QLunch: Emil Mærsk Pedersen

Speaker: Emil Mærsk Pedersen

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

Abstract: The adiabatic theorem states that if a system is prepared in an eigenstate of a Hamiltonian, which is changed infinitely slowly, it will finish in the corresponding eigenstate of the final Hamiltonian. If we pick the initial Hamiltonian with an initial eigenstate that is easy to prepare, we can thus prepare the corresponding eigenstate of some other complex Hamiltonian by slowly interpolating the Hamiltonian from one to the other. At finite speed there will be an error, but in practice the errors can often be made small, establishing adiabatic passage as a powerful protocol for the preparation of Hamiltonian eigenstates. A host of different methods have been explored to minimize the errors, including changing the Hamiltonian slowly where the gap is smaller, varying the Hamiltonian along a favorable path through phase space, adding terms to the Hamiltonian to counter the non-adiabaticity, or full optimal control.

In this talk I will discuss a different approach to reducing the error by setting the derivatives of the Hamiltonian to zero at the beginning and end of adiabatic passage. This improves the error scaling from linear to quadratic in the speed of adiabatic passage. Setting higher order derivatives to zero at the beginning and end as well improves the error scaling even further. This phenomenon has been known since early on in the study of adiabatic passage but has previously not been investigated or used much in practice. I will present numerical results for the Ising model and Rydberg atom chains demonstrating how “vanishing boundary derivatives” can be used to advantage and combined with other techniques.

This talk is based on work in progress with Freek Witteveen, Klaus Mølmer and Matthias Christandl.