  We study Eigen's model of quasi-species, characterized by sequences that
replicate with a specified fitness and mutate independently at single sites.
The evolution of the population vector in time is then closely related to that
of quantum spins in imaginary time. We employ multiple perspectives and tools
from interacting quantum systems to examine growth and collapse of realistic
viral populations, specifically certain HIV proteins. All approaches used,
including the simplest perturbation theory, give consistent results.
