Simulation of a Variational Quantum Perceptron using Grover's Algorithm

Recently, there has been an increasing number of studies to combine the disciplines of quantum information and machine learning, and a variety of theories to merge these fields have consistently been put forward since machine learning is under pressure due to a lack of processing power of the increased amount of data in the world, and quantum computing offers these super computational capabilities. The combination of these two fields invariably leads to a massive interest in innovative information processing mechanisms that open up a new and improved range of solutions for various domains of applications, and the first concept was the research on quantum models of neural networks; it was essentially biologically inspired, in the hope of finding explanations for brain function within the framework of quantum theory [1]. In 2013, this combination got the name quantum machine learning by Lloyd et al. [2] as a definition of an area of research that explores the combination of quantum information and ML principles. However, the development of potential quantum machine learning algorithms has made some progress; several famous classical ML algorithms already have quantum analogs, such as the quantum support vector machine (QSVM), quantum k-means clustering, quantum Boltzmann machine (QBM), and the quantum perceptron (QP) which there have been some papers that mainly overview methods and algorithms of this model. Zhou et al. [3] developed a quantum perceptron approach based on the quantum phase capable of computing the XOR function using only one neuron, then Siomau et al. [4] introduced an autonomous quantum perceptron based on calculating a set of positive valued operators and valued measurements (POVM), after that Sagheer and Zidane [5] proposed a quantum perceptron based on Siomau method capable of constructing its own set of activation operators to be applied widely in both quantum and classical applications to overcome the linearity limitation of the classical perceptron In 2018, a multidimensional input quantum perceptron (MDIQP) was proposed by Yamamoto et al. [6]; their model had an arbitrary number of inputs with different synaptic weights, being able to form large quantum artificial neural networks (QANNs).