Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach

We present an adaptive variational quantum algorithm to estimate the Berry phase accumulated by a nondegenerate ground state under cyclic, adiabatic evolution of a time-dependent Hamiltonian. Our method leverages cyclic adiabatic evolution of the Hamiltonian and employs adaptive variational quantum algorithms for state preparation and evolution, optimizing circuit efficiency while maintaining high accuracy. We benchmark our approach on dimerized Fermi-Hubbard chains with four sites, demonstrating precise Berry phase simulations in both noninteracting and interacting regimes. Our results show that circuit depths reach up to 106 layers for noninteracting systems and increase to 279 layers for interacting systems due to added complexity. Additionally, we demonstrate the robustness of our scheme across a wide range of parameters governing adiabatic evolution and variational algorithm. These findings highlight the potential of adaptive variational quantum algorithms for advancing quantum simulations of topological materials and computing geometric phases in strongly correlated systems.

💡 Research Summary

The paper introduces a novel quantum‑computing protocol for efficiently estimating the Berry phase accumulated by a non‑degenerate ground state undergoing a cyclic, adiabatic evolution of a time‑dependent Hamiltonian. The authors combine two complementary ideas: (i) cyclic adiabatic evolution, where a control parameter λ is varied slowly from 0 to 2π so that the system remains in the instantaneous ground state |G(λ)⟩, and (ii) an adaptive variational quantum dynamics simulation (AVQDS) that dynamically builds a compact variational ansatz while keeping the McLachlan distance L² below a prescribed threshold.

In the cyclic adiabatic framework the total phase after one loop separates into a dynamical contribution ϕ_D = ∫_0^T E_G