Entangled fingerprints for quantum-encoded chemoinformatics: quantum circuits for molecular similarity in the noisy era

Quantum computing holds promise for molecular similarity analysis in chemoinformatics and drug discovery. We propose a quantum circuit to encode the classically pre-computed Tanimoto similarity (T), obtained from extended-connectivity fingerprints (ECFPs) with RDKit, into a compact three-qubit entangled state using Qiskit. A 3-qubit circuit with RY rotations encodes T coefficients, while CNOT gates create an entangled three-qubit state that serves as a sensitive probe for quantum noise and error-mitigation performance. Simulations under noise demonstrate that exponential mitigation reduces errors by 75.0% for similar pairs (e.g., aspirin-aspirin) and 87.5% for dissimilar pairs (e.g., aspirin-butane) at a 1% error rate, maintaining fidelity within ±0.001 deviation. At 10% depolarization noise, error reduction drops to 25.0% and 17.4% for these pairs, respectively. The overall results show that the mitigation is proportionally more effective for low-similarity pairs. Experiments on IBM Quantum hardware confirm Z-basis reliability but reveal challenges with X-basis noise. Our work demonstrates quantum-encoded T representation and recovery on NISQ devices as a proof-of-concept, highlighting the critical role of error mitigation in hybrid quantum-classical workflows.