Adiabatic preparation of many-body quantum states: getting the beginning and ending right

We present numerical calculations, and simulations performed on a Rydberg atom quantum simulator, of the adiabatic evolution of many-body quantum systems around a quantum phase transition. We demonstrate that the end-to-end transfer error, for a given process duration and dissipative losses, can be suppressed by adopting smooth initial and final scheduling functions for the Hamiltonian. We consider a one-dimensional mixed-field Ising model, as well as a chain of Rydberg atoms, and compare numerical calculations and experimental results for the end-to-end transfer error with different schedule functions. We show, in particular, that if the time dependent Hamiltonian is n times differentiable with vanishing 1^st to n^th order derivatives in the beginning and in the end, the infidelity with respect to the final adiabatic eigenstate scales as 1/Tⁿ⁺¹ when evolving for time T.