Calculating nonadiabatic couplings and Berry's phase by variational quantum eigensolvers

The variational quantum eigensolver (VQE) is an algorithm to find eigenenergies and eigenstates of systems in chemistry many-body physics. VQE one the most promising applications near-term devices investigate such systems. Here we propose extension calculate nonadiabatic couplings molecules chemical Berry's phase Both quantities play important role understand properties a system beyond naive adiabatic picture, e.g., dynamics topological matter. We provide circuits classical post-processings phase. Specifically, show that evaluation reduces expectation values observables while also requires additional Hadamard test. Furthermore, simulate photodissociation lithium fluoride molecule using evaluated on real device. Our proposal widens applicability possibility study