Experimental implementation of a discrete-time quantum walk on biological networks

Quantum walks provide a versatile framework for probing the structural and dynamical properties of complex systems ranging from biological networks to synthetic materials. However, their realization on current noisy pre-fault-tolerant quantum computers is fundamentally limited by decoherence. Conventional dense encodings of graph structures require prohibitively deep circuits, making them incompatible with existing hardware. Here we introduce an algorithm that leverages symmetry-sector encoding and trades circuit depth for the number of qubits, while integrating symmetry-respecting postselection as an effective noise-mitigation strategy. This combination enables us to execute practical quantum-walk circuits for biological network motifs on actual quantum hardware. We benchmark the proposed methodology against known state-of-the-art circuit architectures, highlighting significant reduction of circuit depth in our approach at the cost of moderate qubit overhead. Utilizing 40 qubits, we implement quantum walks on complex graphs containing up to 17 nodes and 20 edges—the largest experiment on superconducting hardware to date, with the Hellinger fidelity exceeding 87% throughout 7 steps. We present a proof-of-principle case study that illustrates how experimentally obtained quantum-walk dynamics on a protein-protein-interaction network can be applied to prioritizing disease-associated genes. We discuss the framework scalability in the pre-fault-tolerant era and its potential for studying larger biological networks.