A hybrid quantum-inspired neural networks with sequence inputs
Panchi Li
n
, Hong Xiao, Fuhua Shang, Xifeng Tong, Xin Li, Maojun Cao
School of Computer and Information Technology, Northeast Petroleum University, Daqing, China
article info
Article history:
Received 28 May 2012
Received in revised form
21 January 2013
Accepted 25 January 2013
Communicated by G. Thimm
Available online 4 March 2013
Keywords:
Quantum computation
Quantum rotation gates
Controlled-Hadamard gates
Quantum neuron
Quantum neural networks
abstract
To enhance the performance of classical neural networks, a quantum-inspired neural networks model
based on the controlled-Hadamard gates is proposed. In this model, the inputs are discrete sequences
described by a matrix where the number of rows is equal to the number of input nodes, and the number
of columns is equal to the sequence length. This model includes three layers, in which the hidden layer
consists of quantum neurons, and the output layer consists of classical neurons. The quantum neuron
consists of the quantum rotation gates and the multi-qubits controlled-Hadamard gates. A learning
algorithm is presented in detail according to the basic principles of quantum computation. The
characteristics of input sequence can be effectively obtained from both breadth and depth. The
experimental results show that, when the number of input nodes is closer to the sequence length,
the proposed model is obviously superior to the BP neural networks.
& 2013 Elsevier B.V. All rights reserved.
1. Introduction
In many applications, the system input is a temporal pro-
cesses, such as the chemical reaction process and the stock
market volatility process [1,2]. Many neurophysiological experi-
ments indicate that the information processing character of the
biological nerve system mainly includes the following eight
aspects: the spatial aggregation, the multi-factor aggregation,
the temporal cumulative effect, the activation threshold charac-
teristic, self-adaptability, exciting and restraining characteristics,
delay characteristics, conduction and output characteristics [3].
From the definition of the M-P neuron model, classical ANN
preferably simulates voluminous biological neurons’ characteris-
tics such as the spatial weight aggregation, self-adaptability,
conduction and output, but it does not fully incorporate temporal
cumulative effect because the outputs of ANN depend only on the
inputs at the moment regardless of the prior moment. In the
process of practical information processing, the memory and
output of the biological nerve not only depend on the spatial
aggregation of multidimensional input information, but also
depend on the temporal cumulative effect.
Since Kak firstly proposed the concept of quantum-inspired
neural computation [4] in 1995, quantum neural networks (QNN)
have attracted a great attention by the international scholars
during the past decade, and a large number of novel techniques
have been studied for quantum computation and neural
networks. For example, Ref. [5] proposed the model of quantum
neural networks with multilevel hidden neurons based on the
superposition of quantum states in the quantum theory. In Ref.
[6], an attempt was made to reconcile the linear reversible
structure of quantum evolution with nonlinear irreversible
dynamics of neural networks. In 1998, a new neural networks
model with quantum circuit was developed for quantum compu-
tation, and was proven to exhibit a powerful learning capabil-
ity [7]. Matsui et al. developed a quantum neural networks model
using the single bit rotation gate and two-bit controlled-not gate.
They also investigated its performance in solving the four-bit
parity check and the function approximation problems [8].
Altaisky suggested that a quantum neural networks can be built
using the principles of quantum information processing [9]. In his
model, the input and output qubits in the QNN were implemen-
ted by optical modes with different polarization, the weights of
the QNN were implemented by optical beam splitters and phase
shifters. Ref. [10] proposed a completely different kind of net-
works from the mainstream works. In his model neurons are
states, connected by gates. In our previous work [11],we
proposed a quantum BP neural networks model with learning
algorithm based on the single-qubit rotation gates and two-qubit
controlled-not gates. Ref. [12] proposed a wave probabilities
resonance principle describing quantum entanglement, and
demonstrated the possible applications of the theory. Ref. [13]
presented models of quasi-non-ergodic probabilistic systems that
are defined through the theory of wave probabilistic functions,
and showed two illustrative examples of applications of intro-
duced theories and models. Ref. [14] proposed a weightless model
based on quantum circuit, it is not only quantum-inspired but it is
Contents lists available at SciVerse ScienceDirect
journal homepage: www.elsevier.com/locate/neucom
Neurocomputing
0925-2312/$ - see front matter & 2013 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.neucom.2013.01.029
n
Corresponding author. Tel.: þ86 459 6507708.
E-mail address: lipanchi@vip.sina.com (P. Li).
Neurocomputing 117 (2013) 81–90