Speaker
Description
We study whether symmetry-constrained quantum circuits can avoid the complexity and learning barriers usually associated with Haar-random models. Focusing on circuits drawn from the special orthogonal and unitary symplectic groups, we show that these structured ensembles still generate states of exponentially large strong state complexity, with analogous behavior for group designs. We further prove average-case hardness for statistical-query learning of their output distributions. This has direct implications for quantum circuit Born machines: restricting an overly expressive generative ansatz to a structured subgroup does not, by itself, restore learnability or trainability. Our results clarify the limitations of symmetry as a design principle for quantum generative modeling. This talk is based on [O. Shaya et al., J. Phys. A 59, 205302 (2026)]
| Topic | Theoretical foundations of quantum learning |
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