title: Iterative solutions to the steady-state density matrix for optomechanical systems.
abstract: We present a sparse matrix permutation from graph theory that gives stable incomplete lower-upper preconditioners necessary for iterative solutions to the steady-state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance. This reordering optimizes the condition number of the approximate inverse and is the only method found to be stable at large Hilbert space dimensions. This allows for steady-state solutions to otherwise intractable quantum optomechanical systems.
authors: Department of Physics, Korea University, Seoul 136-713, Korea.
authors: P D
authors: PD
authors: Nation
authors: iTHES Research Group, RIKEN, Saitama 351-0198, Japan.
authors: J R
authors: JR
authors: Johansson
authors: Department of Physics and Astronomy, Dartmouth College, New Hampshire 03755, USA.
authors: M P
authors: MP
authors: Blencowe
authors: Department of Physics and Astronomy, Dartmouth College, New Hampshire 03755, USA.
authors: A J
authors: AJ
authors: Rimberg