Quadratic quantum speedup for perceptron training

作者：Pengcheng Liao, Barry C. Sanders, Tim Byrnes · 发表于：Physical Review A · 年份：2024 · DOI：10.1103/physreva.110.062412 · 被引用次数：4 · 研究领域：Quantum Computing Algorithms and Architecture、Quantum Information and Cryptography、Quantum-Dot Cellular Automata

Perceptrons, which perform binary classification, are the fundamental building blocks of neural networks. Given a data set of size $N$ and margin $\ensuremath{\gamma}$ (how well the given data are separated), the query complexity of the best-known quantum training algorithm scales as either $(\sqrt{N}/{\ensuremath{\gamma}}^{2})log(1/{\ensuremath{\gamma}}^{2})$ or $N/\sqrt{\ensuremath{\gamma}}$, which is achieved by a hybrid of classical and quantum search. In this paper, we improve the version space quantum training method for perceptrons such that the query complexity of our algorithm scales as $\sqrt{N/\ensuremath{\gamma}}$. This is achieved by constructing an oracle for the perceptrons using quantum counting of the number of data elements that are correctly classified. Once such an oracle is constructed, bounded-error quantum search can be used to search over the hyperplane instances. The optimality of our algorithm is proven by reducing the evaluation of a two-level and-or tree (for which the query complexity lower bound is known) to a multicriterion search. Our quantum training algorithm can be generalized to train more complex machine learning models such as neural networks, which are built on a large number of perceptrons.