  State-of-the-art noisy digital quantum computers can only execute short-depth
quantum circuits. Variational algorithms are a promising route to unlock the
potential of noisy quantum computers since the depth of the corresponding
circuits can be kept well below hardware-imposed limits. Typically, the
variational parameters correspond to virtual $R_Z$ gate angles, implemented by
phase changes of calibrated pulses. By encoding the variational parameters
directly as hardware pulse amplitudes and durations we succeed in further
shortening the pulse schedule and overall circuit duration. This decreases the
impact of qubit decoherence and gate noise. As a demonstration, we apply our
pulse-based variational algorithm to the calculation of the ground state of
different hydrogen-based molecules (H$_2$, H$_3$ and H$_4$) using IBM
cross-resonance-based hardware. We observe a reduction in schedule duration of
up to $5\times$ compared to CNOT-based Ans\"atze, while also reducing the
measured energy. In particular, we observe a sizable improvement of the minimal
energy configuration of H$_3$ compared to a CNOT-based variational form.
Finally, we discuss possible future developments including error mitigation
schemes and schedule optimizations, which will enable further improvements of
our approach paving the way towards the simulation of larger systems on noisy
quantum devices.
