Discrete Time
A quantum walk in discrete time is specified by a coin and shift operator, which are applied repeatedly.
Consider what happens when we discretize a massive Dirac operator over one spatial dimension. In the absence of a mass term, we have left-movers and right-movers. They can be characterized by an internal degree of freedom, "spin" or a "coin". When we turn on a mass term, this corresponds to a rotation in this internal "coin" space. A quantum walk corresponds to iterating the shift and coin operators repeatedly.
This is very much like Feynman's model of an electron in 1 spatial and 1 time dimension. He summed up the zigzagging paths, with left-moving segments corresponding to one spin (or coin), and right-moving segments to the other. See Feynman checkerboard for more details.
Read more about this topic: Quantum Walk
Famous quotes containing the words discrete and/or time:
“The mastery of one’s phonemes may be compared to the violinist’s mastery of fingering. The violin string lends itself to a continuous gradation of tones, but the musician learns the discrete intervals at which to stop the string in order to play the conventional notes. We sound our phonemes like poor violinists, approximating each time to a fancied norm, and we receive our neighbor’s renderings indulgently, mentally rectifying the more glaring inaccuracies.”
—W.V. Quine (b. 1908)
“And what avails it that science has come to treat space and time as simply forms of thought, and the material world as hypothetical, and withal our pretension of property and even of self-hood are fading with the rest, if, at last, even our thoughts are not finalities, but the incessant flowing and ascension reach these also, and each thought which yesterday was a finality, to-day is yielding to a larger generalization?”
—Ralph Waldo Emerson (1803–1882)