Proper Agnostic Learning of Matrix Product States and Tree Tensor Networks

@misc{pradenne2026proper,
  title = {{Proper Agnostic Learning of Matrix Product States and Tree Tensor Networks}},
  author = {Constantin Cedillo Vayson de Pradenne and Jordan Cotler},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30148},
  eprint = {2609.30148},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30148},
}

TY  - UNPB
TI  - Proper Agnostic Learning of Matrix Product States and Tree Tensor Networks
AU  - Constantin Cedillo Vayson de Pradenne
AU  - Jordan Cotler
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.30148
UR  - https://arxiv.org/abs/2609.30148
AB  - We establish proper agnostic learning of matrix product states and tree tensor networks. Given copies of an arbitrary quantum state ρ, our algorithms return a state |ψ⟩ of chosen bond dimension such that ⟨ψ| ρ|ψ⟩ is within ε of the optimum over the model class, without assuming that ρ itself belongs to or is well approximated by that class. The main idea is to use improper learning to compress the mixed-state objective, reducing proper agnostic learning to optimization against a finite collection of explicitly specified pure states. We then introduce a comparator-dual compression procedure that reduces the bond dimension of these targets while uniformly preserving their overlaps with all bounded-bond comparators, with an error independent of system size. For matrix product states, this gives polynomial copy complexity in the system size, local dimension, bond dimension, and 1/ε, together with polynomial runtime in the system size for fixed local dimension, bond dimension, and accuracy. The same framework yields proper agnostic learning of tree tensor networks on bounded-degree trees, with both copy complexity and runtime polynomial in the system size when the remaining parameters are fixed.
ER  -