Numerical Integration with Graphical Processing Unit for QKD Simulation

The Air Force Institute of Techology (AFIT) is developing a simulation framework to model a wide variety of existing and proposed Quantum Key Distribution (QKD) systems. This research investigates using graphical processing unit (GPU) technology to more efficiently integrate optical pulses modeled within this framework. The goal is to reduce the simulation execution time. A GPU algorithm is presented for performing numerical integration of optical pulses described by Gaussian curves to improve pulse energy and power calculations. In order to measure the performance of the algorithm a optimal timing method is needed. A timer using Comute Unified Device Architecture (CUDA) events is selected over a Windows system application programming interface (API) timer. The problem sizes studied produce speedups greater than 60x on the NVIDIA Tesla C2075 compared to the Intel i7-3610QM CPU

The Cross-entropy of Piecewise Linear Probability Density Functions

The cross-entropy and its related terms from information theory (e.g.~entropy, Kullback–Leibler divergence) are used throughout artificial intelligence and machine learning. This includes many of the major successes, both current and historic, where they commonly appear as the natural objective of an optimisation procedure for learning model parameters, or their distributions. This paper presents a novel derivation of the differential cross-entropy between two 1D probability density functions represented as piecewise linear functions. Implementation challenges are resolved and experimental validation is presented, including a rigorous analysis of accuracy and a demonstration of using the presented result as the objective of a neural network. Previously, cross-entropy would need to be approximated via numerical integration, or equivalent, for which calculating gradients is impractical. Machine learning models with high parameter counts are optimised primarily with gradients, so if piecewise linear density representations are to be used then the presented analytic solution is essential. This paper contributes the necessary theory for the practical optimisation of information theoretic objectives when dealing with piecewise linear distributions directly. Removing this limitation expands the design space for future algorithms