Variational quantum thermalization of environment-coupled DNA sequence biases

Understanding whether environmental conditions bias the statistical weight of specific genomic configurations requires a framework connecting molecular interactions, thermal fluctuations, and sequence-level observables. Here, we model DNA as an open quantum system coupled to an environmental thermal bath (represented as an external bosonic field) and parameterize the underlying molecular interaction energies (effective Hamiltonian terms) directly from prescribed nucleotide sequences. To evaluate sequence distributions at thermodynamic equilibrium, we compare two finite-temperature strategies at fixed inverse temperature ($\beta=1$): classical Bayesian optimization targeting the exact thermodynamic equilibrium distribution (the Gibbs state), and quantum simulation using a Variational Quantum Thermalizer (VQT) implemented via a nine-layer parameterized quantum circuit. Both methods optimize the same interaction energy model and target-sequence objective across short oligomers ($N=2$--$5$ base pairs), using 200 outer evaluations. Benchmarking against a uniform sequence distribution, exact-Gibbs optimization enhances target-sequence probabilities by factors of $9.11$, $25.64$, $54.51$, and $159.87$. The VQT approach similarly yields substantial target enrichment across all sequence lengths, achieving enhancement factors between $9.85$ and $62.77$. By evaluating the VQT-selected Hamiltonians against exact Gibbs calculations, we decouple optimization errors in parameter learning from approximation errors inherent to the variational quantum circuit. While concordance with the exact-Gibbs optimum is high in shorter oligomers, larger systems exhibit heightened sensitivity to variational thermal approximations. These results demonstrate that environment-induced sequence biases can be systematically captured within a variational quantum simulation framework, bridging biophysical models of DNA thermodynamics with quantum algorithms for finite-temperature state preparation. Crucially, the resulting equilibrium probabilities represent intrinsic thermodynamic biases rather than realized evolutionary substitution rates, which remain governed by kinetic activation barriers, replication fidelity, and enzymatic DNA repair.