Classical and Quantum Error-Correction Coding in Genetics

François Chapeau‐Blondeau

Henrietta Volkova

This paper establishes a rigorous theoretical and analytical framework positioning the double-helix Deoxyribonucleic Acid (DNA) molecule as a functional topological quantum computing system. Traditional molecular biology fails to address the thermodynamic paradox regarding the absolute informational fidelity of genetic transmission against high thermal noise within the intracellular medium (T ≈ 310 K). We propose a quantum bio-cryptographic model where nucleotide base pairs function as highly entangled qubits protected by non-local Quantum Error Correction (QEC) stabilizer codes. By analyzing the density matrix dynamics under localized environmental perturbations via the Lindblad master equation, we demonstrate that non-local quantum correlations suppress thermal dephasing. This mathematical architecture bridges functional quantum mechanics with structural genetics, providing an analytical blueprint for advanced bio-computing and computer-verified topological data storage.

Apoorva Patel

Jan Broulím, Alexander S. Ayriyan, H. Grigorian

Error correction plays a crucial role when transmitting data from the source to the destination through a noisy channel. It has found many applications in television broadcasting services, data transmission in radiation harsh environment (e. g. space probes or physical experiments) or memory storages influenced by Single Event Effects (SEE). Low Density Parity Check (LDPC) codes provide an important technique to correct these errors. The parameters of error correction depend both on the decoding algorithm and on the LDPC code given by the parity-check matrix. Therefore, a particular design of the paritycheck matrix is necessary. Moreover, with the development of high performance computing, the application of genetic optimization algorithms to design the parity-check matrices has been enabled. In this article, we present the application of the genetic optimization algorithm to produce error correcting codes with special properties, especially the burst types of errors. The results show the bounds of correction capabilities for various code lengths and various redundancies of LDPC codes. This is particularly useful when designing systems under the influence of noise combined with the application of the error correction codes.

Robert Rosén

Sultan Alam, Anish Pawar, Md. Irfan Alam

DNA replication upholds genomic integrity with remarkable precision, rectifying inaccuracies that emerge from quantum-level phenomena. This paper introduces a novel framework that models this biological process using the formalism of quantum error correction .We propose that genetic information encoded in DNA base pairs can be represented as the codespace of a Biological Stabilizer Code , where cellular proofreading and mismatch repair mechanisms function as an active error correction protocol.We provide comprehensive proofs that illustrate the code’s capacity to preferentially rectify the most likely types of mutations, thereby guaranteeing elevated logical fidelity. We establish a biological equivalent of the quantum threshold theorem, demonstrating that high-fidelity replication can be achieved if the inherent mutation rate falls below a critical threshold. The performance of the BSC is corroborated through simulations conducted in Qiskit, which reveal its superior efficacy compared to symmetric codes under biologically plausible noise conditions. This research establishes a quantitative relationship between the principles of fault-tolerant quantum computation and the mechanisms that uphold the stability of life’s genetic code.