  We investigate the computational power of creating steady-states of quantum
dissipative systems whose evolution is governed by time-independent and local
couplings to a memoryless environment. We show that such a model allows for
efficient universal quantum computation with the result of the computation
encoded in the steady state. Due to the purely dissipative nature of the
process, this way of doing quantum computation exhibits some inherent
robustness and defies some of the DiVincenzo criteria for quantum computation.
We show that there is a natural class of problems that can be solved with such
a model - the preparation of ground states of frustration free quantum
Hamiltonians. This allows for robust and efficient creation of exotic states
that exhibit features like topological quantum order and the creation of PEPS
and it proves the existence of novel dissipative phase transitions. In
particular the latter can in principle be verified experimentally with present
day technology such as with optical lattices.
