Tensor-network machine learning models (MPS and PEPS) have average generalization risk lower bounded by explicit functions of training-set size and bond dimension, formalizing no-free-lunch limits for quantum-inspired learners.
Matrix Product States, Random Matrix Theory and the Principle of Maximum Entropy
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Using random matrix techniques and the theory of Matrix Product States we show that reduced density matrices of quantum spin chains have generically maximum entropy.
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No-Free-Lunch Theories for Tensor-Network Machine Learning Models
Tensor-network machine learning models (MPS and PEPS) have average generalization risk lower bounded by explicit functions of training-set size and bond dimension, formalizing no-free-lunch limits for quantum-inspired learners.