March 11, 2024 | Chae-Yeun Park, Minhyeok Kang, and Joonsuk Huh
This paper addresses the issue of barren plateaus in variational quantum circuits, which hinders their practical application. The authors propose two novel parameter conditions for the hardware-efficient ansatz (HEA) that prevent barren plateaus regardless of circuit depth. The first condition involves approximating the HEA with a time-evolution operator generated by a local Hamiltonian, ensuring constant gradient magnitudes for both local and global observables. The second condition relates the HEA to a many-body localized (MBL) phase, where the HEA has large gradient components for local observables. By initializing parameters using these conditions, the authors demonstrate improved performance in solving many-body Hamiltonians. The results suggest that barren plateaus are not a significant issue when initial parameters are chosen carefully, and other factors like local minima or circuit expressivity are more critical. The paper also includes numerical simulations and a study on solving quantum many-body Hamiltonians, showing that the proposed parameter initialization schemes outperform random initialization.This paper addresses the issue of barren plateaus in variational quantum circuits, which hinders their practical application. The authors propose two novel parameter conditions for the hardware-efficient ansatz (HEA) that prevent barren plateaus regardless of circuit depth. The first condition involves approximating the HEA with a time-evolution operator generated by a local Hamiltonian, ensuring constant gradient magnitudes for both local and global observables. The second condition relates the HEA to a many-body localized (MBL) phase, where the HEA has large gradient components for local observables. By initializing parameters using these conditions, the authors demonstrate improved performance in solving many-body Hamiltonians. The results suggest that barren plateaus are not a significant issue when initial parameters are chosen carefully, and other factors like local minima or circuit expressivity are more critical. The paper also includes numerical simulations and a study on solving quantum many-body Hamiltonians, showing that the proposed parameter initialization schemes outperform random initialization.