A Quantum Circuit Framework for Protein Ensemble-Level Energetics

<title>Abstract</title> <p> Proteins occupy heterogeneous free-energy landscapes, where broad, high-entropy ensembles converge toward compact, low-energy basins containing multiple sub-states. Molecular dynamics can capture these landscapes at atomic resolution, but exhaustively sampling rare transitions remains computationally demanding. Furthermore, most quantum approaches to protein modelling target only a single optimal structure, leaving the energetic heterogeneity of the full ensemble largely unexplored. We introduce a residue-level, gate-based quantum circuit framework for coarse-graining protein thermodynamics. Each amino acid is represented as a two-state qubit with stabilised and excited solvation states, initialised from solvation energetics. Following this, a structure-informed entanglement block of parametrised controlled gates encodes covalent bonds and non-covalent contacts across the residue network. The circuit is then measured approx 10 ⁶ times, yielding an ensemble of binary thermodynamic microstates, from which we compute energy distributions, residue-level statistical couplings, energetic sensitivities, and information gain relative to total free energy. We showcase the comparative results for Trp-cage miniprotein (PDB:1L2Y) and the disulfide-stabilised chimera (PDB:9GDL), which comprises a structured, folding-funnel-like energy distribution for 1L2Y. Moreover, comparison with 9GDL reveals clear shifts in global energy and residue-level profiles, localising the residues driving stabilisation and ensemble reorganisation. Additionally, dimer- and trimer-level couplings resolve both direct and interaction-mediated dependencies, showing the circuit captures network-level, not just isolated, correlations. The framework moves quantum protein modelling beyond single-structure optimisation toward interpretable, ensemble-level characterisation. </p>