Spectral Born machines are Fourier-phase quantum generative models over Z_d^n that train classically via graph-spectral MMD and show reduced parameters plus apparent overfitting resistance on integer data.
An IQP Born Machine for Calorimeter Image Generation at 64 Qubits with Compiled-IQP Deployment
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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 $\mathrm{MAE}_{\rho}$ = $0.069 \pm 0.008$ 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 $\mathrm{MAE}_{\rho}$ = 0.100. The compiled cIQP reproduces the MoIQP marginal to $0.591 \pm 0.012$ times the Monte Carlo noise floor.
fields
quant-ph 2years
2026 2representative citing papers
Qudit extension of parameterized IQP circuits proposed for generative modeling of integer data, with loss function and covariance matrix, validated on electron shower energy deposits in CLIC electromagnetic calorimeter.
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Spectral Born machines: classically trainable quantum generative models for discrete data
Spectral Born machines are Fourier-phase quantum generative models over Z_d^n that train classically via graph-spectral MMD and show reduced parameters plus apparent overfitting resistance on integer data.
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Qudit extension of parameterized IQP circuits: A generative quantum machine learning approach to integer data
Qudit extension of parameterized IQP circuits proposed for generative modeling of integer data, with loss function and covariance matrix, validated on electron shower energy deposits in CLIC electromagnetic calorimeter.