We explore a quantum mechanical framework for modeling mutation dynamics in viral genomes. Motivated by experimental observations, such as interference-like mutation patterns and an inverse relationship between genome size and per-site mutation rate, we represent the viral genome as a superposition state in a high-dimensional Hilbert space, and model mutations as quantum operators acting on this state. This is not a microscopic theory of replication but an effective, physically inspired model aimed at capturing non-classical features such as interference and entanglement in sequence evolution. We introduce structured mutation operators diagonal, random, and spatially correlated, and study their action on quantum sequence states using numerical simulations. Correlated operators with phase structure produce interference patterns in mutation probabilities, analogous to the electron double-slit experiment. Entangled mutation dynamics, modeled via cluster-state-like correlations, alter the scaling behavior of the per-site mutation rate with genome size. We show that while classical models predict a constant per-site mutation rate for small genomes, entangled models yield size-dependent rates that decrease as \( L^{-\alpha} \), where \( \alpha > 0 \) reflects the strength of correlation. This matches trends observed in RNA viruses with genomes below \(\sim 30\) kb. Finally, we propose two experimental tests: (1) detection of replication-speed-dependent interference fringes using modified viral polymerases, and (2) ensemble-level coherence signatures measurable by nuclear magnetic resonance spectroscopy. Our results offer a testable hypothesis that quantum correlations may influence mutation dynamics in viral genomes below 30 kb in size.