Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach

TL;DR

This paper introduces an adaptive variational quantum algorithm for efficient and accurate Berry phase estimation during adiabatic evolution, demonstrated on Fermi-Hubbard chains with promising results for quantum simulation of topological and correlated systems.

Contribution

It develops a novel adaptive variational quantum approach for Berry phase calculation, optimizing circuit depth and accuracy for complex quantum systems.

Findings

Achieved precise Berry phase simulations with circuit depths up to 279 layers.

Demonstrated robustness of the method across various parameters.

Validated approach on both noninteracting and interacting Fermi-Hubbard chains.

Abstract

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.