (cIQP). Across five seeds at L = 8, 1500 epochs, the model reaches $\mathrm{MAE}_ρ$ = $0.069 \pm 0.008$ 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 $\mathrm{MAE}_ρ$ = 0.100. The compiled cIQP reproduces the MoIQP marginal to $0.591 \pm 0.012$ times the Monte Carlo noise floor.