  Galaxy morphology, a key tracer of the evolution of a galaxy's physical
structure, has motivated extensive research on machine learning techniques for
efficient and accurate galaxy classification. The emergence of quantum
computers has generated optimism about the potential for significantly
improving the accuracy of such classifications by leveraging the large
dimensionality of quantum Hilbert space. This paper presents a quantum-enhanced
support vector machine algorithm for classifying galaxies based on their
morphology. The algorithm requires the computation of a kernel matrix, a task
that is performed on a simulated quantum computer using a quantum circuit
conjectured to be intractable on classical computers. The result shows similar
performance between classical and quantum-enhanced support vector machine
algorithms. For a training size of $40$k, the receiver operating characteristic
curve for differentiating ellipticals and spirals has an under-curve area (ROC
AUC) of $0.946\pm 0.005$ for both classical and quantum-enhanced algorithms.
Additionally, we demonstrate for a small dataset that the performance of a
noise-mitigated quantum SVM algorithm on a quantum device is in agreement with
simulation. Finally, a necessary condition for achieving a potential quantum
advantage is presented. This investigation is among the very first applications
of quantum machine learning in astronomy and highlights their potential for
further application in this field.
