Lecture Notes 3.D

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Unformatted text preview: = |xi|1 f (x)i = |xi|¬f (x)i. ¶9. Therefore, expand Eq. III.21 and apply Uf : | 2i = Uf | 1 i 1 1 = Uf p ( | 0 i + | 1 i ) ⌦ p ( | 0 i | 1 i ) 2 2 1 = [Uf |00i Uf |01i + Uf |10i Uf |11i] 2 1 = [|0, f (0)i |0, ¬f (0)i + |1, f (1)i |1, ¬f (1)i] 2 There are two cases: f (0) = f (1) and f (0) 6= f (1). ¶10. Equal (constant function): If f (0) = f (1), then | 2i = = = = = 1 [|0, f (0)i |0, ¬f (0)i + |1, f (0)i |1, ¬f (0)i] 2 1 [|0i(|f (0)i |¬f (0)i) + |1i(|f (0)i |¬f (0)i)] 2 1 (|0i + |1i)(|f (0)i |¬f (0)i) 2 1 ± (|0i + |1i)(|0i |1i) 2 | + i. The last line applies because global phase (including ±) doesn’t matter. 134 CHAPTER III. QUANTUM COMPUTATION ¶11. Unequal (balanced function): If f (0) 6= f (1), then | 2i = = = = = = 1 [|0, f (0)i |0, ¬f (0)i + |1, ¬f (0)i |1, f (0)i] 2 1 [|0i(|f (0)i |¬f (0)i) + |1i(|¬f (0)i |f (0)i)] 2 1 [|0i(|f (0)i |¬f (0)i) |1i(|f (0)i |¬f (0)i)] 2 1 (|0i |1i)(|f (0)i |¬f (0)i) 2 1 ± (|0i |1i)(|0i |1i) 2 | i Clearly we can discriminate between...
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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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