José Carrasco, Freie Universität Berlin, wird am Dienstag, 14.10.2025 um 15:00, Online, einen Vortrag halten.
Title: The abelian version of the State Hidden Subgroup Problem: Learning stabilizer groups and beyond
Abstract: Identifying the symmetry properties of quantum states is a central theme in quantum information and many-body physics. In this work, we investigate learning problems in which the goal is to identify a hidden symmetry of an unknown quantum state. Building on the recent formulation of the state hidden subgroup problem (StateHSP), we focus on abelian groups and develop an efficient quantum algorithm that learns any hidden symmetry subgroup using a generalized form of Fourier sampling. The approach has concrete applications like learning (i) qubit and qudit stabilizer groups, (ii) cuts along which a state is unentangled, and (iii) hidden translation symmetries. Through these applications, we reveal that well-known quantum learning primitives, such as Bell sampling and Bell difference sampling, are in fact special cases of Fourier sampling. Our results highlight the broad potential of the StateHSP framework for symmetry-based quantum learning tasks.