Accelerating Two-Drug Combination Screening with Grover Search in a 32-Candidate Space

Combination therapies are widely used in multi-target diseases such as cancer and HIV, yet evaluating drug pairs can become computationally expensive as the number of candidates increases. In this work, we investigate whether a small quantum computer can accelerate the identification of an optimal two-drug combination from a simplified library of 32 candidate pairs. We encode the candidates into a 5-qubit register (2^5 = 32 states) and implement Grover's quantum search algorithm, where an oracle marks combinations satisfying predefined efficacy and safety constraints and amplitude amplification increases their likelihood of being measured. For a single optimal candidate in a 32-element search space, we apply 4 Grover iterations, close to the theoretical optimum. In noiseless simulation, we observe a strong increase in the probability of measuring the optimal combination compared to the uniform baseline of 1/32 (~3.1%), reaching above 60% after amplification. Experiments on IBM Quantum hardware reproduce the same qualitative trend while showing reduced success probability due to noise in current NISQ devices. Overall, this study provides a clear benchmark for applying quantum search to drug combination screening and outlines a pathway for scaling to larger candidate spaces as quantum hardware improves.