Universal Bounds for Out-of-Distribution Unitary Learning

@misc{favre2026universal,
  title = {{Universal Bounds for Out-of-Distribution Unitary Learning}},
  author = {Joachim Favre and Armando Angrisani and Zoë Holmes},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03690},
  eprint = {2610.03690},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03690},
}

TY  - UNPB
TI  - Universal Bounds for Out-of-Distribution Unitary Learning
AU  - Joachim Favre
AU  - Armando Angrisani
AU  - Zoë Holmes
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.03690
UR  - https://arxiv.org/abs/2610.03690
AB  - How much can the action of an unknown unitary dynamics on one family of states reveal about its action elsewhere? We develop a general framework for out-of-distribution quantum dynamics learning based on the first and second moments of the input distribution. These define a notion of the bias and expressivity of an ensemble, which together control generalization between arbitrary mixed-state training and testing distributions. Our framework shows that only studying the action of a unitary on random real states can learn its action on random complex states, that tensor products of unbiased pure-state ensembles preserve expressivity, and that single-qubit risks are independent of bias. It also recovers earlier locally scrambling results as loose special cases and yields tight product-to-Haar bounds. We conclude with a series of no-go results and limited generalization bounds for learning certain channels, which further serve to underscore the distinctive role of unitarity in enabling out-of-distribution generalization.
ER  -