Avoiding The Barren Plateau in the Variational Quantum Circuits With Bayesian Learning

 In the era of Noisy Intermediate scale quantum (NISQ) hardware, due to a limited number of qubits and hardware noise, hybrid classical-quantum algorithms are promising strategies for practical applications. Hybrid algorithms are based on variational quantum circuits (VQC), which their flexibility to tune the gates' parameters provide the compelling properties to be robust and adaptive to hardware limitations while giving access to solve a class of problems. However, training the VQCs over the parameters landscape requires classical optimization, which can be a classically hard task. The Effect of a barren plateau and localization of local minima of Hamiltonian, far from the global minima make the regular optimization, are two of the challenges that make regular gradient methods ineffective as the number of qubits increases.  In this work, we introduce the Fast-Slow algorithm based on the Bayesian Learning method to mitigate the mentioned issues.