The simulation of two-phase displacement in porous media, described by the hyperbolic Buckley-Leverett equation, poses a significant numerical challenge due to the formation of sharp saturation discontinuities [1]. Standard physics-informed neural networks often struggle to resolve these shocks without the introduction of unphysical artificial diffusion, as classical architectures exhibit a spectral bias that favors low-frequency approximations [2]. This work introduces a serial hybrid quantum-classical physics-informed neural network (HQPINN) designed to solve the Buckley-Leverett equation while maintaining sharp shock profiles through quantum inductive bias. By utilizing variational quantum circuits with angle encoding, spatiotemporal input features are mapped into a high-dimensional trigonometric space. This approach aligns the network’s expressive capacity with the periodic nature of wave propagation, allowing for the accurate capture of steep gradients without the blurring artifacts common in monotonic activation functions. A primary contribution of this work is the demonstration of unprecedented parameter efficiency. The HQPINN architecture achieves accuracy comparable to classical multilayer perceptrons while utilizing approximately 89% fewer trainable parameters. Specifically, effective simulations are performed with as few as 157–253 parameters, whereas classical baselines typically require over 3,000. The reduction in parameter space mitigates the risk of overfitting at collocation points and offers a scalable path toward solving high-dimensional reservoir modeling problems. Analysis of hybrid topologies, including data re-uploading and strongly entangling layers, confirms that periodic feature mapping provides a robust framework for hyperbolic conservation laws. This approach offers a computationally efficient alternative for complex fluid dynamics tasks where traditional numerical methods face the curse of dimensionality.