Mapping Quantum States with Network Theory

A new approach uses network analysis of wave function snapshots to classify different phases of quantum matter.

A new approach uses network analysis of wave function snapshots to classify different phases of quantum matter.
![The system leverages a Gibbs state, defined as $ \rho_0 = e^{-\beta H}/Z $ with Hamiltonian $ H = \sum_{k=1}^{N} H^{(k)} $, as a probe, encoding parameters through a unitary process $ U_\lambda$ to generate a parameter-dependent state $ \rho_\lambda $, and establishes that the precision with which these parameters can be estimated is fundamentally bounded by the seminorm of the commutator $ ||i[H, h_\lambda]|| $ of the Hamiltonian and its transformed local generator $ h_\lambda $.](https://arxiv.org/html/2512.02366v1/x1.png)
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