  This work studies pulse based variational quantum algorithms (VQAs), which
are designed to determine the ground state of a quantum mechanical system by
combining classical and quantum hardware. In contrast to more standard gate
based methods, pulse based methods aim to directly optimize the laser pulses
interacting with the qubits, instead of using some parametrized gate based
circuit. Using the mathematical formalism of optimal control, these laser
pulses are optimized. This method has been used in quantum computing to
optimize pulses for quantum gate implementations, but has only recently been
proposed for full optimization in VQAs. Pulse based methods have several
advantages over gate based methods such as faster state preparation, simpler
implementation and more freedom in moving through the state space. Based on
these ideas, we present the development of a novel adjoint based variational
method. This method can be tailored towards and applied in neutral atom quantum
computers. This method of pulse based variational quantum optimal control is
able to approximate molecular ground states of simple molecules up to chemical
accuracy and is able to compete with the gate based variational quantum
eigensolver in terms of total number of quantum evaluations. The total
evolution time $T$ and the form of the control Hamiltonian $H_c$ are important
factors in the convergence behavior to the ground state energy, both having
influence on the quantum speed limit and the controllability of the system.
