Full- and low-rank exponential Euler integrators for the Lindblad equation
This work provides novel numerical methods for simulating open quantum systems, ensuring physical constraints are met, which is crucial for quantum physics and chemistry simulations.
The authors develop full- and low-rank exponential Euler integrators for the Lindblad equation that unconditionally preserve positivity and trace, with sharp error estimates and numerical experiments showing improved performance over existing methods.
The Lindblad equation is a widely used quantum master equation to model the dynamical evolution of open quantum systems whose states are described by density matrices. These solution matrices are characterized by semi-positiveness and trace preserving properties, which must be guaranteed in any physically meaningful numerical simulation. In this paper, novel full- and low-rank exponential Euler integrators are developed for approximating the Lindblad equation that preserve positivity and trace unconditionally. Theoretical results are presented that provide sharp error estimates for the two classes of exponential integration methods. Results of numerical experiments are discussed that illustrate the effectiveness of the proposed schemes, beyond present state-of-the-art capabilities.