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

被引:1
|
作者
Sidles, John A. [1 ]
Garbini, Joseph L. [2 ]
Harrell, Lee E. [3 ]
Hero, Alfred O. [4 ]
Jacky, Jonathan P. [1 ]
Malcomb, Joseph R. [2 ]
Norman, Anthony G. [5 ]
Williamson, Austin M. [2 ]
机构
[1] Univ Washington, Sch Med, Dept Orthopaed & Sports Med, Seattle, WA 98195 USA
[2] Univ Washington, Dept Mech Engn, Seattle, WA 98195 USA
[3] US Mil Acad, Dept Phys, West Point, NY 10996 USA
[4] Univ Michigan, Dept Elect Engn, Houghton, MI 49931 USA
[5] Univ Washington, Dept Bioengn, Seattle, WA 98195 USA
来源
NEW JOURNAL OF PHYSICS | 2009年 / 11卷
基金
美国国家卫生研究院;
关键词
ROBUST UNCERTAINTY PRINCIPLES; STATISTICAL ESTIMATION; DANTZIG SELECTOR; MOLECULAR-DYNAMICS; FIBEROPTIC INTERFEROMETER; RANDOM PROJECTIONS; SIGNAL RECOVERY; MAGNETIC-MOMENT; SPOOKY ACTION; NOISE;
D O I
10.1088/1367-2630/11/6/065002
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Practical recipes are presented for simulating high-temperature and nonequilibrium 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 state-space manifolds having reduced dimensionality and possessing a Kahler potential of multilinear algebraic form. These state-spaces can be regarded as ruled algebraic varieties upon which a projective quantum model order reduction (MOR) is performed. The Riemannian sectional curvature of ruled Kahlerian varieties is analyzed, and proved to be non-positive upon all sections that contain a rule. These manifolds are shown to contain Slater determinants as a special case and their identity with Grassmannian varieties is demonstrated. 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.
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页数:96
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