Single-cell RNA sequencing (scRNA-seq) data simulation is limited by classical methods that rely on linear correlations, failing to capture the intrinsic, nonlinear dependencies. No existing simulator jointly models gene-gene and cell-cell interactions. We introduce qSimCells, a novel quantum computing-based simulator that employs entanglement to model intra- and inter-cellular interactions, generating realistic single-cell transcriptomes with cellular heterogeneity. The core innovation is a quantum kernel that uses a parameterized quantum circuit with CNOT gates to encode complex, nonlinear gene regulatory network (GRN) as well as cell-cell communication topologies with explicit causal directionality. The resulting synthetic data exhibits non-classical dependencies: standard correlation-based analyses (Pearson and Spearman) fail to recover the programmed causal pathways and instead report spurious associations driven by high baseline gene-expression probabilities. Furthermore, applying cell-cell communication detection to the simulated data validates the true mechanistic links, revealing a robust, up to 75-fold relative increase in inferred communication probability only when quantum entanglement is active. These results demonstrate that the quantum kernel is essential for producing high-fidelity ground-truth datasets and highlight the need for advanced inference techniques to capture the complex, non-classical dependencies inherent in gene regulation.