  Current quantum computers are small and error-prone systems for which the
term noisy intermediate-scale quantum (NISQ) has become established. Since
large scale, fault-tolerant quantum computers are not expected to be available
in the near future, the task of finding NISQ suitable algorithms has received a
lot of attention in recent years. The most prominent candidates in this context
are variational quantum algorithms. Due to their hybrid quantum-classical
architecture they require fewer qubits and quantum gates so that they can cope
with the limitations of NISQ computers. An important class of variational
quantum algorithms is the quantum circuit learning (QCL) framework. Consisting
of a data encoding and a trainable, parametrized layer, these schemes implement
a quantum model function that can be fitted to the problem at hand. For
instance, in combination with the parameter shift rule to compute derivatives,
they can be used to solve differential equations. QCL and related algorithms
have been widely studied in the literature. However, numerical experiments are
usually limited to simulators and results from real quantum computers are
scarce. In this paper we close this gap by executing QCL circuits on a
superconducting IBM quantum processor in conjunction with an analysis of the
hardware errors. We show that exemplary QCL circuits with up to three qubits
are executable on the IBM quantum computer. For this purpose, multiple
functions are learned and an exemplary differential equation is solved on the
quantum computer. Moreover, we present how the QCL framework can be used to
learn different quantum model functions in parallel, which can be applied to
solve coupled differential equations in an efficient way.
