  In conventional variational quantum eigensolvers (VQEs), trial states are
prepared by applying series of parameterized gates to a reference state, with
the gate parameters being varied to minimize the energy of the target system.
Recognizing that the gates are intermediates which are ultimately compiled into
a set of control pulses to be applied to each qubit in the lab, the recently
proposed ctrl-VQE algorithm takes the amplitudes, frequencies, and phases of
the pulse as the variational parameters used to minimize the molecular energy.
In this work, we explore how all three degrees of freedom interrelate with one
another. To this end, we consider several distinct strategies to parameterize
the control pulses, assessing each one through numerical simulations of a
transmon-like device. For each parameterization, we contrast the pulse duration
required to prepare a good ansatz, and the difficulty to optimize that ansatz
from a well-defined initial state. We deduce several guiding heuristics to
implement practical ctrl-VQE in hardware, which we anticipate will generalize
for generic device architectures.
