Exploring Clifford and Near-Clifford Initialization Strategies for Quantum Variational Optimization

Variational Quantum Algorithms are promising candidates for near-term quantum advantage, but face significant scalability challenges due to barren plateaus. In this work, we address the trainability of the Variational Quantum Eigensolver for combinatorial portfolio optimization by evaluating three warm-start initialization strategies: Clifford, Near-Clifford, and a Mixed approach. We compare these against a cold-start baseline initialized with the initial parameters close to zero across system sizes from N = 2 to N = 10. Our results show that while the uninformed cold start fails to converge for larger systems, all warm-start strategies achieve a 100% success rate and high initial-state fidelities. Crucially, we observe no clear difference in convergence behavior among the warm-start methods. Consequently, for this class of QUBO-based portfolio optimization problems, we identify the purely Clifford-based approach as the most efficient strategy; it consistently places the optimizer in a region from which the variational optimization converges successfully while remaining polynomially simulable on classical hardware during the quantum phase of the algorithm, indicating that the additional computational cost of non-Clifford resources offers negligible benefits for initialization in this specific context.