Getting the Most Out of Local Counterdiabatic Control

Counterdiabatic driving has been demonstrated to aid in the preparation of quantum states across a wide variety of physical systems. However, even in the well-controlled environment of modern quantum simulators, only local interaction terms are accessible. In virtually every many-particle setting, local control is insufficient for exact counterdiabatic driving. Previous work has demonstrated how one can obtain a local (approximate) counterdiabatic drive, if a continuous path of Hamiltonians is provided. In this work, we extend this by asking the following question: since the initial and final Hamiltonians determine the initial and target states, how can we schedule the intermediate Hamiltonian to get the best state preparation from a local drive? We answer this systematically by framing the control problem through a framework analogous to Lagrangian mechanics. Because the resulting equations are classical and do not require exact diagonalization, this approach can find improved control protocols for interacting systems, and those beyond one dimension.