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Q-CVaR-Fold: A Quantum CVaR Contrastive LearningFramework for Protein-Folding Decoy Scoring

Parham Ghayour

Published Dec 16, 2025• 0 citations
Publisher

Abstract

Abstract Protein structure prediction and decoy ranking remain central challenges in computational biophysics. Classical scoring functions often struggle todiscriminate near-native conformations from large populations of plausible decoys,particularly in the critical low-energy tail of the conformational distribution. Weintroduce Q-CVaR-Fold, a hybrid quantum–classical architecture that integratesa geometric graph neural network encoder with a small parameterized quantumcircuit acting as a nonlinear scoring head. To focus optimization on near-nativeconformations, we combine contrastive ranking with Conditional Value-at-Risk(CVaR) tail reweighting, yielding a risk-sensitive training objective aligned withstructural evaluation metrics.Despite using only four qubits and shallow entangling layers, Q-CVaR-Fold exhibits stable end-to-end training and avoids barren plateaus. On a decoy-rankingbenchmark, the model achieves a ROC-AUC of 0.984 and perfect top-5 nativeenrichment across all sequences, outperforming classical baselines of comparablesize. The score distributions and monotonic reduction of CVaR loss demonstratethat quantum feature transformations, coupled with tail-focused optimization, provide discriminative power beyond standard MLP heads. To our knowledge, this isthe first demonstration of a quantum-enhanced, risk-sensitive scoring model thatachieves near-perfect recovery of native structures in decoy-ranking tasks.Q-CVaR-Fold highlights the potential of hybrid quantum models for energylandscape modeling, fragment selection, and structural refinement, and offers apromising foundation for next-generation quantum–geometric methods in computational structural biology.

DOI
10.21203/rs.3.rs-8302298/v1

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Protein folding has been one of the most difficult problems for over a half-century,Therandom thermal motions causing conformational changes that lead energeticallydownhill towards the native structure, a principle captured in funnel-shaped energylandscapes.Unfolded polypeptides have a wide range of possible conformations. Thesearch problem becomes intractable for classical computers due to the exponentialgrowth of potential conformations with chain length. So far, there is theoretical andexperimental evidence that solving such optimization problems using QuantumComputing approaches such as Quantum Annealing, VQE, and QAOA has anadvantage. Although Google's DeepMind-AlphaFold has accomplished much,But wecan go even further with the quantum approach.Here we show how to predict structureof protein as well as RNA folding using the Variational Quantum Eigensolver withConditional Value at Risk (CVaR) expectation values for the solution of the problem andfor finding the minimum configuration energy and our task is to identify a protein'sminimal energy structure. The protein's structure is optimized to reduce energy. Alsomaking sure that all physical constraints are met and encoding the protein foldingproblem into a qubit operator.
Accurate prediction of mRNA secondary structure is critical for understanding gene expression, translation efficiency, and advancing mRNA-based therapeutics. However, the combinatorial complexity of possible foldings, especially in long sequences, poses significant computational challenges for classical algorithms. In this work, we propose a scalable, quantum-centric optimization framework that integrates quantum sampling with classical post-processing to tackle this problem. Building on a Quadratic Unconstrained Binary Optimization (QUBO) formulation of the mRNA folding task, we develop two complementary workflows: a Conditional Value at Risk (CVaR)-based variational quantum algorithm enhanced with gauge transformations and local search, and an Instantaneous Quantum Polynomial (IQP) circuit-based scheme where training is done classically and sampling is delegated to quantum hardware. We demonstrate the effectiveness of these approaches using IBM quantum processors, solving problem instances with up to 156 qubits and circuits containing up to 950 nonlocal gates, corresponding to mRNA sequences of up to 60 nucleotides. Additionally, we validate scalability of the CVaR algorithm on a tensor network simulator, reaching up to 354 qubits in noiseless settings. These results demonstrate the growing practical capabilities of hybrid quantum-classical methods for tackling large-scale biological optimization problems.
Protein folding has been one of the most difficult problems for over a half-century,The random thermal motions causing conformational changes that lead energetically downhill towards the native structure, a principle captured in funnel-shaped energy landscapes.Unfolded polypeptides have a wide range of possible conformations. The search problem becomes intractable for classical computers due to the exponential growth of potential conformations with chain length. So far, there is theoretical and experimental evidence that solving such optimization problems using Quantum Computing approaches such as Quantum Annealing, VQE, and QAOA has an advantage. Although Google's DeepMind-AlphaFold has accomplished much,But we can go even further with the quantum approach.Here we show how to predict structure of protein as well as RNA folding using the Variational Quantum Eigensolver with Conditional Value at Risk (CVaR) expectation values for the solution of the problem and for finding the minimum configuration energy and our task is to identify a protein's minimal energy structure. The protein's structure is optimized to reduce energy. Also making sure that all physical constraints are met and encoding the protein folding problem into a qubit operator.
Protein folding is a computationally intensive problem in bioinformatics that involves predicting the three-dimensional structure of a protein from its amino acid sequence. Classical approaches face challenges due to the exponential complexity of the search space. In this paper, we propose Q-ProteinFold, a quantum-classical hybrid system that leverages the Variational Quantum Eigensolver (VQE) for protein folding approximation. The system encodes protein sequences into parameterized quantum circuits using Qiskit and explores multiple conformations through quantum superposition and entanglement. A classical optimizer iteratively minimizes the energy function to identify stable protein structures. The implementation is developed using Python, Streamlit, and Qiskit Aer simulator. Experimental results demonstrate energy convergence, probabilistic state distribution, and effective fold prediction. This work highlights the potential of quantum computing in solving complex biological optimization problems.
Abstract Quantum computing in biology is one of the most rapidly evolving field of technology. Protein folding is one of the key challenges which requires accurate and efficient algorithms with a quick computational time. Structural conformations of proteins with disordered regions need colossal amount of computational resource to map its least energy conformation state. In this regard, quantum algorithms like Variational quantum eigensolver (VQE) are applied in the current research work to predict the lowest energy value of 50 peptides of 7 amino acids each. VQE is initially used to calculate the energy values over which Variational Quantum Optimization is applied via Conditional Value at Risk (CVaR) over 100 iterations of 500000 shots each to obtain least ground state energy value. This is compared to the molecular dynamics-based simulations of 50 nanoseconds each to calculate the energy values along with the folding pattern. The results suggest efficient folding outcomes from CvaR-VQE compared to MD based simulations. With the ever-expanding quantum hardware and improving algorithms the problem of protein folding can be resolved to obtain in depth insights on the biological process and drug design.