Quantum Perceptron Models

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.