Radial basis function (RBF) network is a simple but useful neural network model that contains wide applications in machine learning. The training of an RBF network reduces to solve a linear system, which is time consuming classically. Based on the HHL algorithm, we propose two quantum algorithms to train RBF networks. To apply the HHL algorithm, we choose using the Hamiltonian simulation algorithm proposed in [P. Rebentrost, A. Steﬀens, I. Marvian and S. Lloyd, Phys. Rev. A 97, 012327, 2018]. However, to use this result, an oracle to query the entries of the matrix of the network should be constructed. We apply the amplitude estimation technique to build this oracle. The ﬁnal results indicate that if the centers of the RBF network are the training samples, then the quantum computer achieves exponential speedup in the number and the dimension of training samples over the classical computer; if the centers are determined by the K-means algorithm, then the quantum computer achieves quadratic speedup in the number of samples and exponential speedup in the dimension of samples.
|Number of pages||17|
|Journal||Quantum Information and Computation|
|Publication status||Published - 30 Jun 2019|
- quantum algorithm
- quantum machine learning
- radial basis function network