Lecture Notes 3.D

# Least two evaluations with a classical apparatus

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Unformatted text preview: mprovement by Cleve et al. least two evaluations. with a classical apparatus, which would require atto Deutsch’s 1985 algorithm (Nielsen & Chuang, 2010, p. 59). This example highlights the difference between quantum parallelism and classical randomized algorithms. Naively, one might think that the state |0i|f (0)i + |1i|f (1)i corresponds rather closely to a probabilistic classical computer that evaluates f (0) with probability one-half, or f (1) with probability one-half. The difference is that in a classical computer these two alternatives forever exclude one another; in a quantum computer it is D. QUANTUM ALGORITHMS 133 ¶5. Superposition: Transform it to a pair of superpositions | 1i 1 1 = p ( | 0i + |1i ) ⌦ p ( | 0i 2 2 | 1i ) = | + by two tensored Hadamard gates. 1 Recall H |0i = p2 (|0i + |1i) = |+i and H |1i = ¶6. Function application: Next apply Uf to | ¶7. Note Uf |xi|0i = |xi|0 1 p ( | 0i 2 1i =|+ i. (III.21) | 1i ) = | i . i. f ( x) i = | xi | f ( x) i . ¶8. Also note Uf |xi|1i...
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## This document was uploaded on 03/14/2014 for the course COSC 494/594 at University of Tennessee.

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