Non-Markovian decoherence in the adiabatic quantum search algorithm

Details Non-Markovian decoherence in the adiabatic quantum search algorithm Non-Markovian decoherence in the adiabatic quantum search algorithm

2006-08-15

arxiv.org/abs/quant-ph/0608123v1

Phys. Rev. A 75, 062313 (2007)

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevA.75.062313

We consider an adiabatic quantum algorithm (Grover's search routine) weakly coupled to a rather general environment, i.e., without using the Markov approximation. Markovian errors generally require high-energy excitations (of the reservoir) and tend to destroy the scalability of the adiabatic quantum algorithm. We find that, under appropriate conditions (such as low temperatures), the low-energy (i.e., non-Markovian) modes of the bath are most important. Hence the scalability of the adiabatic quantum algorithm depends on the infra-red behavior of the environment: a reasonably small coupling to the three-dimensional electromagnetic field does not destroy the scaling behavior, whereas phonons or localized degrees of freedom can be problematic. PACS: 03.67.Pp, 03.67.Lx, 03.67.-a, 03.65.Yz.

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