  Interactions between particles are usually a resource for quantum computing,
making quantum many-body systems intractable by any known classical algorithm.
In contrast, noise is typically considered as being inimical to quantum
many-body correlations, ultimately leading the system to a classically
tractable state. This work shows that noise represented by two-body processes,
such as pair loss, plays the same role as many-body interactions and makes
otherwise classically simulable systems universal for quantum computing. We
analyze such processes in detail and establish a complexity transition between
simulable and nonsimulable systems as a function of a tuning parameter. We
determine important classes of simulable and nonsimulable two-body dissipation.
Finally, we show how using resonant dissipation in cold atoms can enhance the
performance of two-qubit gates.
