The Harris Hawks Optimization (HHO) algorithm has shown strong performance on a variety of optimization tasks but often suffers from limited diversity and premature convergence in high-dependency landscapes. This paper proposes a Quantum-Enhanced HHO (QE-HHO) algorithm that integrates a quantum-inspired entanglement mechanism to promote structured interactions among candidate solutions and preserve population diversity. A complementary quantum-inspired local search further accelerates convergence by refining promising regions. The method is evaluated on the CEC 2017 benchmark suite across 10-, 30-, 50-, and 100-dimensional instances. Results demonstrate that QE-HHO consistently achieves competitive or superior performance against conventional (HHO, PSO, DE) and quantum-based optimizers, particularly on multimodal and epistatic functions. While EBOwithCMAR performs best on specific benchmarks, QE-HHO offers a balanced trade-off between solution quality and search stability. These findings position QE-HHO as a promising direction for hybrid quantum-classical metaheuristics.