Abstract
In this chapter, we demonstrate how real-time quantum Krylov subspace methods can be adapted to investigate open quantum systems described by the Lindblad formalism. We apply these methods to a two-photon-driven superconducting Kerr resonator and illustrate their use in estimating the Liouvillian gap within the Kerr Cat qubit regime. This is based on work done between November 2025 and January 2026 and on the talk given in early February 2026 at the Kwekfest 2026 conference, to celebrate L.C. Kwek's lifetime achievements.