Intelligent traffic signal control has become a central research topic in urban mobility, aiming to reduce congestion and improve operational efficiency under increasingly complex traffic conditions. Although classical evolutionary algorithms have shown strong performance in traffic signal optimization, the practical integration of quantum computing into evolutionary processes remains largely unexplored, particularly under realistic microscopic traffic simulation. This paper presents a novel quantum genetic evolutionary approach for traffic signal timing optimization, implemented in a real signalized roundabout in Vitoria-Gasteiz, Spain, using the Simulation of Urban Mobility. The proposed method combines a classical GA for global exploration with a Grover-inspired quantum module embedded directly within the evolutionary cycle. Unlike conventional hybrid schemes in which quantum routines are treated as external solvers or purely simulated components, the proposed quantum GA is executed on real IBM Quantum hardware under NISQ conditions. Comparative experiments against fixed time control and a purely classical GA demonstrate substantial reductions in delay and improved convergence stability.