Quantum Perceptron Models
This work addresses efficiency challenges in machine learning for researchers and practitioners by providing quantum-enhanced algorithms, though it is incremental as it builds on existing quantum techniques applied to a classical model.
The paper tackled the problem of improving the computational and statistical complexity of perceptron learning by developing quantum algorithms that achieve sublinear steps in data points and improved mistake bounds, with concrete improvements such as O(√N) steps and O(1/√γ) mistake bound.
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 $O(\frac{1}{γ^2})$ can be further improved to $O(\frac{1}{\sqrtγ})$ 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.