In intercity expressway traffic, a driver frequently makes decisions to adjust driving behavior according to time, location and traffic conditions, which further affects when and where the driver will leave away from the expressway traffic. Spontaneous exit choices by drivers are hard to observe and thus it is a challenge to model intercity expressway traffic sufficiently. In this paper, we developed a Spontaneous Quantum Traffic Model (SQTM), which models the stochastic traffic fluctuation caused by spontaneous exit choices and the residual regularity fluctuation with Quantum Walk and Autoregressive Moving Average model (ARMA), respectively. SQTM considers the spontaneous exit choice of a driver as a quantum stochastic process with a dynamical probability function varies according to time, location and traffic conditions. A quantum walk is applied to update the probability function, which simulates when and where a driver will leave the traffic affected by spontaneous exit choices. We validate our model with hourly traffic data from 7 exits from the Nanjing-Changzhou expressway in Eastern China. For the 7 exits, the coefficients of determination of SQTM ranged from 0.5 to 0.85. Compared with classical random walk and ARMA model, the coefficients of determination were increased by 21.28% to 104.98%, and relative mean square error decreased by 11.61% to 32.92%. We conclude that SQTM provides new potential for modeling traffic dynamics with consideration of unobservable spontaneous driver's decision-making.