Chapter 1 Quantum Neural Network 1.1 Introduction and context The field of artificial neural networks (ANN) draws inspiration from the functioning of the human brain and the way the brain processes information. An ANN is a directed graph with highly interconnected nodes called neurons. Each edge of the graph has a weight associated with it to model synaptic capacity. The training process involves updating the weights of the network so that the network learns to solve the problem. Neurons in the network work together to solve specific problems. The network can be trained to perform various tasks such as pattern recognition, data classification, function approximation, etc. ANNs are widely used in the fields of computer vision and speech recognition. 1.1.1 Architecture of an arti cial neural network 1.1.2 Backward propagation Learning is how we acquire knowledge about the world around us, and it is through this process of acquiring knowledge that the environment alters our behavioral responses. Similarly, in artificial neural networks, learning rules are used to change the behavior of the network in response to external stimuli (input). For multilayer feedforward networks, a commonly used algorithm for weight adjustment is the backpropagation algorithm. There is some mathematics involved in deriving the formula which can be referenced from [4]. The final form of the formula is similar to: wij = jyiWhere,wij is the weight between the neurons i; jj is the local gradient of the jth neuron, yi is the output of ithneuron1.2 Quantum Mechanics and ANNThere are computationally difficult problems, for example ...... middle of the paper ......, which are discussed in detail in [5].1.3.3 Training and performanceTraining the network can be done using the backpropagational algorithm. Due to the unavailability of quantum hardware, the network cannot be tested but we can simulate it on a classical computer. 1.4 Summary and discussion Provide a summary and discuss what you understand. summarize the main points and also mention if you found any difficult subtopics. Bibliography[1] A. Narayanan, T. Menneer, Information Sciences 128 (2000) 231-255[2][3] H. Everett, Relative state formulation of quantum mechanics, Reviews of Modern Physics 29 (1957) 454-462.[ 4] Satish Kumar, Neural Networks: A Classroom Approach[5] TSI Menneer, Quantum Arti cial Neural Networks, Ph.D. Thesis, Department of Computer Science, University of Exeter, Exeter, EX4 4PT, United Kingdom, 19987