Wilson Rosa de Oliveira

Classical and superposed learning for quantum weightless neural networks

A supervised learning algorithm for quantum neural networks (QNN) based on a novel quantum neuron node implemented as a very simple quantum circuit is proposed and investigated. In contrast to the QNN published in the literature, the proposed model can perform both quantum learning and simulate the classical models. This is partly due to the neural model used elsewhere which has weights and non-linear activations functions. Here a quantum weightless neural network model is proposed as a quantisation of the classical weightless neural networks (WNN). The theoretical and practical results on WNN can be inherited by these quantum weightless neural networks (qWNN). In the quantum learning algorithm proposed here patterns of the training set are presented concurrently in superposition. This superposition-based learning algorithm (SLA) has computational cost polynomial on the number of patterns in the training set.

Quantum Logical Neural Networks

Quantum analogues of the (classical) logical neural networks (LNN) models are proposed in (q-LNN for short). We shall here further develop and investigate the q-LNN composed of the quantum analogue of the probabilistic logic node (PLN) and the multiple-valued PLN (MPLN) variations, dubbed q-PLN and q-MPLN respectively. Besides a clearer mathematical description, we present a computationally efficient and simply described quantum learning algorithm in contrast to what has been proposed to the quantum weighted version.

NONCOMMUTATIVITY FROM THE SYMPLECTIC POINT OF VIEW

The great deal in noncommutative (NC) field theories started when it was noted that NC spaces naturally arise in string theory with a constant background magnetic field in the presence of D-branes. In this work we explore how NC geometry can be introduced into a commutative field theory besides the usual introduction of the Moyal product. We propose a nonperturbative systematic new way to introduce NC geometry into commutative systems, based mainly on the symplectic approach. Further, as example, this formalism describes precisely how to obtain a Lagrangian description for the NC version of some systems reproducing well-known theories.

Quantum perceptron over a field and neural network architecture selection in a quantum computer

In this work, we propose a quantum neural network named quantum perceptron over a field (QPF). Quantum computers are not yet a reality and the models and algorithms proposed in this work cannot be simulated in actual (or classical) computers. QPF is a direct generalization of a classical perceptron and solves some drawbacks found in previous models of quantum perceptrons. We also present a learning algorithm named Superposition based Architecture Learning algorithm (SAL) that optimizes the neural network weights and architectures. SAL searches for the best architecture in a finite set of neural network architectures with linear time over the number of patterns in the training set. SAL is the first learning algorithm to determine neural network architectures in polynomial time. This speedup is obtained by the use of quantum parallelism and a non-linear quantum operator.

Weightless neural models

Abstract Of the many types of neural networks that have recently emerged this paper reviews weightless neuron models. Some advantages of this model are: (1) systems may be built using conventional digital circuits, without the need to develop special VLSI devices, (2) learning is not unreasonably slow, and (3) conventional Theory of Computation tools can be used to analyse their properties. The paper describes the origin of the model, the initial, actual and future works with their main results. A comparative study between weightless and weighted models is presented.

Comments on quantum artificial neural networks with applications

In a recent paper, H. Cao etźal. (Information Science 290 (2015) 1-6) proposed a neural network model called the quantum artificial neural network, which we dub the CCWNN. The main properties of the CCWNN are its capacity to receive quantum inputs, the possibility of implementing it in a quantum computer and its universal approximation theorem. In this comment, we show that the CCWNN is in fact equivalent to a classical neural network and that its universal approximation theorem can be derived from previous results in the literature.

A Weightless Neural Node Based on a Probabilistic Quantum Memory

The success of quantum computation is most commonly associated with speed up of classical algorithms, as the Shors factoring algorithm and the Grovers search algorithm. But it should also be related with exponential storage capacity such as the super dense coding. In this work we use a probabilistic quantum memory proposed by Trugen berger, where one can store

Synthesis of Probabilistic Automata in pRAM Neural Networks

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Superposition Based Learning Algorithm

patterns with only

Chaos in Quantum Weightless Neuron Node Dynamics

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