| （英） |
Quantum neural networks (QNN) are one of the quantum-classical hybrid algorithms, which can be realized with the current Noisy Intermediate-Scale Quantum computers and may have the advantage of using quantum computers. However, one of the serious problems of QNN is that the loss of training is non-convex, and convergence to the global minimum is not guaranteed. A similar problem can be observed in classical NNs, where it is known that the learning process of classical NNs asymptotically approaches kernel regression in the region where the number of training parameters is excessively large.
In this study, we analyze the convergence of training loss in QNN in the over-parameterized regime, as in the classical case.
As a result, we found analytically that when the loss function and data encoding methods are well chosen, the training loss converges globally to the smallest eigenvalue of the data-dependent Hamiltonian.
We also verify the theory through numerical experiments. |