QSyncFold: quantum neural network for multidimensional sync-discovery in protein folding

Quantum computing provides alternative encoding and sampling paradigms for protein structure prediction (PSP), but existing quantum-PSP methods are often limited by resource-scaling issues and by discrete or inefficient encodings for continuous coordinates. To address these limitations, we propose QSyncFold, a hybrid quantum-classical neural network framework that combines quantum superposition with differentiable learning. QSyncFold employs ProtaQode to simultaneously achieve reversible continuous-space encoding of residue coordinates and parameterized interaction modeling. This is realized by encoding residue-pair interactions in superposition via a decomposable Any-State RY (ASRY) operator that is efficient for a limited qubit budget. Algorithmically, QSyncFold trades register size for iteration count, reducing the qubit requirement for each iteration from $O(N)$ to $3+\lceil \log _{2} N \rceil $, where $N$ is the number of residues. This design ensures the framework is experimentally viable under NISQ constraints. On short peptide structure prediction, QSyncFold achieved a 5.25-fold improvement in the lDDT metric compared with the Variational Quantum Eigensolver baseline and demonstrated a clear trade-off between qubit budget and convergence speed. While using quantum baselines as the primary comparison, the method performance approaches AlphaFold2 in the short peptide domain, with classical methods serving as background reference. This study advances the precision and methodology of quantum computing in PSP, illustrating a viable pathway for quantum algorithms in biomolecular modeling.