The authors define quantum generalization and training losses via classical shadows and prove that QWAIC is an asymptotically unbiased estimator of the quantum generalization loss for singular quantum state models.
31 For our purposes, we refer to an alternative version of this theorem that is more directly applicable to our context, as Atiyah wrote [86]
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Statistical inference for quantum singular models
The authors define quantum generalization and training losses via classical shadows and prove that QWAIC is an asymptotically unbiased estimator of the quantum generalization loss for singular quantum state models.