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A resource-efficient variational quantum algorithm for mRNA codon optimization

Hongfeng Zhang, Aritra Sarkar, Koen Bertels

TL;DR

This work addresses the NP-hard problem of mRNA codon optimization by introducing a resource-efficient quantum approach that uses dense encoding to dramatically reduce qubit requirements. A Hamiltonian $H(q)=H_f(q)+H_{gc}(q)+H_r(q)+H_p(q)$ encodes codon bias, GC targets, sequential repeats, and encoding constraints, with a VQE-based workflow implemented in Qiskit to locate the ground state and recover optimal codon sequences for protein fragments. Results on the P0DTC2 protein demonstrate substantial reductions in both qubits and gates compared with one-hot encoding, with fragment solutions closely matching exact values, highlighting the practical potential for quantum-assisted codon design. The study contributes to bioinformatics by enabling longer mRNA sequence optimization on near-term quantum hardware, while outlining limitations and avenues for incorporating additional biological constraints.

Abstract

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.

A resource-efficient variational quantum algorithm for mRNA codon optimization

TL;DR

This work addresses the NP-hard problem of mRNA codon optimization by introducing a resource-efficient quantum approach that uses dense encoding to dramatically reduce qubit requirements. A Hamiltonian encodes codon bias, GC targets, sequential repeats, and encoding constraints, with a VQE-based workflow implemented in Qiskit to locate the ground state and recover optimal codon sequences for protein fragments. Results on the P0DTC2 protein demonstrate substantial reductions in both qubits and gates compared with one-hot encoding, with fragment solutions closely matching exact values, highlighting the practical potential for quantum-assisted codon design. The study contributes to bioinformatics by enabling longer mRNA sequence optimization on near-term quantum hardware, while outlining limitations and avenues for incorporating additional biological constraints.

Abstract

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.
Paper Structure (8 sections, 10 equations, 4 figures, 2 tables)

This paper contains 8 sections, 10 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related research
  3. Method
  4. Synonymous codons encoding
  5. Hamiltonian construction
  6. Quantum algorithm execution
  7. Results
  8. Conclusion

Figures (4)

  • Figure 2: The structure of mRNA sequence
  • Figure 3: The number of required qubits on protein P0DTC2
  • Figure 4: The required number of qubits distribution between one hot and dense encoding on protein P0DTC2
  • Figure 5: Exact and optimal value of protein P0DTC2 on Qiskit