Logarithmic-scale variational quantum eigensolver for off-lattice protein structure prediction in continuous torsional angle space
Abstract
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 Å Cα RMSD in retained snapshots and 1.199 Å in final models; Trp-cage achieved a 2.501 Å RMSD among snapshots (3.512 Å in final models). Execution on IBM processors (ibm_cleveland, ibm_miami) successfully recovered native-like structures with a best RMSD of 1.758 Å. 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.
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BibTeX
@misc{cumbo2026logarithmicscale,
title = {{Logarithmic-scale variational quantum eigensolver for off-lattice protein structure prediction in continuous torsional angle space}},
author = {Fabio Cumbo and Bryan Raubenolt and Varun Puram and Natalie Katzenmeyer and Jayadev Joshi and Daniel Blankenberg},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02113},
eprint = {2609.02113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02113},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Logarithmic-scale variational quantum eigensolver for off-lattice protein structure prediction in continuous torsional angle space
AU - Fabio Cumbo
AU - Bryan Raubenolt
AU - Varun Puram
AU - Natalie Katzenmeyer
AU - Jayadev Joshi
AU - Daniel Blankenberg
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02113
UR - https://arxiv.org/abs/2609.02113
AB - 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 Å Cα RMSD in retained snapshots and 1.199 Å in final models; Trp-cage achieved a 2.501 Å RMSD among snapshots (3.512 Å in final models). Execution on IBM processors (ibm_cleveland, ibm_miami) successfully recovered native-like structures with a best RMSD of 1.758 Å. 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.
ER -