Neuromorphic Adiabatic Quantum Computation

Neuromorphic Adiabatic Quantum Computation

Shigeo Sato (Tohoku University, Japan) and Mitsunaga Kinjo (University of the Ryukus, Japan)
DOI: 10.4018/978-1-60566-214-5.ch014
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The advantage of quantum mechanical dynamics in information processing has attracted much interest, and dedicated studies on quantum computation algorithms indicate that a quantum computer has remarkable computational power in certain tasks. Quantum properties such as quantum superposition and quantum tunneling are worth studying because they may overcome the weakness of gradient descent method in classical neural networks. Also, the technique established for neural networks can be useful for developing a quantum algorithm. In this chapter, first the authors show the effectiveness of incorporating quantum dynamics and then propose neuromorphic adiabatic quantum computation algorithm based on the adiabatic change of Hamiltonian. The proposed method can be viewed as one of complex-valued neural networks because a qubit operates like a neuron. Next, the performance of the proposed algorithm is studied by applying it to a combinatorial optimization problem. Finally, they discuss the learning ability and hardware implementation.
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Real parallel computing is possible with a quantum computer which makes use of quantum states (Nielsen & Chuang, 2000). It is well known that a quantum computation algorithm for factorization discovered by Shor (1994) is faster than any classical algorithm. Also a quantum algorithm for database search in quantum computation steps instead of classical steps has been proposed by Grover (1996). These algorithms are often referred to as representative quantum algorithms utilizing features of quantum dynamics. A quantum algorithm not limited to a specific problem is needed for the development of a quantum computer from the practical viewpoint. Farhi et al. have proposed an adiabatic quantum computation (AQC) for solving the three-satisfiability (3-SAT) problem (Farhi, Goldstone, Gutmann, & Sipser, 2000). AQC can be applied to various problems including non-deterministic polynomial time problems (NP Problems) if one can obtain proper Hamiltonians. A few methods have been proposed such as the original AQC by Farhi et al. (Farhi & Gutmann, 1996; Farhi et al., 2000; Farhi et al., 2001), AQCs utilizing analogy to quantum circuits (Aharonov et al., 2004; Siu, 2005), and neuromorphic AQC(Sato, Kinjo, & Nakajima 2003; Kinjo, Sato, Nakamiya, & Nakajima, 2005).

Neural networks can be applied to such combinatorial optimization problems. The most popular approach is to utilize a Hopfield neural network (HNN) (Hopfield, 1982). However, it has been known that an HNN is often trapped in local minima, and an optimal solution is not obtained in this case. This is because the dynamics of the network is determined by the local features of the energy potential. On the other hand, if we can incorporate quantum dynamics into a neural network, such undesired behavior could be avoided.

Many studies inspired by quantum computation or quantum mechanics have been reported in order to improve the performance of neural networks related to associative memories, learning ability, and so on (Ventura & Martinez, 2000; Ezhov & Ventura, 2000; Matsui, Takai, & Nishimura 1998, 2000; Peruš, Bischof, Caulfield, & Loo, 2004; Mori, Isokawa, Kouda, Matsui, & Nishimura, 2006). Neural networks having quantum properties can be viewed as one of complex-valued neural networks since its neuron state is expressed in complex numbers. Good introductions on quantum neural networks (QNN) are found in some chapters of this book. Also the study described in this chapter is related to QNN, and the research purpose is to introduce methods used in conventional neural networks to quantum computation. We focus on AQC inspired from an HNN. First the advantages of quantum dynamics and quantum computation are described together with simple examples. Next, neuromorphic adiabatic quantum computation (NAQC) is proposed by relating AQC with HNN in order to incorporate neuromorphic techniques to quantum computation. The performance of NAQC is evaluated when it is applied to the N-queen problem, which is one of the NP problems. The effect of energy dissipation is studied for favorable state transitions to lower energy states resulting in performance enhancement. Then, a learning method in NAQC is studied for practical use. Finally, hardware implementation of the proposed method is discussed.

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Editorial Advisory Board
Table of Contents
Sven Buchholz
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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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