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arXiv:2505.05782 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Towards Secondary Structure Prediction of Longer Mrna Sequences Using a Quantum-Centric Optimization Scheme

Vaibhaw Kumar, Dimitris Alevras, Mihir Metkar, Eline Welling, Chris Cade, Ido Niesen, Triet Friedhoff, Jae-Eun Park, Saurabh Shivpuje, Mariana LaDue, Wade Davis, Alexey Galda

Published Aug 30, 2025• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/qce65121.2025.00254

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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.
Recent advancements in quantum computing have created new opportunities for tackling long-standing, complex combinatorial optimization problems that are intractable for classical computers. Predicting the secondary structure of mRNA is one such notoriously difficult problem that can benefit from the rapid advancements in quantum computing technology. Accurate prediction of mRNA secondary structure is crucial for designing RNA-based therapeutics, as it dictates various stages of the mRNA life cycle, including transcription, translation, and decay. The current generation of quantum computers has reached a utility scale, enabling us to explore relatively large problem sizes. In this paper, we examine the feasibility of solving mRNA secondary structures on a quantum computer for sequence lengths up to 60 nucleotides, representing problems in the qubit range of 10 to 80. We use the Conditional Value at Risk (CVaR)-based VQE algorithm to solve optimization problems derived from mRNA secondary structure prediction on the IBM Eagle and Heron quantum processors. Encouragingly, even with minimal error mitigation and fixed-depth circuits, our hardware runs yield accurate predictions of minimum free energy (MFE) structures that match the results of the classical solver CPLEX. Our results provide substantial evidence for the viability of solving mRNA structure prediction problems on a quantum computer and motivate continued research in this direction.
Co-optimizing mRNA sequences for both codon optimality and secondary structure is crucial for producing stable and efficacious mRNA therapeutics. Codon optimization, which adjusts nucleotide sequences to enhance translational efficiency, inherently influences mRNA secondary structure - a key determinant of molecular stability both in-vial and in-cell. Because both properties are governed by the same underlying sequence, optimizing one directly impacts the other. To address this interdependence, we introduce a novel variational framework that simultaneously optimizes codon usage and secondary structure. Our method employs a dual-objective function that balances the codon adaptation index (CAI) and minimum free energy (MFE), incorporating variational parameters for codon selection. Leveraging a hybrid quantum-classical computational strategy and building on prior advancements in quantum algorithms for secondary structure prediction, we effectively navigate this complex optimization space. We demonstrate the feasibility of executing this end-to-end workflow on real quantum hardware, using IBM's 127-qubit Eagle processor. We validate our approach through both simulations and quantum hardware experiments on sequences of up to 30 nucleotides. These results highlight the potential of our framework to accelerate the design of optimal mRNA constructs for therapeutic and research applications.
It is the first step for understanding how RNA structure folds from base sequences that to know how its secondary structure is formed. Traditional energy-based algorithms are short of precision, particularly for non-nested sequences, while learning-based algorithms face challenges in obtaining high-quality training data. Recently, quantum annealer has rapidly predicted the folding of the secondary structure, highlighting that quantum computing is a promising solution to this problem. However, gate model algorithms for universal quantum computing are not available. In this paper, gate-based quantum algorithms will be presented, which are highly flexible and can be applied to various physical devices. Mapped all possible secondary structure to the state of a quadratic Hamiltonian, the whole folding process is described as a quadratic unconstrained binary optimization model. Then the model can be solved through quantum approximation optimization algorithm. We demonstrate the performance with both numerical simulation and experimental realization. Throughout our benchmark dataset, simulation results suggest that our quantum approach is comparable in accuracy to classical methods. For non-nested sequences, our quantum approach outperforms classical energy-based methods. Experimental results also indicate our method is robust in current noisy devices. It is the first instance of universal quantum algorithms being employed to tackle RNA folding problems, and our work provides a valuable model for utilizing universal quantum computers in solving RNA folding problems.
Optimizing the mRNA codon has an essential impact on gene expression for a specific target protein. It is an NP-hard problem; thus, exact solutions to such optimization problems become computationally intractable for realistic problem sizes on both classical and quantum computers. However, approximate solutions via heuristics can substantially impact the application they enable. Quantum approximate optimization is an alternative computation paradigm promising for tackling such problems. Recently, there has been some research in quantum algorithms for bioinformatics, specifically for mRNA codon optimization. This research presents a denser way to encode codons for implementing mRNA codon optimization via the variational quantum eigensolver algorithms on a gate-based quantum computer. This reduces the qubit requirement by half compared to the existing quantum approach, thus allowing longer sequences to be executed on existing quantum processors. The performance of the proposed algorithm is evaluated by comparing its results to exact solutions, showing well-matching results.
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.
Abstract Predicting the three-dimensional structure of a protein from its primary sequence of amino acids is known as the protein folding problem. Due to the central role of proteins’ structures in chemistry, biology and medicine applications, this subject has been intensively studied for over half a century. Although classical algorithms provide practical solutions for the sampling of the conformation space of small proteins, they cannot tackle the intrinsic NP-hard complexity of the problem, even when reduced to the simplest Hydrophobic-Polar model. On the other hand, while fault-tolerant quantum computers are beyond reach for state-of-the-art quantum technologies, there is evidence that quantum algorithms can be successfully used in noisy state-of-the-art quantum computers to accelerate energy optimization in frustrated systems. In this work, we present a model Hamiltonian with O(N4){\mathcal{O}}({N}^{4})O(N4) O ( N 4 ) scaling and a corresponding quantum variational algorithm for the folding of a polymer chain with N monomers on a lattice. The model reflects many physico-chemical properties of the protein, reducing the gap between coarse-grained representations and mere lattice models. In addition, we use a robust and versatile optimization scheme, bringing together variational quantum algorithms specifically adapted to classical cost functions and evolutionary strategies to simulate the folding of the 10 amino acid Angiotensin on 22 qubits. The same method is also successfully applied to the study of the folding of a 7 amino acid neuropeptide using 9 qubits on an IBM 20-qubit quantum computer. Bringing together recent advances in building gate-based quantum computers with noise-tolerant hybrid quantum-classical algorithms, this work paves the way towards accessible and relevant scientific experiments on real quantum processors.