MPO-BMs have NP-hard KL approximation in continuous settings but admit efficient polynomial-bond-dimension approximations with provable KL guarantees for structured targets under locality and spectral-gap conditions.
arXiv preprint arXiv:2510.22138 , year=
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On the Approximation Complexity of Matrix Product Operator Born Machines
MPO-BMs have NP-hard KL approximation in continuous settings but admit efficient polynomial-bond-dimension approximations with provable KL guarantees for structured targets under locality and spectral-gap conditions.