Cardinality-constrained binary optimization, a crucial computational problem, has been tackled with a novel quantum algorithm based on Grover's search, achieving exponential improvements in solving quadratic objectives1. This breakthrough has significant implications for various fields, including machine learning, finance, and scientific computing, where such optimization problems are ubiquitous. The proposed approach leverages the structure of the feasible subspace, exploiting a natural promise on solution existence to enhance the algorithm's efficiency. By harnessing the power of quantum computing, researchers can now tackle complex optimization problems that were previously intractable or required an unfeasible amount of computational resources. The potential impact of this development is substantial, as it can lead to breakthroughs in fields that rely heavily on optimization, such as portfolio optimization in finance or feature selection in machine learning. This matters to practitioners because it challenges traditional assumptions about computational limits, potentially rendering certain cryptographic systems vulnerable to quantum-powered attacks.