An Etymological Dictionary of Astronomy and Astrophysics
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A → quantum walk taking place entirely in the position space. Continuous-time quantum walk was introduced by E. Farhi & S. Gutmann (1998, Phys. Rev. A 58, 915).

→ continuous; → time; → quantum; → walk.

A → quantum walk involving a probabilistic → operator that changes the direction while leaving the position fixed, and a shift operator that changes the position. Discrete-time quantum walk was introduced by J. Watrous (2001, Journal of Computer and System Sciences 62, 376)

→ discrete; → time; → quantum; → walk.

A generalization of the classical concept of → random walk using quantum mechanical laws such as the → superposition principle and → interference of quantum amplitudes. In the classical version the particle moves in the position space with a certain probability. In contrast, in the quantum counterpart the particle moves by exploring multiple possible paths simultaneously with the amplitudes corresponding to the influence of different paths. The concept of quantum walk is studied in two standard forms: → continuous-time quantum walk and → discrete-time quantum walk. Quantum walk was first introduced by Aharonov et al. (1993, Phys. Rev. A, 48, 1687).

→ continuous; → walk.