The cacophony of urban sounds presents a significant challenge for smart city applications that rely on accurate acoustic scene analysis. Effectively analyzing these complex soundscapes, often characterized by overlapping sound sources, diverse acoustic events, and unpredictable noise levels, requires precise source separation. This task becomes more complicated when only limited training data is available. This paper introduces a novel Quantum-Inspired Genetic Algorithm (p-QIGA) for source separation, drawing inspiration from quantum information theory to enhance acoustic scene analysis in smart cities. By leveraging quantum superposition for efficient solution space exploration and entanglement to handle correlated sources, p-QIGA achieves robust separation even with limited data. These quantum-inspired concepts are integrated into a genetic algorithm framework to optimize source separation parameters. The effectiveness of our approach is demonstrated on two datasets: the TAU Urban Acoustic Scenes 2020 Mobile dataset, representing typical urban soundscapes, and the Silent Cities dataset, capturing quieter urban environments during the COVID-19 pandemic. Experimental results show that the p-QIGA achieves accuracy comparable to state-of-the-art methods while exhibiting superior resilience to noise and limited training data, achieving up to 8.2 dB signal-to-distortion ratio (SDR) in noisy environments and outperforming baseline methods by up to 2 dB with only 10% of the training data. This research highlights the potential of p-QIGA to advance acoustic signal processing in smart cities, particularly for noise pollution monitoring and acoustic surveillance.