Quantum State Driving along Arbitrary Trajectories

TL;DR

This paper develops a method to determine the minimal time-dependent Hamiltonian needed to steer quantum states along arbitrary paths, extending to mixed states and analyzing the role of Berry phase in the process.

Contribution

It introduces a novel solution for quantum state driving along arbitrary trajectories, including mixed states, and compares it with counterdiabatic driving, highlighting the Berry phase involvement.

Findings

Derived minimal time Hamiltonian for pure states

Extended the solution to mixed states and complex trajectories

Compared with counterdiabatic driving, emphasizing Berry phase role

Abstract

Starting with the quantum brachistochrone problem of the infinitesimal form, we solve the minimal time and corresponding time-dependent Hamiltonian to drive a pure quantum state with limited resources along arbitrary pre-assigned trajectories. It is also shown that out of all possible trajectories, with limited resources, which are physically accessible and which are not. The solution is then generalized to the mixed quantum state cases, and applied to trajectories parameterized by single or multiple parameters with discrete or continuous spectrum. We then compare the solution to that of the counterdiabatic driving, and show how the Berry phase is directly involved in both driving processes.