Quantum Graphical Models and Belief Propagation

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersely-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.Comment: 58 pages, 9 figure

A Framework for Intelligent Inventory Prediction in Small and Medium- Scale Enterprise

The aim of this research is to apply an intelligent technique to predict optimal inventory quantity in small and medium-scale enterprise. This is in view of the fact that the conventional models such as the EOQ model use only deterministic while some decision variables are non- deterministic in nature. Forecasted average demand of items for ten months in a small-scale retail outlet was collected and trained using an Artificial Neural Networks (ANN) of 5 neurons in the input layer with eight neurons in the first hidden layer and four neurons in the second hidden layer. Two feed-forward training algorithms of quasi-newton and quick propagation were employed in the training with the results of fuzzy logic technology found in the literature as the target output. Results obtained show that the quasi-newton algorithm covaries stronger with the fuzzy logic results than the quick propagation results. The objective and subjective feelings of the inventory manager were also captured to optimise the results of the training. The study is at a framework stage and will proceed to implementation level when more datasets are collected. Data collection in a small-scale outlet is a daunting task as record keeping is hardly done. The inclusion of non-deterministic circumstances such as emotional and objective feelings of the inventory manager to predict inventory is novel considering the fact that studies in the available intelligent inventory prediction have not employed such variables in their predictions. Keywords: Artificial Neural networks, Fuzzy logic, Quasi newton, Quick propagation, EOQ, Inventory, Forecast. DOI: 10.7176/EJBM/13-2-03 Publication date: January 31st 202

A framework for intelligent inventory prediction in small and medium- scale enterprise.

The aim of this research is to apply an intelligent technique to predict optimal inventory quantity in small and medium-scale enterprise. This is in view of the fact that the conventional models such as the EOQ model use only deterministic while some decision variables are non-deterministic in nature. Forecasted average demand of items for ten months in a small-scale retail outlet was collected and trained using an Artificial Neural Networks (ANN) of 5 neurons in the input layer with eight neurons in the first hidden layer and four neurons in the second hidden layer. Two feed-forward training algorithms of quasi-newton and quick propagation were employed in the training with the results of fuzzy logic technology found in the literature as the target output. Results obtained show that the quasi-newton algorithm covaries stronger with the fuzzy logic results than the quick propagation results. The objective and subjective feelings of the inventory manager were also captured to optimise the results of the training. The study is at a framework stage and will proceed to implementation level when more datasets are collected. Data collection in a small-scale outlet is a daunting task as record keeping is hardly done. The inclusion of non-deterministic circumstances such as emotional and objective feelings of the inventory manager to predict inventory is novel considering the fact that studies in the available intelligent inventory prediction have not employed such variables in their predictions

Towards Quantum Belief Propagation for LDPC Decoding in Wireless Networks

We present Quantum Belief Propagation (QBP), a Quantum Annealing (QA) based decoder design for Low Density Parity Check (LDPC) error control codes, which have found many useful applications in Wi-Fi, satellite communications, mobile cellular systems, and data storage systems. QBP reduces the LDPC decoding to a discrete optimization problem, then embeds that reduced design onto quantum annealing hardware. QBP's embedding design can support LDPC codes of block length up to 420 bits on real state-of-the-art QA hardware with 2,048 qubits. We evaluate performance on real quantum annealer hardware, performing sensitivity analyses on a variety of parameter settings. Our design achieves a bit error rate of $10^{-8}$ in 20 $\mu$s and a 1,500 byte frame error rate of $10^{-6}$ in 50 $\mu$s at SNR 9 dB over a Gaussian noise wireless channel. Further experiments measure performance over real-world wireless channels, requiring 30 $\mu$s to achieve a 1,500 byte 99.99$\%$ frame delivery rate at SNR 15-20 dB. QBP achieves a performance improvement over an FPGA based soft belief propagation LDPC decoder, by reaching a bit error rate of $10^{-8}$ and a frame error rate of $10^{-6}$ at an SNR 2.5--3.5 dB lower. In terms of limitations, QBP currently cannot realize practical protocol-sized ($\textit{e.g.,}$ Wi-Fi, WiMax) LDPC codes on current QA processors. Our further studies in this work present future cost, throughput, and QA hardware trend considerations

A Black-Box Physics-Informed Estimator based on Gaussian Process Regression for Robot Inverse Dynamics Identification

In this paper, we propose a black-box model based on Gaussian process regression for the identification of the inverse dynamics of robotic manipulators. The proposed model relies on a novel multidimensional kernel, called \textit{Lagrangian Inspired Polynomial} (\kernelInitials{}) kernel. The \kernelInitials{} kernel is based on two main ideas. First, instead of directly modeling the inverse dynamics components, we model as GPs the kinetic and potential energy of the system. The GP prior on the inverse dynamics components is derived from those on the energies by applying the properties of GPs under linear operators. Second, as regards the energy prior definition, we prove a polynomial structure of the kinetic and potential energy, and we derive a polynomial kernel that encodes this property. As a consequence, the proposed model allows also to estimate the kinetic and potential energy without requiring any label on these quantities. Results on simulation and on two real robotic manipulators, namely a 7 DOF Franka Emika Panda and a 6 DOF MELFA RV4FL, show that the proposed model outperforms state-of-the-art black-box estimators based both on Gaussian Processes and Neural Networks in terms of accuracy, generality and data efficiency. The experiments on the MELFA robot also demonstrate that our approach achieves performance comparable to fine-tuned model-based estimators, despite requiring less prior information