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arXiv:2610.00887

A Gate-Based Quantum Computing Framework for Codon Optimization

Fatemeh Ghasemi, Kion Kim

quant-phSubmitted Oct 1, 2026• Announced Oct 2, 2026• 0 citations
arXivHTMLPDF

Abstract

Codon optimization is a challenging combinatorial optimization problem with important applications in synthetic biology, protein expression, and biotechnology. While quantum annealing has previously been explored for this problem, the application of gate-based quantum algorithms remains largely unexplored. In this work, we present a gate-based quantum computing framework for codon optimization by formulating the optimization objective as an Ising Hamiltonian and expressing it in terms of Pauli operators suitable for gate-based quantum processors. The proposed framework is investigated using the Variational Quantum Eigensolver (VQE), Sampling Variational Quantum Eigensolver (SVQE), and the Quantum Approximate Optimization Algorithm (QAOA), with benchmarking against exact diagonalization, classical optimization, and quantum annealing. Using a three-amino-acid benchmark, the proposed implementations successfully reproduce the exact ground-state solutions while identifying optimized ansatz selections, optimization strategies, initialization schemes, and hardware execution settings that provide reproducible performance on current noisy quantum hardware. Hardware demonstrations are performed on IBM Quantum processors to evaluate the practical implementation of the proposed workflow. As a work in progress, this study establishes a reproducible computational framework for gate-based quantum codon optimization and provides the foundation for future investigations of larger protein sequences as quantum hardware and algorithms continue to advance.

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Codon optimization is a challenging combinatorial optimization problem with important applications in synthetic biology, protein expression, and biotechnology. While quantum annealing has previously been explored for this problem, the application of gate-based quantum algorithms remains largely unexplored. In this work, we present a gate-based quantum computing framework for codon optimization by formulating the optimization objective as an Ising Hamiltonian and expressing it in terms of Pauli operators suitable for gate-based quantum processors. The proposed framework is investigated using the Variational Quantum Eigensolver (VQE), Sampling Variational Quantum Eigensolver (SVQE), and the Quantum Approximate Optimization Algorithm (QAOA), with benchmarking against exact diagonalization, classical optimization, and quantum annealing. Using a three-amino-acid benchmark, the proposed implementations successfully reproduce the exact ground-state solutions while identifying optimized ansatz selections, optimization strategies, initialization schemes, and hardware execution settings that provide reproducible performance on current noisy quantum hardware. Hardware demonstrations are performed on IBM Quantum processors to evaluate the practical implementation of the proposed workflow. As a work in progress, this study establishes a reproducible computational framework for gate-based quantum codon optimization and provides the foundation for future investigations of larger protein sequences as quantum hardware and algorithms continue to advance.
Reverse translation of polypeptide sequences to expressible mRNA constructs is a NP-hard combinatorial optimization problem. Each amino acid in the protein sequence can be represented by as many as six codons, and the process of selecting the combination that maximizes probability of expression is termed codon optimization. This work investigates the potential impact of leveraging quantum computing technology for codon optimization. A Quantum Annealer (QA) is compared to a standard genetic algorithm (GA) programmed with the same objective function. The QA is found to be competitive in identifying optimal solutions. The utility of gate-based systems is also evaluated using a simulator resulting in the finding that while current generations of devices lack the hardware requirements, in terms of both qubit count and connectivity, to solve realistic problems, future generation devices may be highly efficient.
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 Reverse translation of polypeptide sequences to expressible mRNA constructs is a NP-hard combinatorial optimization problem. Each amino acid in the protein sequence can be represented by as many as six codons, and the process of selecting the combination that maximizes probability of expression is termed codon optimization. This work investigates the potential impact of leveraging quantum computing technology for codon optimization. An adiabatic quantum computer (AQC) is compared to a standard genetic algorithm (GA) programmed with the same objective function. The AQC is found to be competitive in identifying optimal solutions and future generations of AQCs may be able to outperform classical GAs. The utility of gate-based systems is also evaluated using a simulator resulting in the finding that while current generations of devices lack the hardware requirements, in terms of both qubit count and connectivity, to solve realistic problems, future generation devices may be highly efficient.
A study published on bioRxiv proposes for the first time a hybrid approach combining quantum annealing and the Lagrange multiplier method by formulating the codon optimization problem as a constrained quadratic binary problem. It demonstrates the overwhelming performance of this quantum-classical hybrid protocol by applying it to practical scenarios: optimizing the SARS-CoV-2 spike protein sequence in a human host and the insulin sequence in an E. coli host. As a result of evaluating biological metrics, it established a robust workflow through which quantum computing can practically contribute to next-generation genetic engineering and new drug development by successfully optimizing codon usage patterns that govern protein translation efficiency and stability. [Quantum Biology Society] To efficiently produce specific proteins in heterologous hosts, a codon optimization process that adjusts the genetic code and codon usage frequencies to suit the host's characteristics is essential. While this is a core task in biotechnology to maximize the expression level and stability of therapeutic proteins like vaccines or insulin, the exponentially large number of possible gene sequence combinations has incurred massive computational costs to find optimal solutions using conventional classical computing methods. Recently, the achievements of a domestic research team that achieved groundbreaking optimization by directly applying quantum computing to this complex biological problem have been published. The paper titled "Quantum-classical hybrid approach for codon optimization and its practical applications," published on the preprint repository bioRxiv, presents a new protocol that will change the paradigm of gene sequence design utilizing quantum annealing. A joint domestic research team led by Professor Joonsuk Huh and researcher You Kyoung Chung from the Department of Chemistry at Sungkyunkwan University, Professor Daniel K Park from the Department of Applied Statistics at Yonsei University, and researcher Dongkeun Lee from the Korea Institute of Science and Technology Information (KISTI) spearheaded this innovative research. ■ Transformation into a Constrained Quadratic Binary Problem and Quantum Computation The research team newly formulated the complex codon optimization process into a mathematical constrained quadratic binary problem. In particular, they adopted a quantum-classical hybrid approach that organically integrates the parallel computing capabilities of quantum annealing hardware with the Lagrange multiplier method, a classical numerical analysis technique. Through this, they overcame the computational bottleneck occurring in the vast sequence search space and rapidly and accurately derived the optimal gene sequence that can maximize protein translation efficiency while simultaneously considering the host's codon usage bias. ■ Demonstrated Achievements Applied to COVID-19 Vaccine and Insulin The true value of this hybrid protocol was clearly proven through two practical biological scenarios. The research team successfully applied this algorithm to models for optimizing the codon sequence of the SARS-CoV-2 spike protein tailored to a human host environment and optimizing the insulin sequence within an E. coli host. As a result of rigorous biological metric evaluations, the sequences designed by the quantum algorithm demonstrated an overwhelming ability to perfectly optimize the codon usage patterns that govern protein translation efficiency. This demonstration is an important milestone declaring that quantum computing technology has moved beyond mere theoretical possibility to establish itself as a powerful and practical tool that can immediately contribute to next-generation gene therapeutics and customized new drug design pipelines. https://www.biorxiv.org/content/10.1101/2024.06.08.598046v1
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.
Quantum optimization allows for up to exponential quantum speedups for specific, possibly industrially relevant problems. As the key algorithm in this field, we motivate and discuss the Quantum Approximate Optimization Algorithm (QAOA), which can be understood as a slightly generalized version of Quantum Annealing for gate-based quantum computers. We delve into the quantum circuit implementation of the QAOA, including Hamiltonian simulation techniques for higher-order Ising models, and discuss parameter training using the parameter shift rule. An example implementation with Pennylane source code demonstrates practical application for the Maximum Cut problem. Further, we show how constraints can be incorporated into the QAOA using Grover mixers, allowing to restrict the search space to strictly valid solutions for specific problems. Finally, we outline the Variational Quantum Eigensolver (VQE) as a generalization of the QAOA, highlighting its potential in the NISQ era and addressing challenges such as barren plateaus and ansatz design.