Parametrization and optimizability of pulse-level variational quantum eigensolvers
Kyle Sherbert, Hisham Amer, Sophia E. Economou, Edwin Barnes, Nicholas J. Mayhall · Physical Review Applied · 2025
In conventional variational quantum eigensolvers (VQEs), trial states are prepared by applying series of parametrized 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 3 degrees of freedom interrelate with one another. To this end, we consider several distinct strategies to parametrize the control pulses, assessing each one through numerical simulations of a transmonlike device. For each parametrization, 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.