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(N−−√). The second algorithm illustrates how the classical mistake bound of O(1γ2) can be further improved to O(1γ√) through quantum means, where γ denotes the margin. Such improvements are achieved through the application of quantum amplitude amplification to the version space interpretation of the perceptron model.