Unformatted text preview: ﬁrst calculate the L(Hnof the Hadamard transform
in the form of a it helps transform Uf 2 effect +1 , H) (Fig. III.23).
on a state |xi. By checking the cases x = 0 and x = 1 separately we see that for a single
qubit H |xi = z ( 1)xz |z i/ 2. Thus
¶3. We are told only that fP either constant or balanced, which means
x1 z1 +·· +xn zn
|z1 , . , zn i
that it is 0non , half xn i = z1 ,...,zand1)1 on the other. .half. .Our task is to
H |x1 . . . , its domain n
determine into which class a given f falls. This can be summarized more succinctly in the very useful equation
¶4. Classical: Consider ﬁrst the classical·zsituation. We can try di↵erent
( 1)x |z i
H |xi = z p
input bit strings x.
2n We might (if we’re lucky) discover after the second query of f that it where x · z constant.
is not is the bitwise inner product of x and z , modulo 2. Using this equation
and (1.48) we can now evaluate | 3 i,
But we might require as many as 2n /2+1 queries to answer the question.
X ) function (x) |z i |0i
So we’re facing O(2n 1 X ( 1)x·z+fevaluations.|1i
| 3i =
x ¶5. Initial state:...
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- Fall '13
- Quantum computer, Qubit, Theoretical Computer Science, Quantum information science