# A Quantum Implementation Model for Artificial Neural Networks. (arXiv:1609.05884v2 [quant-ph] UPDATED)

The learning process for multi layered neural networks with many nodes makes

heavy demands on computational resources. In some neural network models, the

learning formulas, such as the Widrow-Hoff formula, do not change the

eigenvectors of the weight matrix while flatting the eigenvalues. In infinity,

this iterative formulas result in terms formed by the principal components of

the weight matrix: i.e., the eigenvectors corresponding to the non-zero

eigenvalues. In quantum computing, the phase estimation algorithm is known to

provide speed-ups over the conventional algorithms for the eigenvalue-related

problems. Combining the quantum amplitude amplification with the phase

estimation algorithm, a quantum implementation model for artificial neural

networks using the Widrow-Hoff learning rule is presented. The complexity of

the model is found to be linear in the size of the weight matrix. This provides

a quadratic improvement over the classical algorithms.