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Decoherence models and their effects on quantum maps and algorithms

Mario Leandro Aolita·Marcos Saraceno
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Abstract

In this work we study several models of decoherence and how different quantum maps and algorithms react when perturbed by them. Following closely Ref. [1], generalizations of the three paradigmatic one single qubit quantum channels (these are the depolarizing channel, the phase damping channel and the amplitude damping channel) for the case of an arbitrarily-sized finite-dimensional Hilbert space are presented, as well as other types of noise in phase space. More specifically, Grover's search algorithm's response to decoherence is analyzed; together with those of a family of quantum versions of chaotic and regular classical maps (the baker's map and the cat maps). A relationship between how sensitive to decoherence a quantum map is and the degree of complexity in the dynamics of its associated classical counterpart is observed; resulting in a clear tendency to react the more decoherently the more complex the associated classical dynamics is.

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Mario Leandro Aolita, Marcos Saraceno. 2005-04-27. Decoherence models and their effects on quantum maps and algorithms. https://arxiv.org/abs/quant-ph/0504211

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