Predictive supremacy of informationally-restricted quantum perceptron

TL;DR

This paper introduces a quantum perceptron model with informational restrictions, demonstrating its universal predictive advantage over classical perceptrons for binary input functions under the same resources.

Contribution

It proposes a new quantum perceptron model with input restrictions and proves its universal superiority over classical perceptrons in predictive tasks.

Findings

Quantum IMP predicts better than classical IMP under the same resources.

The quantum advantage is universal for all non-trivial binary functions.

Quantum perceptrons can outperform classical ones with identical learning and resources.

Abstract

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.