<p>Variational quantum algorithms (VQAs) are constrained by a trade-off: deeper circuits can cover a larger reachable quantum states but suffer from barren plateaus, while shallow circuits remain trainable yet can have insufficient reachability to the target state. Here, we propose a general framework to address this challenge by enhancing the VQA performance with a designed input state constructed using a linear combination technique. This approach modifies the set of states reachable by the original circuit, enhancing accuracy while preserving efficiency. We provide a rigorous proof that such framework increases the performance of any given VQA ansatz, and demonstrate its broad applicability across different ansatz families. In ground state preparation for representative quantum many-body models, it achieves consistently higher accuracy than standard methods at the same gate budget. These results highlight input-state design as a powerful complement to circuit design for improving reachability of the target state within a fixed ansatz.</p>