Quantum computation is increasingly presented as a potential response to difficult molecular-simulation, optimization, and machine-learning problems in drug discovery. However, the existence of computationally demanding pharmaceutical tasks does not establish that quantum methods can solve them more accurately, efficiently, or usefully than contemporary classical approaches. This horizon-scanning review evaluates which problem classes currently justify bounded quantum research programs and which remain dependent on unresolved hardware, algorithmic, benchmarking, data, or translational assumptions. The review applies an evidence-gated assessment that separates technical execution, benchmark performance, plausible computational utility, experimental confirmation, pharmaceutical decision impact, and routine readiness. The synthesis distinguishes near-term variational and hybrid approaches from fault-tolerant molecular simulation, quantum-assisted classical workflows, quantum machine learning, and optimization-oriented proposals. Current evidence supports the feasibility of selected small-system calculations, restricted molecular-property models, and hybrid workflow components, but it does not support routine pharmaceutical readiness for any broad drug-discovery problem class. The most defensible long-horizon opportunities concern chemically consequential electronic-structure and dynamical problems in which strong correlation limits classical approximations. Nearer-term value is more plausibly sought through tightly scoped hybrid experiments, application-structured benchmarking, and prospective evaluations that isolate the contribution of the quantum component. The article proposes a quantum readiness horizon map and a problem-level assessment framework rather than a universal technology maturity ranking. These conceptual contributions are intended to organize evidence and research priorities; they are not validated prediction tools. Readiness judgments remain conditional on continuing improvements in classical computation, hardware architecture, error control, resource estimation, data suitability, experimental validation, and integration into pharmaceutical decision workflows.