March 11, 2024 | Chae-Yeun Park, Minhyeok Kang, and Joonsuk Huh
This paper introduces two novel parameter conditions that ensure the hardware-efficient ansatz (HEA) is free from barren plateaus for any circuit depth. Barren plateaus are flat regions in the cost function landscape that make training quantum circuits difficult. The first condition ensures that the HEA approximates a time-evolution operator generated by a local Hamiltonian, and it is proven that the gradient magnitudes are bounded below by a constant for both local and global observables. The second condition is based on the many-body localized (MBL) phase, where the HEA is shown to have large gradient components for local observables. By initializing the parameters of the HEA using these conditions, the paper demonstrates improved performance in solving many-body Hamiltonians. The results show that barren plateaus are not an issue when initial parameters are smartly chosen, and other factors, such as local minima or the expressivity of the circuit, are more crucial. The paper also discusses the practical advantages of these parameter conditions, including their applicability to a wide range of quantum circuits and their potential to overcome the limitations of previous initialization methods. The findings are supported by numerical simulations and theoretical analysis, demonstrating that the proposed parameter conditions lead to better convergence and performance in solving quantum many-body Hamiltonians.This paper introduces two novel parameter conditions that ensure the hardware-efficient ansatz (HEA) is free from barren plateaus for any circuit depth. Barren plateaus are flat regions in the cost function landscape that make training quantum circuits difficult. The first condition ensures that the HEA approximates a time-evolution operator generated by a local Hamiltonian, and it is proven that the gradient magnitudes are bounded below by a constant for both local and global observables. The second condition is based on the many-body localized (MBL) phase, where the HEA is shown to have large gradient components for local observables. By initializing the parameters of the HEA using these conditions, the paper demonstrates improved performance in solving many-body Hamiltonians. The results show that barren plateaus are not an issue when initial parameters are smartly chosen, and other factors, such as local minima or the expressivity of the circuit, are more crucial. The paper also discusses the practical advantages of these parameter conditions, including their applicability to a wide range of quantum circuits and their potential to overcome the limitations of previous initialization methods. The findings are supported by numerical simulations and theoretical analysis, demonstrating that the proposed parameter conditions lead to better convergence and performance in solving quantum many-body Hamiltonians.