Information Technology Reference
In-Depth Information
ˆ
(14)
Uxy
=
→
xyf
().
x
⊕
This operator changes the second
y
qubit to zero if
f
is 1 during the first
x
qubit; if
f
is 0
1
no change is seen. Considering
y
1
2
(
)
=
0
1
ˆ
Uxy
=
→
xyf
().
x
(15)
⊕
where the function
f
has been isolated in an
x
phase-dependent. If
x
1
2
1
2
(
)
(
)
=
0
+
1
y
=
0
1
and
is immediately checked that
1
1
1
1
ˆ
:
(
)
(
)
(
)
⎡
()
f
(0)
()
f
(1)
⎤
(16)
U
0
−
1
0
+
1
→
−
1
0
+ −
1
1
0
−
1
.
⎣
⎦
2
2
2
2
In this way, it is only necessary to make an orthogonal projection of the
first qubit in a
{
}
+
,
base, where
1
(
)
±=
01.
±
(17)
2
The problem proposed in Eq. (14) has been resolved with an only one
computation. This is possible because at the moment of using a quantum
gadget, this has no limit to evaluate
f
(0)
or
f
(1)
, but instead, acting on
a superposition of the states
0
and
1
allowing to take out global in-
formation of function, namely, information that depends on combination
between
f
(0)
and
f
(1)
. This is the quantum parallelism.
Similarly, parallel processing can be used to identify some properties
of more complex functions. Thus, if we want to calculate all the possible
combinations on a set of
n
bits, the value of whichever function
f
,
a
classical computer will need to perform
2
n
evaluations of the function.
However, using a quantum computer, we only need to perform on an
n
given set: only one transformation given by the unitary operator
U
r
, in
which case
ˆ
r
Ux
:
0
→
xf
( ) .
x
(18)
⊕
The operation
denotes the binary addition or module 2, which is defined by
0
⊕=
0
0, 0
⊕=
1
1, 1
⊕=
0
1
and
11 0.
⊕=
Search WWH ::
Custom Search