Speaker
Description
Quantum generative models face two well-known obstacles: barren plateau which affects the trainability of the model; and mode collapse is the failure of a trained model to reproduce all of the target distribution's modes. The two are sometimes linked, because the low-resolution cost functions used to avoid barren plateaus are also the ones least able to tell which modes carry probability. In this work, we introduce a target-free coverage regularizer: a penalty against mode collapse that uses only the model's own probability in each mode and the fixed geometry of the modes, and never the target mode populations one is trying to learn. Its central property is that it is trainability-neutral: because the observables that read off the mode occupations act on only a few qubits (they have low Pauli weight), adding the regularizer does not worsen the barren plateau. On a molecular-conformation benchmark whose modes are physically defined and exactly countable, it recovers about $80\%$ of the modes lost by a collapsing quantum generative adversarial network (QGAN) at no trainability cost. The method also has a definite limit, which we characterize: how well a starved mode can be refilled is set by how strongly the base cost concentrates probability away from it (a quantity labelled $g_{\rm base}$); recovery is effective when $g_{\rm base}$ is small but is exponentially suppressed when $g_{\rm base}$ is large. Energy-based generation, whose $g_{\rm base}$ is more than an order of magnitude larger than the adversarial case, is therefore beyond the regularizer's reach.
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