We experimentally investigate the viability of a variational quantum gate optimization
protocol informed by the underlying physical Hamiltonian of fixed-frequency transmon
qubits. Through the successful experimental optimization of two and three qubit quan-
tum gates the utility of the scheme for obtaining gates based on static effective Hamilto-
nians is demonstrated. The limits of such a strategy are investigated through the opti-
mization of a time-dependent, Floquet-engineered gate, however parameter drift is iden-
tified as a key limiting factor preventing the implementation of such a scheme which the
variational optimization protocol is unable to overcome.