Iterative solutions to the steady-state density matrix for optomechanical systems

Paul Nation, J. R. Johansson, M. P. Blencowe, A. J. Rimberg

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.

Original languageEnglish
Article number013307
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume91
Issue number1
DOIs
Publication statusPublished - 2015 Jan 23

Fingerprint

iterative solution
Reordering
Iterative Solution
Density Matrix
Preconditioner
Quantum Systems
graph theory
Approximate Inverse
permutations
Steady-state Solution
Sparse matrix
Hilbert space
Condition number
Graph theory
Tolerance
Permutation
Optimise
Benchmark
requirements
Necessary

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Iterative solutions to the steady-state density matrix for optomechanical systems. / Nation, Paul; Johansson, J. R.; Blencowe, M. P.; Rimberg, A. J.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 91, No. 1, 013307, 23.01.2015.

Research output: Contribution to journalArticle

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