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Implementation of quantum and classical discrete fractional Fourier transforms.

ABSTRACT: Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

SUBMITTER: Weimann S

PROVIDER: S-EPMC4814576 | biostudies-literature | 2016 Mar

REPOSITORIES: biostudies-literature

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Implementation of quantum and classical discrete fractional Fourier transforms.

Weimann Steffen S Perez-Leija Armando A Lebugle Maxime M Keil Robert R Tichy Malte M Gräfe Markus M Heilmann René R Nolte Stefan S Moya-Cessa Hector H Weihs Gregor G Christodoulides Demetrios N DN Szameit Alexander A

Nature communications 20160323

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete ...[more]

PMID: 27006089

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Project description:Fast Fourier transform (FFT)-based protein ligand docking together with parallel simulated annealing for both rigid and flexible receptor docking are implemented on graphical processing unit (GPU) accelerated platforms to significantly enhance the throughput of the CDOCKER and flexible CDOCKER - the docking algorithms in the CHARMM program for biomolecule modeling. The FFT-based approach for docking, first applied in protein-protein docking to efficiently search for the binding position and orientation of proteins, is adapted here to search ligand translational and rotational spaces given a ligand conformation in protein-ligand docking. Running on GPUs, our implementation of FFT docking in CDOCKER achieves a 15 000 fold speedup in the ligand translational and rotational space search in protein-ligand docking problems. With this significant speedup it becomes practical to exhaustively search ligand translational and rotational space when docking a rigid ligand into a protein receptor. We demonstrate in this paper that this provides an efficient way to calculate an upper bound for docking accuracy in the assessment of scoring functions for protein-ligand docking, which can be useful for improving scoring functions. The parallel molecular dynamics (MD) simulated annealing, also running on GPUs, aims to accelerate the search algorithm in CDOCKER by running MD simulated annealing in parallel on GPUs. When utilized as part of the general CDOCKER docking protocol, acceleration in excess of 20 times is achieved. With this acceleration, we demonstrate that the performance of CDOCKER for redocking is significantly improved compared with three other popular protein-ligand docking programs on two widely used protein ligand complex data sets: the Astex diverse set and the SB2012 test set. The flexible CDOCKER is similarly improved by the parallel MD simulated annealing on GPUs. Based on the results presented here, we suggest that the accelerated CDOCKER platform provides a highly competitive docking engine for both rigid-receptor and flexible-receptor docking studies and will further facilitate continued improvement in the physics-based scoring function employed in CDOCKER docking studies.

Dataset Information

Implementation of quantum and classical discrete fractional Fourier transforms.

Publications

Implementation of quantum and classical discrete fractional Fourier transforms.

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