  Of all novel computing methods, quantum computation (QC) is currently the
most likely to move from the realm of the unconventional into the conventional.
As a result some initial work has been done on applications of QC outside of
science: for example music. The small amount of arts research done in hardware
or with actual physical systems has not utilized any of the advantages of
quantum computation (QC): the main advantage being the potential speed increase
of quantum algorithms. This paper introduces a way of utilizing Grover's
algorithm - which has been shown to provide a quadratic speed-up over its
classical equivalent - in algorithmic rule-based music composition. The system
introduced - qgMuse - is simple but scalable. Example melodies are composed
using qgMuse using the ibmqx4 quantum hardware. The paper concludes with
discussion on how such an approach can grow with the improvement of quantum
computer hardware and software.
