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I will discuss two questions related to quantum coherence. The first question is whether it is possible to perform quantum information processing in presence of strong dissipation. I will consider a strongly dissipative system admitting a nontrivial manifold of steady states. I will show how one can enact quantum logical gates inside this steadystate manifold by adding a weak, timerescaled, Hamiltonian term into the systemâ€™s Liouvillian. The effective dynamics is governed by a projected Hamiltonian which results from the interplay between the weak unitary control and the fast relaxation process. The leakage outside the steadystate manifold entailed by the Hamiltonian term is suppressed by an environmentinduced symmetrization of the dynamics. Given sufficient resources this approach allows for universal quantum computation and even completely dissipativegenerated quantum gates. In the second part I will discuss adiabatic quantum computation in presence of noise and in particular examine whether a speedup can survive at finite temperature. I will introduce a framework where the adiabatic preparation time can naturally be compared to the relaxation time of a classical Markov chain. Using known bounds for the mixing time and for the opensystem adiabatic theorem, one is led to a rather astonishing paradox. Namely relaxation seems always faster than adiabatic preparation. In systems describing thermalization I resolve the paradox by estimating an adiabatic bound in the low temperature limit. In this seeting, systems admitting a speedup at zerotemperature will still show a speedup for sufficiently low temperature. Host: Rolando Somma 