Practical recipes for the model order reduction, dynamical simulation, and compressive sampling of large-scale open quantum systems

@misc{citeulike:2796366, abstract = {This article presents numerical recipes for simulating high-temperature and non-equilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process, and finally, projection of the trajectory onto a state-space manifold having reduced dimensionality and possessing a Kahler potential of multi-linear form. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low-dimensionality Kahler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candes-Tao sparsity limit is observed, a deterministic construction for sampling matrices is given, and methods for quantum state optimization by Dantzig selection are given.}, author = {Sidles, John A. and Garbini, Joseph L. and Harrell, Lee E. and Hero, Alfred O. and Jacky, Jonathan P. and Malcomb, Joseph R. and Norman, Anthony G. and Williamson, Austin M. }, citeulike-article-id = {2796366}, eprint = {0805.1844}, keywords = {algorithms, computation, data-structures, physics, quantum, quantum-computation}, month = {May}, posted-at = {2008-05-14 21:05:56}, priority = {2}, title = {Practical recipes for the model order reduction, dynamical simulation, and compressive sampling of large-scale open quantum systems}, url = {http://arxiv.org/abs/0805.1844}, year = {2008} }

TY - ELEC ID - citeulike:2796366 L3 - citeulike-article-id:2796366 TI - Practical recipes for the model order reduction, dynamical simulation, and compressive sampling of large-scale open quantum systems N2 - This article presents numerical recipes for simulating high-temperature and non-equilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process, and finally, projection of the trajectory onto a state-space manifold having reduced dimensionality and possessing a Kahler potential of multi-linear form. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low-dimensionality Kahler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candes-Tao sparsity limit is observed, a deterministic construction for sampling matrices is given, and methods for quantum state optimization by Dantzig selection are given. KW - algorithms KW - computation KW - data-structures KW - physics KW - quantum KW - quantum-computation AU - Sidles, John AU - Garbini, Joseph AU - Harrell, Lee AU - Hero, Alfred AU - Jacky, Jonathan AU - Malcomb, Joseph AU - Norman, Anthony AU - Williamson, Austin PY - 2008/May/13/ UR - http://arxiv.org/abs/0805.1844 ER -