This paper investigates the performances of a greedy randomized algorithm to optimize the realization of nearest-neighbor compliant quantum circuits. Current technological limitations (decoherence effect) impose that ...
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ISBN:
(纸本)9783319930312;9783319930305
This paper investigates the performances of a greedy randomized algorithm to optimize the realization of nearest-neighbor compliant quantum circuits. Current technological limitations (decoherence effect) impose that the overall duration (makespan) of the quantum circuit realization be minimized One core contribution of this paper is a lexicographic two-key ranking function for quantum gate selection: the first key acts as a global closure metric to minimize the solution makespan;the second one is a local metric acting as "tie-breaker" for avoiding cycling. Our algorithm has been tested on a set of quantum circuit benchmark instances of increasing sizes available from the recent literature. We demonstrate that our heuristic approach outperforms the solutions obtained in previous research against the same benchmark, both from the CPU efficiency and from the solution quality standpoint.
Compressive spectral imaging systems (CSI) use a focal plane array (FPA) to measure two-dimensional (2D) coded projections of a three-dimensional (3D) spatio-spectral scene. A reconstruction algorithm based on compres...
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ISBN:
(纸本)9781509002290
Compressive spectral imaging systems (CSI) use a focal plane array (FPA) to measure two-dimensional (2D) coded projections of a three-dimensional (3D) spatio-spectral scene. A reconstruction algorithm based on compressive sensing theory exploits the projections to retrieve the underlying 3D scene. Compressive sensing relies on two principles: sparsity and incoherence. Higher incoherence drives to better reconstructed images quality. The Colored Coded Aperture Spectral Imager (C-CASSI) is a CSI system where the coded projections are produced by optical elements named coded apertures. The C-CASSI system can be modeled as a linear transformation. The transformation matrix represents the physical effects of the coded aperture and the prism on the scene. The transformation matrix is also called the system representative matrix. The colored coded apertures modulate spatially and spectrally the light from the scene. The reconstruction image quality is highly dependent on the colored coded apertures design. An algorithm that randomly designs the coded apertures maintains the incoherence between the sensing matrix and the representation base. However, a coded aperture designed completely random, may cause the voxel information be sensed more than once, or not be sensed. This paper presents a random algorithm for colored coded apertures design by homogenizing defined parameters of the C-CASSI system representative matrix. Homogenization parameters guarantee that a voxel information would be sensed at least once. The homogenization is achieved leveling the selected parameters of the matrix, like the average of unblocking elements per column and the average of unblocking elements per row. Simulations show improvement up to 3.10 dB in the PSNR reconstructed images by using the colored coded apertures designs compared with traditional random coded apertures.
The Stirling numbers for graphs provide a combinatorial interpretation of the number of cycle covers in a given graph. The problem of generating all cycle covers or enumerating these quantities on general graphs is co...
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The Stirling numbers for graphs provide a combinatorial interpretation of the number of cycle covers in a given graph. The problem of generating all cycle covers or enumerating these quantities on general graphs is computationally intractable, but recent work has shown that there exist infinite families of sparse or structured graphs for which it is possible to derive efficient enumerative formulas. In this paper, we consider the case of trees and forests of a fixed size, proposing an efficient algorithm based on matrix algebra to approximate the distribution of Stirling numbers. We also present a model application of machine learning to enumeration problems in this setting, demonstrating that standard regression techniques can be applied to this type of combinatorial structure.
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