High accuracy steady states obtained from the Universal Lindblad Equation*

We show that the universal Lindblad equation (ULE) captures steady-state expectation values of observables up to rigorously bounded corrections that scale linearly with the system-bath coupling, Γ. We moreover identify a simple quasilocal transformation, whose application guarantees a relative deviation generically scaling to zero with Γ, even for observables such as currents whose steady-state values themselves vanish in the weak coupling limit. This result provides a solution to recently identified limitations on the accuracy of Lindblad-form master equations, which imply significant relative errors for observables whose steady-state values vanish with Γ, while most generic observables are otherwise captured faithfully. The transformation allows for high-fidelity computation of sensitive observables while retaining the stability and physicality of a Lindblad-form master equation