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.
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.