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Center for Nonlinear Studies |
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 non-trivial manifold of steady states. I will show how one can enact quantum logical gates inside this steady-state manifold by adding a weak, time-rescaled, Hamiltonian term into the system’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 steady-state manifold entailed by the Hamiltonian term is suppressed by an environment-induced symmetrization of the dynamics. Given sufficient resources this approach allows for universal quantum computation and even completely dissipative-generated 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 open-system 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 zero-temperature will still show a speedup for sufficiently low temperature.
Host: Rolando Somma