Noise-regularized training of quantum circuit Born machines under a finite shot budget

The paper investigates how hardware noise influences the generalization ability of quantum circuit Born machines (QCBMs) trained with maximum mean discrepancy. It establishes that the generalization gap is bounded by the complexity of distributions reachable under any noise process, and shows that scrambled local Pauli noise reduces this complexity while biasing the model toward uniformity, thereby acting as a regularizer with an optimal intermediate strength. The authors introduce GENIE, a framework that implements a target noise level with capped error mitigation and dynamically selects the optimal noise during training using held‑out data, achieving provably bounded regret and outperforming fixed‑noise strategies in simulations on synthetic and census datasets.

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