  Optimizing open quantum system evolution is an important step on the way to
achieving quantum computing and quantum thermodynamic tasks. In this article,
we approach optimisation via variational principles and derive an open quantum
system variational algorithm explicitly for Lindblad evolution in Liouville
space. As an example of such control over open system evolution, we control the
thermalisation of a qubit attached to a thermal Lindbladian bath with a damping
rate $\gamma$. Since thermalisation is an asymptotic process and the
variational algorithm we consider is for fixed time, we present a way to
discuss the potential speedup of thermalisation that can be expected from such
variational algorithms.
