Deep Quantum Neural Networks are Gaussian Process

Understand

The overparameterization of variational quantum circuits, as a model of Quantum Neural Networks (QNN), not only improves their trainability but also serves as a method for evaluating the property of a given ansatz by investigating their kernel behavior in this regime.

• In this study, we shift our perspective from the traditional viewpoint of training in parameter space into function space by employing the Bayesian inference in the Reproducing Kernel Hilbert Space (RKHS).
• We observe the influence of initializing parameters using random Haar distribution results in the QNN behaving similarly to a Gaussian Process (QNN-GP) at wide width or, empirically, at a deep depth.
• This outcome aligns with the behaviors observed in classical neural networks under similar circumstances with Gaussian initialization.