IQP Born Machines under Data-dependent and Agnostic Initialization Strategies

TL;DR

This paper investigates how different initialization strategies affect the training landscape of IQP-based quantum generative models, revealing that data-dependent initializations can improve convergence and provide theoretical insights into loss variance.

Contribution

It proves that random full-angle initializations cause barren plateaus in the MMD loss landscape and demonstrates that data-dependent initializations can lead to faster convergence with provable gradients.

Findings

Random full-angle initializations cause barren plateaus.

Data-dependent initializations improve convergence.

Variance lower bounds apply to general non-linear losses.

Abstract

Quantum circuit Born machines based on instantaneous quantum polynomial-time (IQP) circuits are natural candidates for quantum generative modeling, both because of their probabilistic structure and because IQP sampling is provably classically hard in certain regimes. Recent proposals focus on training IQP-QCBMs using Maximum Mean Discrepancy (MMD) losses built from low-body Pauli-$Z$ correlators, but the effect of initialization on the resulting optimization landscape remains poorly understood. In this work, we address this by first proving that the MMD loss landscape suffers from barren plateaus for random full-angle-range initializations of IQP circuits. We then establish lower bounds on the loss variance for identity and an unbiased data-agnostic initialization. We then additionally consider a data-dependent initialization that is better aligned with the target distribution and, under suitable assumptions, yields provable gradients and generally converges quicker to a good minimum (as indicated by our training of circuits with 150 qubits on genomic data). Finally, as a by-product, the developed variance lower bound framework is applicable to a general class of non-linear losses, offering a broader toolset for analyzing warm-starts in quantum machine learning.