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This paper introduces a logarithmic-scale variational quantum eigensolver (VQE) that significantly reduces the qubit requirements for protein structure prediction from N to O(log2N), enabling off-lattice, all-atom simulations. The method utilizes statevector simulations to extract molecular torsions and employs a classical algorithm to generate heavy-atom coordinates, achieving native-like conformations for proteins like chignolin and Trp-cage with RMSD values as low as 0.623 脜. This work demonstrates that high-resolution protein structure prediction is feasible with exponentially fewer qubits, laying the groundwork for scalable hybrid quantum biophysics applications.
Achieving native-like protein structures with a quantum algorithm that requires exponentially fewer qubits could revolutionize protein modeling.
Classical and current quantum approaches to protein structure prediction (QPSP) face limitations, notably massive qubit requirements restricting near-term models to simplistic on-lattice simulations. We propose a logarithmic-scale variational quantum eigensolver (VQE) that reduces qubit requirements for N torsional degrees of freedom to O(log2N), enabling off-lattice, all-atom simulations. Our architecture extracts molecular torsions from relative phases in statevector simulations. On quantum hardware, a decoder maps the empirical cumulative distribution function (CDF) from basis-state probabilities to bounded torsional variables. These feed a classical algorithm to build heavy-atom coordinates. We use an EfficientSU2 ansatz and multi-stage relaxation to mitigate barren plateaus. Structures are evaluated via a custom hybrid quantum-classical Hamiltonian, alongside Rosetta and OpenMM benchmarks. Evaluation on chignolin and Trp-cage yielded native-like conformations. Chignolin reached a 0.623 {\AA} C{\alpha} RMSD in retained snapshots and 1.199 {\AA} in final models; Trp-cage achieved a 2.501 {\AA} RMSD among snapshots (3.512 {\AA} in final models). Execution on IBM processors (ibm_cleveland, ibm_miami) successfully recovered native-like structures with a best RMSD of 1.758 {\AA}. The custom energy function performed best overall, though energy-ranking imbalances persisted across sampled landscapes for all functions. This introduces the first all-atom, continuous-space quantum algorithm for QPSP. By converting physical qubit constraints into circuit depth constraints, it proves high-resolution prediction is feasible with exponentially fewer qubits. Despite current limits like computational overhead and energy function sensitivity, it establishes a scalable foundation for hybrid quantum biophysics.
