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Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE)

Chaotic time series prediction by qubit neural network with complex-valued representation

Taisei Ueguchi, Nobuyuki Matsui, Teijiro Isokawa

Published Sep 1, 2016• 10 citations
Publisher

Abstract

A qubit neural network (QNN) is a neural network that incorporates the quantum computing and representation. QNN is constructed from a set of qubit neuron model, of which internal state is a coherent superposition of qubit states. This paper evaluates the performance of QNN through a prediction of well-known Lorentz attractor, which produces chaotic time series by three dynamical systems. The experimental results show that QNN can predict time series more precisely, compared with conventional (real-valued) neural networks.

DOI
10.1109/sice.2016.7749232

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A qubit neural network (QNN) is a neural network that incorporates the quantum computing and representation. QNN is constructed from a set of qubit neuron model, of which internal state is a coherent superposition of qubit states. This paper evaluates the performance of QNN through a prediction of well-known Lorentz attractor, which produces chaotic time series by three dynamical systems. The experimental results show that QNN can predict time series more precisely, compared with conventional (real-valued) neural networks.
We propose a neural network model based on quantum information processing with quaternionic representation and operations, called Quaternionic Qubit Neural Network. The state of a neuron is represented by a point on the Bloch sphere with incorporating quaternionic representation. The operations for this neuron also follow the operations in quaternions. The proposed neural networks are evaluated through numerical experiments for predicting chaotic time series produced by a Lorentz system. They have better performances in predicting long-term series, as compared to conventional (real-valued) neural networks.
Time series forecasting is a critical problem with applications in various fields, such as finance, energy, and environmental science. While classical machine learning methods have shown significant progress in this domain, the advent of quantum machine learning introduces a new perspective to address the complexities of time series prediction. In this research, we propose a novel Quantum Neural Network (QNN) approach for time series forecasting, leveraging the unique capabilities of quantum computing to capture intricate temporal dependencies and exploit quantum parallelism. By encoding time series data into quantum states and designing quantum circuits for processing, the QNN aims to achieve improved predictive accuracy compared to classical neural networks. Through extensive experiments on diverse time series datasets, we demonstrate the potential of our QNN framework and discuss the future prospects of quantum-powered time series prediction in real-world applications.
Recent advancements in artificial neural networks have enabled impressive tasks on classical computers, but they demand significant computational resources. While quantum computing offers potential beyond classical systems, the advantages of quantum neural networks (QNNs) remain largely unexplored. In this work, we present and examine a quantum circuit (QC) that implements and aims to improve upon the classical echo-state network (ESN), a type of reservoir-based recurrent neural networks (RNNs), using quantum computers. Typically, ESNs consist of an extremely large reservoir that learns high-dimensional embeddings, enabling prediction of complex system trajectories. Quantum echo-state networks (QESNs) aim to reduce this need for prohibitively large reservoirs by leveraging the unique capabilities of quantum computers, potentially allowing for more efficient and higher performing time-series prediction algorithms. The proposed QESN can be implemented on any digital quantum computer implementing a universal gate set, and does not require any sort of stopping or re-initialization of the circuit, allowing continuous evolution of the quantum state over long time horizons. We conducted simulated QC experiments on the chaotic Lorenz system, both with noisy and noiseless models, to demonstrate the circuit's performance and its potential for execution on noisy intermediate-scale quantum (NISQ) computers.
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.
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.Request access from your librarian to read this chapter's full text.