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Kendon, Viv

Decoherence in quantum walks - a review. (English) Zbl 1130.81325

Math. Struct. Comput. Sci. 17, No. 6, 1169-1220 (2007).
Summary: The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, has led rapidly to several new quantum algorithms. These all follow a unitary quantum evolution, apart from the final measurement. Since logical qubits in a quantum computer must be protected from decoherence by error correction, there is no need to consider decoherence at the level of algorithms. Nonetheless, enlarging the range of quantum dynamics to include non-unitary evolution provides a wider range of possibilities for tuning the properties of quantum walks. For example, small amounts of decoherence in a quantum walk on the line can produce more uniform spreading (a top-hat distribution), without losing the quantum speed up. This paper reviews the work on decoherence, and more generally on non-unitary evolution, in quantum walks and suggests what future questions might prove interesting to pursue in this area.

Cited in 2 Reviews
Cited in 63 Documents

MSC:

81P68 Quantum computation
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
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\textit{V. Kendon}, Math. Struct. Comput. Sci. 17, No. 6, 1169--1220 (2007; Zbl 1130.81325)
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