Quantum query complexity of Hurwitz stability testing

arXiv:2610.41180v1 Announce Type: new Abstract: Determining whether every trajectory of the linear system $\dot{x}=Ax$ converges to zero (or, equivalently, whether $A$ is Hurwitz stable) is a fundamental problem in control theory. It arises, for example, in verifying the stability of feedback controllers and state observers, as well as of linearized dynamical models. We study the quantum query complexity of deciding whether a matrix $A\in\mathbb{C}^{n\times n}$ is Hurwitz stable, given an exact normalized block-encoding of $A$.