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Lecture Notes 2.C

interaction gates tthe bridgecontrol signal c 16

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Unformatted text preview: g signal crossover. a planar grid, one path (a), introduce a sideways shift (b), introduce a delay (c), and realize nontrivial crossover (d).” (Fredkin & To↵oli, 1982) 7 (This is non-trivial crossover; trivial crossover is when two balls cannot possibly be at the same place at the same time.) 4 Note that the interaction gate has four output lines but only four (rather than 2 ) output states-in other words, the 14. Fig. II.24 shows constrained. Whenrealizing these its inverse (Figure 13b), the same ¶ output variables are mechanisms for one considers functions. constraints appear on the input variables. In composing functions of this kind, one must exercise due care that the16.¶The switch satisfied.its inverse. Input signal x is routed to one of two output multiple Figure constraints are gate and 15. Fig. II.25 shows a realization of the Fredkin gate in terms of paths depending on he value of the indicates non-trivial crossover.) interaction gates. t(The “bridge”control signal, C. ¶16. Practical problems: Minuscule errors of any sort (position, velocity, alignment) will accumulate rapidly (by about a factor of 2 at each collision). ¶17. E.g., initial random error of 1/1015 in position or velocity (about what D.156 SOURCES duction to computer science Intro 65 ` ? ? > > = = Figure 3.14. A simple billiard ball computer, with three input bits and three output bits, shown entering on the left Figure II.25: Realization of the Fredkin gatea in terms of multiple interaction and leaving on the right, respectively. The presence or absence of billiard ball indicates a 1 or a 0, respectively. Empty circles gates. [NC]illustrate potential paths due to collisions. This particular computer implements the Fredkin classical reversible logic gate, discussed in the text. we will ignore the effects of noiseuncertainty principle) would lead to a comwould be expected from on the billiard ball computer, and concentrate on understanding the essential elements of reversible a few dozen collisions. pletely unpredictable...
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