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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 WalshHadamard 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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 Fall '13
 BruceMacLennan

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