On Quantum Perceptron Learning via Quantum Search

• URL: http://arxiv.org/abs/2503.17308v1
• Date: Fri, 21 Mar 2025 16:57:30 GMT
• Title: On Quantum Perceptron Learning via Quantum Search
• Authors: Xiaoyu Sun, Mathieu Roget, Giuseppe Di Molfetta, Hachem Kadri,
• Abstract summary: We show that the probability of sampling from a normal distribution for a $D$-dimensional hyperplane perfectly classifies the data scales as $Omega(gammaD)$ instead of $Theta(gamma)$.<n>We show how quantum search algorithms can be leveraged to enhance the overall complexity of perceptron learning.
• Score: 5.172382862031037
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms based on Grover's search, were developed in arXiv:1602.04799 to accelerate training and improve statistical efficiency in perceptron learning. This paper points out and corrects a mistake in the proof of Theorem 2 in arXiv:1602.04799. Specifically, we show that the probability of sampling from a normal distribution for a $D$-dimensional hyperplane that perfectly classifies the data scales as $\Omega(\gamma^{D})$ instead of $\Theta({\gamma})$, where $\gamma$ is the margin. We then revisit two well-established linear programming algorithms -- the ellipsoid method and the cutting plane random walk algorithm -- in the context of perceptron learning, and show how quantum search algorithms can be leveraged to enhance the overall complexity. Specifically, both algorithms gain a sub-linear speed-up $O(\sqrt{N})$ in the number of data points $N$ as a result of Grover's algorithm and an additional $O(D^{1.5})$ speed-up is possible for cutting plane random walk algorithm employing quantum walk search.

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