Random Gaussian Augmented Matrix Product States

@misc{puri2026random,
  title = {{Random Gaussian Augmented Matrix Product States}},
  author = {Stavya Puri and Poetri Sonya Tarabunga and Piotr Sierant},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25458},
  eprint = {2609.25458},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25458},
}

TY  - UNPB
TI  - Random Gaussian Augmented Matrix Product States
AU  - Stavya Puri
AU  - Poetri Sonya Tarabunga
AU  - Piotr Sierant
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.25458
UR  - https://arxiv.org/abs/2609.25458
AB  - Strong entanglement limits the reach of tensor-network descriptions of quantum many-body systems. We study Gaussian-augmented matrix product states (GAMPS), formed by applying a free-fermionic (Gaussian) unitary to a matrix product state. To explore the capabilities of this family, we consider random GAMPS}, a minimally structured ensemble obtained by independently sampling random matrix product states and Gaussian unitaries. Exploiting the algebraic structure of Gaussian unitaries, we develop a replica tensor-network method that computes averages over the random GAMPS ensemble for hundreds of qubits. Random GAMPS exhibit nearly maximal volume-law entanglement already at modest bond dimension, while other quantum resource quantifiers rapidly approach Haar-random state values as the bond dimension increases. The entanglement scaling suggests an exponential reduction in the bond dimension needed to approach the volume-law entropy compared with unaugmented matrix product states. We find a state two-design behavior of random GAMPS at fixed accuracy with a bond dimension independent of system size. Our results reveal how Gaussian augmentation expands the expressive power of tensor networks.
ER  -