Searching for innovative approaches to detect single photons remains at the center of science and technology for decades. This paper proposes a zero transit-time, non-avalanche quantum capacitive photodetector to register single photons. In this detector, the absorption of a single photon changes the wave function of a single electron trapped in a quantum dot (QD), leading to a charge density redistribution nearby. This redistribution translates into a voltage signal through capacitive coupling between the QD and the measurement probe. Using InAs QD/AlAs barrier as a model system, the simulation shows that the output signal reaches ~4 mV per absorbed photon, promising for high-sensitivity, ps single-photon detection.