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evaluation. This is ±|0i a|0very1iinteresting = f (1)
if f (0) problem (since there are
2 it is a warmup for the Deutsch-Jozsa
only four such functions), but
| 3i =
: ±|1i p 2 if f (0) 6= f (1). ¶3. It could be expensive to decide on a classical computer. For example,
Realizing that f (0) f (1) is 0 if f (0) = f (1) and 1 otherwise, we can rewrite this result
suppose f (0) = the millionth digit of ⇡ and f (1) = the millionth digit
of e. Then the problem is to decide if the millionth digits of ⇡ and e |0i |1i
are the same.
| 3 i = ±|f (0) f (1)i
It is mathematically simple, but computationally complex.
so by measuring the ﬁrst qubit we may determine f (0) f (1). This is very interesting indeed: the quantum Begin with the the ability i determine
¶4. Initial state: circuit has given us qubits | 0to = |01i. a global property of f (x), namely f (0) f (1), using only one evaluation of f (x)! This is faster than is possible
This is the 1998 i...
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- Fall '13