Robust quantum searching with spontaneously decaying qubits
  We present a modification of the standard single-item quantum search procedure that acquires robustness from spontaneous decay of the qubits. This damps the usual oscillation of populations, driving the system to a steady state with a strongly enhanced population of the solution. Numerical evaluation of the steady state was performed for up to 36 qubits. The huge size of the state space in our analysis is dealt with by exploiting a symmetry in the master equation that reduces the scaling of computer resources from exponential to polynomial. Based on these results we estimate that an error-free solution can be retrieved from the steady state after O(log log N) repetitions, with near-unit probability. This brings the overall scaling to O(sqrt{N} log log N), only slightly worse than for the ideal quantum case. 
Robert J. C. Spreeuw and Tom W. Hijmans