Quantum Neural Networks
This is the paper that I published and presented at the ICICSE-2018 (International Conference on Innovations in Computer Science & Engineering) in Guru Nanak Institutions, Hyderabad.
I. INTRODUCTION
Artificial Intelligence is a branch of Computer Science which deals with the simulation of intelligent behavior in computers. The question ‘Where does this intelligence come from?’ takes us to the concept of Machine Learning. It is the technology of using mathematical and logical algorithms to analyze data, learn it and make a prediction of something that is required. Various algorithms are used to train machines to parse data and more accurate and precise data results and prediction results can be achieved by using the concept of Deep Learning [3]. It is the most efficient way of implementing machine learning algorithms. Deep Learning consists of a technology, which is inspired by the way of biological working of the brain. Billions of Neurons are present in the human brain carrying out trillions of calculations and processing. Relation among the above terms is shown in fig.1

To implement this way of processing in computers, the new concept of Neural Networks came up. Neural Networks are also referred to as Artificial Neural Networks (ANN).
It is defined as a computing system made up of several simple, highly interconnected processing elements which process information by their dynamic state response to external inputs. There is a more advanced branch of Neural Networks called Quantum Neural Networks.
II. QUANTUM NEURAL NETWORKS
The neural network models which are based on the principles of quantum mechanics are called Quantum Neural Networks (QNNs). Neural Networks are inspired by the working of the brain and system of neurons; the coordination among them is replicated into computers.
This working system, which is also defined as a neural network model, consists of layers of neurons interconnected through certain weights that prioritize certain inputs over others. These layers of neurons include activation functions, one for each neuron, that determines its output.
The neural network models which are based on the principles of quantum mechanics are called Quantum Neural Networks (QNNs). As Neural Networks are inspired by the working of the brain and system of neurons; the coordination among them is replicated into computers.
This working system, which is also defined as a neural network model, consists of layers of neurons interconnected through certain weights that prioritize certain inputs over others. These layers of neurons include activation functions, one for each neuron, that determines its output.
A. The idea of Quantum Neural Networks — The Past
The 1st idea of Quantum Neural Computation was given by two scientists Ron Chrisley and Subhash Kak in late 1995. They started comparing the concept of neural activation function from artificial neural networks, with the quantum mechanical principle called Eigenvalue Equation. Limitations of the use of only-ANNs led to the deeper study of the functioning of the brain. Using this study, Ajit Narayan and Tammy Menneer proposed that the mixture[2] of photonics and neural networks would start a new branch called quantum neural networks. It was said that the perfection of superior quantum neural models would change the way of implementation of artificial neural networks in the field of Deep Learning.
B. Rise of Quantum Neural Networks — The Present
In today’s rapidly growing technology, it is no wonder in believing that one day, human life will be fully automated. But this era proved itself that it belongs to technologies like AI, ML, ANNs, QNNs, etc. Neural networks went one step ahead in utilizing the concepts of quantum physics to achieve greater results in a large number of applications.
Applications are being developed in such a way that mankind is going closer and closer to 100% correct prediction rates. Physicists today have developed a way of using ANNs to characterize the wave function of the quantum man-body system. These pair of physicists started themselves by observing that the system, which defeated the Go World champion recently, could have been modified in a way to simulate a man-body system. It was created using a simplified version of a neural network model, whose neurons would follow the ‘quantum wave function’[5] as their activation functions. This worked well in a brute-force approach and was successfully defined as a working Quantum Neural Network Model.
C. The era of Quantum Neural Networks — The Future
Researchers are amazed by the outcomes and predictions achieved by a simple quantum neural network model. So, this generation solemnly focuses on improving QNNs by shifting from artificial neural networks, which functions basically to pass information like neurons in the brain.
Google is now able to predict when a person will die with more than 75% accuracy rate. Let us assume that it may achieve 80–85% accurate prediction in 2–3 years with heavy research and training on neural networks. It would still take more powerful algorithms on neural networks based on the principles of quantum physics (QNNs) to achieve absolute accuracy of more than 90% [3] on this application.
There are many more fields of research today which require the use of QNNs to solve major problems of the world and make human life easier. So, Quantum Neural Networks would be more studied and experimented over Artificial Neural Networks.
III. MECHANISM OF QUANTUM NEURAL NETWORKS
A. The Basic Neural Network Model
Computers can build predictive models by learning the patterns in historical data. Neural networks are powered by small interconnected processing elements called nodes. Each node processes a small part of the task. A multi-layer perceptron is a highly used neural network model. [3]. The multi-layer perceptron consists of organized layers of nodes. The first and last layers are called the Input Layer and the Output layer respectively. Layers between these 2 layers are called hidden layers.
The independent variables are sent as input to the input layer. The nodes of the hidden layer take their inputs from the input layer, process it and pass it on to the nodes of the output layer. When a node receives data and variables from multiple nodes of the previous layer, these are multiplied by certain weights and added together with a small value called a bias. A function called activation function processes the results and leads the node as output. This process proceeds until data variables reach the output layer and confirm it as a prediction for the dependent variable.

The network then compares the prediction with the actual value of the dependent variable. If these do not match, it adjusts all the weights in the network and repeats the process. These iterations get repeated until the neural network produces accurate predictions for most of the observations. Once this is achieved, it is left with a neural network model that can be applied to a new set of data to provide predictions.
B. The Advanced Quantum Neural Computer
In the transport network, power network and the internet (shown in figure 2), the need to optimize these very complex networks is increasing. This optimization requirement is to solve the Combinatorial Optimization problem [5] (relating to the selection of a given number of elements from a larger number without regard to their arrangement). Such a problem requires huge amounts of computations and takes a long time on ordinary computers. At NTT basic research laboratories (Japanese Govt Organization), a computer-based on new principle which can solve combinatorial optimization problems in an instant has been created.
This computer consists of an optical fiber of 1 km long and several other devices. This is the computer called a Quantum Neural Network.
Its basic structure consists of just three main components.
1. An optical fiber
2. A special optical amplifier called the PSA (Phase-Sensitive Amplifier)
3. An electronic circuit called an FPGA (Field Programmable Gate Array)

The PSA receives pump light and uses its energy to amplify light. It efficiently amplifies light with phase 0 or π relative to the pump phase. The light with the same phase is 0 and the shifted phase is π. Pulses of pump lights are input into the PSA, which outputs Noise Optical Pulses varying randomly in phase from 0 to 2π. These random phases are generated intentionally. Using the measurement results of optical pulses, the FPGA creates a new pulse according to a theoretical model called ‘The Ising model’ and superimposes it on the original light.


As a result, the pulses affect each other to have either the same phase or the opposite phase (2π). The FPGA repeats this process each time the light pulse circles the loop. This leads to the effects of the PFA, each pulse gradually approaches either 0 or π. When it is determined to be either 0 or π, computation results are obtained.
C. Max Cut Problem using Quantum Neural Networks
This system can easily solve one type of combinatorial optimization problems, the max cut problem. Consider the case of dividing people into two groups. the mass cut problem is to avoid placing people who do not get along into the same group as much as possible. If the number of people is only 4 or 5, then it is easier to do it manually. But when the number of people increases, the number of incompatible combinations of people increases explosively. So, dividing them into compatible groups requires a huge amount of computation.
A quantum neural network is used to solve a huge example with 2000 people and 20,000 incompatible combinations. Each person is represented with a light pulse and the 2 groups as 0 and π. Then the incompatible relationships enter the FPGA and begin the computation which is already done. The time to complete the computation is only 5 thousand of a second (0.005 seconds).
The quantum neural network compares the huge number of combinations all at once and determines the grouping in just an instant. It can solve the social problems introduced its beginning and shows its strength for problems such as developing pharmaceuticals and image analysis. The quantum neural network for solving interactable problems using light. Figures 7 and 8 represent the solution of this problem given by this quantum neural computer and the output results.

IV. CONCLUSION
The computer that is built using the concept of quantum neural networks, as mentioned above, has a great demand to solve today’s complicated and time taking problems. On deeper studies, one day, QNNs will become older and give rise to more advanced neural network models for more amazing precise results. Marking these statements as pointers, this paper discusses Quantum Neural Networks, from its past to its scope in the future. It also explains the technical mechanism of systems builds having QNNs as their foundation. This paper can be used to explore the QNN computer built by the NTT — Japan. The arrival of QNNs from Artificial Intelligence is an exciting journey.
V. REFERENCES
- Quantum Computational Networks, 9 September 1989. Volume 425, Issue 1868
- Quantum Neural Network on Cloud, NTT Press Releases, 20th Nov 2017, The University of Tokyo.
- https://www.ibm.com/developerworks/library/cc-models-machine-earning/index.html
- https://www.hpcwire.com/2017/11/22/japan-unveils-first-quantum-computer-prototype/
- https://futurism.com/artificial-neural-networks-are-revealing-the-quantum-world/
- https://skymind.ai/wiki/neural-network
- http://pages.cs.wisc.edu/~bolo/shipyard/neural/local.html
- https://youtu.be/plcKVSld6ak
