Berry phase estimation in gate-based adiabatic quantum simulation

Gate-based quantum computers can in principle simulate the adiabatic dynamics of a large class of Hamiltonians. Here, we consider the cyclic adiabatic evolution of a parameter in the Hamiltonian. We propose a quantum algorithm to estimate the Berry phase and use it to classify the topological order of both single-particle and interacting models, highlighting the differences between the two. This algorithm is extensible to an interacting topological system. Our results evidence the potential of near-term quantum hardware for the topological classification of quantum matter.B.M. and J.F.R. acknowledge the FCT Functionalized Graphene for Quantum Technologies project (PTDC/FIS-NAN/4662/2014). G.C. acknowledges support from Fundação para a Ciência e Tecnologia (FCT) Ph.D. Scholarship No. SFRH/BD/138806/2018