Few of the known quantum algorithms can be reliably executed on a quantum computer. Therefore, as an extension, we propose a Parallel Quantum Hough transform (PQHT) algorithm that we execute on a quantum computer. We give its implementation and discuss the results obtained. The PQHT algorithm is conceptually divided into a parallel rotation stage consisting of a set of connected programmable $\texttt{RZ}$ rotation gates, with adjustable node connections of coincidence detectors realized with quantum logic gates. The modules were developed using IBM Quantum Composer and tested using the IBM QASM simulator. Finally, the modules were programmed using the Python package Qiskit and the jobs were sent to distributed IBM Q System One quantum computers. The successful run results on Fraunhofer Q System One in Ehningen will be presented as a proof of concept for the PQHT algorithm.