Parity Supervision as a Driver of Generalization in Quantum Generative Modeling

TL;DR

This paper investigates how parity supervision can serve as an effective inductive bias, improving generalization in quantum generative models, specifically IQP Born machines, by transferring structural information from observed to unseen states.

Contribution

It demonstrates that parity supervision enhances generalization in IQP quantum models, providing a tractable training signal and a structural bias aligned with the distribution and circuit architecture.

Findings

Parity supervision improves exact KL fit over MSE training.

Parity moments transfer evidence from observed to unseen states.

Maximum-entropy control does not replicate the effects of parity supervision.

Abstract

Generalizing from finite samples to unseen valid states is central to discrete generative modeling. In a controlled, exactly enumerable setting, we test whether parity losses, commonly used for tractable Instantaneous Quantum Polynomial-time (IQP) training, also provide an inductive bias for generalization. We compare an IQP circuit Born machine trained by parity supervision with the same circuit trained by coordinate-wise mean-squared-error (MSE), and with a classical maximum-entropy control given the same parity moments. Parity supervision improves exact forward Kullback-Leibler (KL) fit and unseen high-value-state recovery over IQP-MSE, while the maximum-entropy control does not reproduce the full effect. A parameter-free spectral reconstruction shows that parity moments already transfer evidence from observed samples to structurally compatible unseen states, which the IQP circuit further refines. This identifies parity supervision not only as a tractable training signal, but also as a generalization mechanism for IQP Born machines when the distribution to be learned, the parity objective, and the circuit architecture are structurally aligned.