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Lecture Notes 3.D

# Note p 0 i x 0in 1i 2n lets look at the two possible

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Unformatted text preview: As in the Deutsch that the amplitude for the state |0i n is algorithm, prepare the initial state Alice now observes the query register. Note P | 0 i (x) |0i⌦n |1i. =/2n . Let’s look at the two possible cases – f constant and f balanced – to ( 1)f x discern what happens. In the case where f is constant the amplitude for |0i n is +1 or 1 depending on the constant value f (x) takes. Because 3 i is of unit length it follows ¶6. , Superposition: Use the Walsh-Hadamard |transformation to create a that all the other amplitudes must be zero, and an observation will yield 0s for all qubits in the query register. If f is balanced then the positive and negative contributions to the amplitude for |0i n cancel, leaving an amplitude of zero, and a measurement must yield a result other than 0 on at least one qubit in the query register. Summarizing, if Alice 136 CHAPTER III. QUANTUM COMPUTATION superposition of all possible inputs: | 1i = ( H ⌦n ⌦ H ) | 0i = X x 22 n 1 p |x, i. 2n ¶7. Claim: We will show that...
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