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International Journal of Wavelets Multiresolution and Information Processing

Quaternion quantum neurocomputing

Eduardo Jose Bayro-Corrochano, Samuel Solis-Gamboa

Published May 31, 2020• 6 citations
Publisher

Abstract

Since the introduction of quaternion by Hamilton in 1843, quaternions have been used in a lot of applications. One of the most interesting qualities is that we can use quaternions to carry out rotations and operate on other quaternions; this characteristic of the quaternions inspired us to investigate how the quantum states and quantum operator work in the field of quaternions and how we can use it to construct a quantum neural network. This new type of quantum neural network (QNN) is developed in the quaternion algebra framework that is isomorphic to the rotor algebra [Formula: see text] of the geometric algebra and is based on the so-called qubit neuron model. The quaternion quantum neural network (QQNN) is tested and shows robust performance.

DOI
10.1142/s0219691320400019

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Since the introduction of quaternion by Hamilton in 1843, quaternions have been used in a lot of applications. One of the most interesting qualities is that we can use quaternions to carry out rotations and operate on other quaternions; this characteristic of the quaternions inspired us to investigate how the quantum states and quantum operator work in the field of quaternions and how we can use it to construct a quantum neural network. This new type of quantum neural network (QNN) is developed in the quaternion algebra framework that is isomorphic to the rotor algebra [Formula: see text] of the geometric algebra and is based on the so-called qubit neuron model. The quaternion quantum neural network (QQNN) is tested and shows robust performance.
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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.
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The Neural Network is a well-known computational model that widely applied in machine learning (ML) inspired by human brains, which can perform the ML tasks including classification and feature extraction. Contemporarily it has been succeeded in all areas functioning as a powerful tool. Quantum computing is an emerging field based on quantum computers, which is a different calculation logic in the context of quantum dynamic theory providing an exponential computation power edge over traditional computers. Quantum Neural Network (QNN) is an intersection of the two areas, leveraging the advantage of quantum computing in the neural network, providing a strikingly powerful algorithm with promising potential. On this basis, this paper will demonstrate the state-of-art of QNN, which briefly explains the basic principle of QNN and an introduction of several typical QNN models. In addition, the current defects and drawbacks will also be discussed simultaneously. Overall, these results serve as a preliminary introduction to the topic, which shed light on guiding further exploration of quantum computing algorithms.
A hybrid model called thegeometric (Clifford) quanvolutional neural network(GQNN) that merges elements of geometric (Clifford) convolutional neural networks (GCNNs) and variational quantum circuits (VQCs) is presented. In this model, a randomized quantum convolution operation is applied to the input image, giving as a result four output channels, which are treated as a single entity (quaternion image) by the subsequent quaternion layers. This approach is extended to Clifford algebras by choosing the number of qubits of the quantum circuit according to the dimension of the Clifford algebra so that the resulting output channels are regarded as the components of a multivector image to be further processed by Clifford layers.
The goal of the artificial neural network is to create powerful artificial problem solving systems. The field of quantum computation applies ideas from quantum mechanics to the study of computation and has made interesting progress. Quantum Neural Network (QNN) is one of the new paradigms built upon the combination of classical neural computation and quantum computation. It is argued that the study of QNN may explain the brain functionality in a better way and create new systems for information processing including solving some classically intractable problems. In this paper we have given an introductory representation of quantum artificial neural network to show how it can be modelled on the basis of double-slit experiment. Also an attempt is made to show the quantum mechanical representation of a classical neuron to implement Hadamard transformation.