  Emerging quantum hardware provides new possibilities for quantum simulation.
While much of the research has focused on simulating closed quantum systems,
the real-world quantum systems are mostly open. Therefore, it is essential to
develop quantum algorithms that can effectively simulate open quantum systems.
Here we present an adaptive variational quantum algorithm for simulating open
quantum system dynamics described by the Lindblad equation. The algorithm is
designed to build resource-efficient ansatze through the dynamical addition of
operators by maintaining the simulation accuracy. We validate the effectiveness
of our algorithm on both noiseless simulators and IBM quantum processors and
observe good quantitative and qualitative agreement with the exact solution. We
also investigate the scaling of the required resources with system size and
accuracy and find polynomial behavior. Our results demonstrate that near-future
quantum processors are capable of simulating open quantum systems.
