Variational Quantum Circuits (VQCs) have emerged as a cornerstone
of hybrid quantum–classical algorithms designed to harness the
computational potential of near-term quantum devices. By
combining parameterized quantum gates with classical optimization,
VQCs provide a flexible framework for tackling machine learning,
chemistry, and optimization problems intractable for classical
methods. This review comprehensively overviews VQC design
principles, ansatz structures, optimization strategies, and real-world
applications. Furthermore, we discuss fundamental challenges such
as barren plateaus, the expressibility–trainability trade-off, and
current noisy intermediate-scale quantum (NISQ) hardware
limitations. Finally, we highlight emerging directions that could
enable scalable, noise-resilient, and physically interpretable
variational quantum models for future quantum computing
applications.