Quantum Perceptron Models

TL;DR

This paper introduces quantum algorithms that enhance perceptron learning by reducing computational steps and improving mistake bounds using quantum amplitude amplification, offering significant theoretical advantages over classical methods.

Contribution

The paper develops two novel quantum algorithms for perceptron learning that outperform classical algorithms in efficiency and mistake bounds.

Findings

Quantum algorithms determine separating hyperplanes in O(√N) steps.

Mistake bounds are improved from O(1/γ²) to O(1/√γ) using quantum techniques.

Quantum amplitude amplification enhances perceptron model performance.

Abstract

We demonstrate how quantum computation can provide non-trivial improvements in the computational and statistical complexity of the perceptron model. We develop two quantum algorithms for perceptron learning. The first algorithm exploits quantum information processing to determine a separating hyperplane using a number of steps sublinear in the number of data points $N$, namely $O(\sqrt{N})$. The second algorithm illustrates how the classical mistake bound of $O(\frac{1}{\gamma^2})$ can be further improved to $O(\frac{1}{\sqrt{\gamma}})$ through quantum means, where $\gamma$ denotes the margin. Such improvements are achieved through the application of quantum amplitude amplification to the version space interpretation of the perceptron model.