The realization of quantum complex-valued backpropagation neural network in pattern recognition problem

Abstract

This paper presents the approach of the quantum complex-valued backpropagation neural network or QCBPN. The challenge of our research is the expected results fiom the development of the quantum neural network using complex-valued backpropagation learning algorithm to solve classification problems. The concept of QCBPN emerged fiom the quantum circuit neural network research and the complex-valued backpropagation algorithm. We found that complex value and the quantum states share some natural representation suitable for the parallel computation. The quantum circuit neural network provides a qubit-like neuron model based on quantum mechanics with quantum backpropagationlearning rule, while the complex-valued backpropagation algorithm modifies standard backpropagation algorithm to learn complex number pattem in a natural way. The quantum complex-valued neuron model and the QCBPN learning algorithm are described. Finally, the realization of the QCBPN is exploited with a simple pattem recognition problem.

A quantum-inspired hybrid methodology for financial time series prediction

“…The QuMLP differs from classical MLP in the sense that its neurons uses quantum mechanics concepts. Kouda et al [25] and Mitr panont and Srisuphab [23], presented a QuBit MultiLayer Perceptron (QuMLP) in the attempt to adjust the relative phase information of neurons quantum states, where all information that flows through the Qubit Neuron is complex encoded.…”

“…The Qubit MultiLayer Perceptron (QuMLP) used in this work is proposed by [23] and [25]. The QuMLP uses the Complex Back-Propagation (CBP) [28] to learn the relative phase information of neurons quantum states.…”

“…Quantum Ar tificial Neural Networks (QANN) represent a new paradigm based on classical neural computation and quantum comput ing [21]. Quantum-inspired computing [22] have been widely used to develop several quantum-inspired neural networks models (which is the branch of study characterized by some quantum mechanics concepts and it is performed into digital computers) like the Qubit Neural Networks Models [21], [23]- [26], showing its superior performance when compared to classical ANNs [3].…”

“…It is inspired on Takens Theorem [27] and consists of a hybrid model composed of a Qubit MultiLayer Percep tron (QuMLP) [23] with a Quantum-Inspired Evolutionary Algorithm (QIEA) [12], which searches for the best time lags able to optimally represent the time series generator phenomenon, as well as to evolve the complete QuMLP architecture and parameters. Each individual of the QIEA population is trained and adjusted by the Complex Back Propagation (CBP) [28] algorithm to further improve the QuMLP parameters supplied by the QIEA.…”

Controller Application of a Multi-Layer Quantum Neural Network with Qubit Neurons

“…The qubit state |ψ maintains a coherent superposition of states: |ψ = a |0 + b |1 , where a and b are complex numbers called the probability amplitudes that satisfy |a| 2 + |b| 2 = 1. A multi-layer quantum neural network that utilizes qubit neurons as an information processing unit was proposed (10), (11) , where the qubit neuron model is one in which the neuron states are connected to the quantum states and the transitions between neuron states are based on operations derived from quantum logic gates. In the qubit neuron model, the neural state of firing or non-firing corresponds to the qubit state of |1 or |0 , respectively, and the state of an arbitrary neuron is a coherent superposition of the two.…”