Qubit Neural Network: Its Performance and Applications

Qubit Neural Network: Its Performance and Applications

Nobuyuki Matsui (University of Hyogo, Japan), Haruhiko Nishimura (University of Hyogo, Japan) and Teijiro Isokawa (University of Hyogo, Japan)
DOI: 10.4018/978-1-60566-214-5.ch013
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Abstract

Recently, quantum neural networks have been explored as one of the candidates for improving the computational efficiency of neural networks. In this chapter, after giving a brief review of quantum computing, the authors introduce our qubit neural network, which is a multi-layered neural network composed of quantum bit neurons. In this description, it is indispensable to use the complex-valued representation, which is based on the concept of quantum bit (qubit). By means of the simulations in solving the parity check problems as a bench mark examination, we show that the computational power of the qubit neural network is superior to that of the conventional complex-valued and real-valued neural networks. Furthermore, the authors explore its applications such as image processing and pattern recognition. Thus they clarify that this model outperforms the conventional neural networks.
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Introduction

Since Shor (1994) proposed a way of factorizing large integers in polynomial time by using a quantum computing algorithm, the study of quantum information science, including quantum communication, quantum cryptography, quantum computer and so on, has been intensified (Nielsen & Chuang,2000). Shor’s proposal has not only proved itself to be a milestone in quantum computing, but also created a novel research paradigm of neural computing, i.e., quantum neural computing (Kak, 1995). Since then, various quantum neural computing models have been proposed for the improvement of the computational ability of neural networks so as to expand their applications (Peruš, 1996, 2004; Behrman, Nash, Steck, Chandrashekar, & Skinner, 2000; Narayanan, & Menneer, 2000; Ezhov, Nifanova, & Ventura, 2000; Matsui, Takai, & Nishimura, 1998, 2000; Kouda, Matsui, & Nishimura, 2002, 2004; Kouda, Matsui, Nishimura, & Peper, 2005a, 2005b; Mori, Isokawa, Kouda, Matsui, & Nishimura, 2006; Rigui, Nan, & Qiulin, 2006). In this chapter, we introduce a qubit neural network model that is a complex-valued multi-layered neural network composed of quantum bit neurons. We also clarify its learning performance numerically through the benchmark simulations by comparing it to that of the conventional neural networks. The quantum bit (hereafter qubit) neuron model was one that we proposed for the first time, inspired by quantum computation and quantum circuit (see the reference, Matsui, Takai, & Nisimura,1998 in Japanese, 2000 in English) and we also proved that our qubit neural network model (hereafter Qubit NN) is more excellent in learning ability than the conventional real-valued neural network model through solving the image compression problem (Kouda, Matsui, & Nishimura, 2002) and the control problem of inverted pendulum (Kouda, Matsui, Nishimura, & Peper, 2005b). We indicated that these results could be ascribed to the effects of quantum superposition and probabilistic interpretation in the way of applying quantum computing to neural network, in addition to the complex number representation. In the formulation of our model, complex numbers play an essential role, as a qubit is based on the concept of quantum mechanics. Here, to clarify these quantum effects, we show the characteristic features of Qubit NN are superior to those of the old-fashioned conventional complex-valued and/or real-valued neural networks by means of the simulations in solving the parity check problems and the function identification problem as a bench mark examination (see, Kouda, Matsui, Nishimura, & Peper, 2005a). Lastly, we add to the results of the new application examples: the well-known iris data classification and the night vision image processing. Thus we conclude that Qubit NN model outperforms Classical NNs. Here, we call the conventional neural networks Classical NNs according to the traditional comparison: Classical physics versus Quantum physics.

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Editorial Advisory Board
Table of Contents
Foreword
Sven Buchholz
Acknowledgment
Tohru Nitta
Chapter 1
Masaki Kobayashi
Information geometry is one of the most effective tools to investigate stochastic learning models. In it, stochastic learning models are regarded as... Sample PDF
Complex-Valued Boltzmann Manifold
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Chapter 2
Takehiko Ogawa
Network inversion solves inverse problems to estimate cause from result using a multilayer neural network. The original network inversion has been... Sample PDF
Complex-Valued Neural Network and Inverse Problems
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Chapter 3
Boris Igelnik
This chapter describes the clustering ensemble method and the Kolmogorovs Spline Complex Network, in the context of adaptive dynamic modeling of... Sample PDF
Kolmogorovs Spline Complex Network and Adaptive Dynamic Modeling of Data
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Chapter 4
V. Srinivasa Chakravarthy
This chapter describes Complex Hopfield Neural Network (CHNN), a complex-variable version of the Hopfield neural network, which can exist in both... Sample PDF
A Complex-Valued Hopfield Neural Network: Dynamics and Applications
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Chapter 5
Mitsuo Yoshida, Takehiro Mori
Global stability analysis for complex-valued artificial recurrent neural networks seems to be one of yet-unchallenged topics in information science.... Sample PDF
Global Stability Analysis for Complex-Valued Recurrent Neural Networks and Its Application to Convex Optimization Problems
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Chapter 6
Yasuaki Kuroe
This chapter presents models of fully connected complex-valued neural networks which are complex-valued extension of Hopfield-type neural networks... Sample PDF
Models of Complex-Valued Hopfield-Type Neural Networks and Their Dynamics
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Chapter 7
Sheng Chen
The complex-valued radial basis function (RBF) network proposed by Chen et al. (1994) has found many applications for processing complex-valued... Sample PDF
Complex-Valued Symmetric Radial Basis Function Network for Beamforming
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Chapter 8
Rajoo Pandey
The equalization of digital communication channel is an important task in high speed data transmission techniques. The multipath channels cause the... Sample PDF
Complex-Valued Neural Networks for Equalization of Communication Channels
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Chapter 9
Cheolwoo You, Daesik Hong
In this chapter, the complex Backpropagation (BP) algorithm for the complex backpropagation neural networks (BPN) consisting of the suitable node... Sample PDF
Learning Algorithms for Complex-Valued Neural Networks in Communication Signal Processing and Adaptive Equalization as its Application
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Chapter 10
Donq-Liang Lee
New design methods for the complex-valued multistate Hopfield associative memories (CVHAMs) are presented. The author of this chapter shows that the... Sample PDF
Image Reconstruction by the Complex-Valued Neural Networks: Design by Using Generalized Projection Rule
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Chapter 11
Naoyuki Morita
The author proposes an automatic estimation method for nuclear magnetic resonance (NMR) spectra of the metabolites in the living body by magnetic... Sample PDF
A Method of Estimation for Magnetic Resonance Spectroscopy Using Complex-Valued Neural Networks
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Chapter 12
Michele Scarpiniti, Daniele Vigliano, Raffaele Parisi, Aurelio Uncini
This chapter aims at introducing an Independent Component Analysis (ICA) approach to the separation of linear and nonlinear mixtures in complex... Sample PDF
Flexible Blind Signal Separation in the Complex Domain
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Chapter 13
Nobuyuki Matsui, Haruhiko Nishimura, Teijiro Isokawa
Recently, quantum neural networks have been explored as one of the candidates for improving the computational efficiency of neural networks. In this... Sample PDF
Qubit Neural Network: Its Performance and Applications
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Chapter 14
Shigeo Sato, Mitsunaga Kinjo
The advantage of quantum mechanical dynamics in information processing has attracted much interest, and dedicated studies on quantum computation... Sample PDF
Neuromorphic Adiabatic Quantum Computation
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Chapter 15
G.G. Rigatos, S.G. Tzafestas
Neural computation based on principles of quantum mechanics can provide improved models of memory processes and brain functioning and is of primary... Sample PDF
Attractors and Energy Spectrum of Neural Structures Based on the Model of the Quantum Harmonic Oscillator
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Chapter 16
Teijiro Isokawa, Nobuyuki Matsui, Haruhiko Nishimura
Quaternions are a class of hypercomplex number systems, a four-dimensional extension of imaginary numbers, which are extensively used in various... Sample PDF
Quaternionic Neural Networks: Fundamental Properties and Applications
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About the Contributors