Higher moment theory and learnability of bosonic states
Quantum Physics
2025-10-03 v1
Abstract
We present a sample- and time-efficient algorithm to learn any bosonic Fock state acted upon by an arbitrary Gaussian unitary. As a special case, this algorithm efficiently learns states produced in Fock state BosonSampling, thus resolving an open question put forth by Aaronson and Grewal (Aaronson, Grewal 2023). We further study a hierarchy of classes of states beyond Gaussian states that are specified by a finite number of their higher moments. Using the higher moments, we find a full spectrum of invariants under Gaussian unitaries, thereby providing necessary conditions for two states to be related by an arbitrary (including active, e.g. beyond linear optics) Gaussian unitary.
Keywords
Cite
@article{arxiv.2510.01610,
title = {Higher moment theory and learnability of bosonic states},
author = {Joseph T. Iosue and Yu-Xin Wang and Ishaun Datta and Soumik Ghosh and Changhun Oh and Bill Fefferman and Alexey V. Gorshkov},
journal= {arXiv preprint arXiv:2510.01610},
year = {2025}
}
Comments
6+20 pages