Quantum Perceptron Models

02/15/2016

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by   Nathan Wiebe, et al.

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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(1/γ^2) can be further improved to O(1/√(γ)) 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.