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

## TL;DR

This paper introduces a quantum circuit to encode molecular similarity using entangled qubits, demonstrating effective error mitigation on quantum hardware.

## Contribution

A novel quantum circuit encodes Tanimoto similarity into entangled qubits, enabling error-mitigated similarity analysis on NISQ devices.

## Key findings

- Exponential error mitigation reduces errors by 75.0% for similar molecule pairs at 1% error rate.
- Mitigation effectiveness decreases to 25.0% at 10% depolarization noise for similar pairs.
- Quantum-encoded Tanimoto similarity is successfully demonstrated on IBM Quantum hardware with Z-basis reliability.

## Abstract

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.

Diagram illustrating a comparison between quantum and classical computing. On the left, chemical structures are shown with Tanimoto similarity and error rate plotted. Quantum computing is linked to lower error rates. On the right, a Bloch sphere represents quantum states, with angles \( \theta \) and \( \phi \) indicated. An arrow connects the graph to the Bloch sphere, highlighting the relationship.