Quantum Learning and Quantum Perceptrons

Ri‐Gui Zhou, Ling Qin, Nan Jiang

Shubhayan Sarkar

In the current world, the use of artificial intelligence is penetrating every aspect of human life. The basic element of any artificial intelligence is a digital neuron, called a perceptron, while its quantum analogue is called a quantum perceptron. Here, we introduce a model of perceptron called the informationally-restricted measurement-based perceptron (IMP), where each input is composed of two bits, while at the node, depending on a free input variable, the perceptron decides which bit to evaluate. Additionally, the states transmitted from the input to the node are restricted to a bit (qubit). We establish that under this restriction, the quantum IMP predicts better than a classical IMP. This means that under dimensional restriction of the transmitted states, when both the classical and quantum perceptrons learn the same, the quantum perceptron predicts better than the classical perceptron. For our purpose, we find specific learned values of the perceptron that can display the advantage of a quantum perceptron over its classical counterpart. Restricting to discrete binary inputs, we establish that the observed quantum advantage is universal, that is, for any non-trivial function implementable by both the quantum and classical IMP, one can always find a quantum implementation that outperforms the predictive capability of every classical one. This points to the fact that, given identical learning and resources, a quantum perceptron would predict better than any classical one.

Do Ngoc Diep

M. Andrecut, Mazhar Ali

The task of a classical perceptron is to classify two classes of patterns by generating a separation hyperplane. Here, we give a complete description of a quantum perceptron. The quantum algorithms for classification and learning are formulated in terms of unitary quantum gates operators. In the quantum case, the concept of separable or non-separable classes is irrelevant because the quantum perceptron can learn a superposition of patterns which are not separable by a hyperplane.

Andreas Wichert

The classical perceptron describes an algorithm for supervised learning that considers only linearly separable problems in which groups can be separated by a line or hyperplane. A quantum perceptron can be used as building block of larger systems, it can process an arbitrary number of input vectors in parallel. This chapter presents a simple example of the quantum perceptron for two-dimensional input. The classical perceptron describes an algorithm for supervised learning that considers only linearly separable problems in which groups can be separated by a line or hyperplane. A quantum Perceptron can be used as building block of larger systems, it can process an arbitrary number of input vectors in parallel.

M. V. Altaĭsky, N. E. Kaputkina