Dresden 2026 – scientific programme

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QI: Fachverband Quanteninformation

QI 13: Quantum Control

QI 13.8: Talk

Wednesday, March 11, 2026, 17:15–17:30, BEY/0245

Autonomous reachability of quantum states on random graphs — •Konrad Szymański¹, Tomasz Andrzejewski², Yuri Minoguchi², and Phila Rembold² — ¹Research Center for Quantum Information, Bratislava, Slovakia — ²Atominstitut, TU Wien, Vienna, Austria

We study a particle hopping on a graph under a Hamiltonian with fixed but tunable couplings (no time-dependent control). We ask: which states can be reached from a given initially localized state via such autonomous dynamics? The Hamiltonian is a linear combination of generators corresponding to graph edges, with weights chosen freely but held constant during evolution. We develop three criteria to determine whether a given state is reachable from another. The first is analytical: if a certain matrix constructed from expectation values of the two states is strictly positive definite, the target state is certified unreachable from the initial one. The remaining two rely on numerical optimization over overlaps in the Hamiltonian eigenspaces and Krylov subspace structure. Applying these tools to random graph ensembles, we characterize how the fraction of Haar-random pure states that are unreachable from a localized initial state depends on graph connectivity.

Keywords: autonomous evolution; random graph; Krylov subspace