Journal of Innovative Science

Abstract: Combinatorial optimization and large-scale data analytics present NP-hard computational challenges, where quantum algorithms promise potential exponential speedups. However, the practical realization of such advantage on Noisy Intermediate-Scale Quantum (NISQ) hardware remains uncertain. This systematic review synthesizes relevant literature to critically evaluate the empirical feasibility and scaling limitations of leading quantum algorithms. The analysis reveals that Variational Quantum Algorithms (VQAs) face persistent reliability challenges such as inconsistent optimality gaps and systemic failures to produce feasible solutions for constrained problems. The principal barrier to VQA scalability is the Measurement Imprecision Wall, where stochastic noise accumulation drives the required measurement shots to scale exponentially with system size, creating a resource deadlock that undermines quantum advantage for large problem instances. For data-centric algorithms, the exponential speedup of Quantum Linear Systems Problem (QLSP) solvers, such as HHL, is largely theoretical for arbitrary classical data due to the Encoding Bottleneck, which requires O(N) runtime for input state preparation. In contrast, Quantum Kernel Methods (QKM) exhibit superior empirical performance and efficient resource scaling, representing the most promising near-term pathway. Achieving practical quantum advantage therefore depends on noise-aware algorithmic design and effective solutions to the classical data ingestion challenge.