Quantum Information Processing

i ← meas
end
return b A ,b B
end
Any classical programming language can be extended with statements to access and
manipulate quantum registers.
Now, that we have looked at the quantum solution to the parity problem, let us
consider the question of the least number of black-box applications required by a classical
algorithm: Each classical use of the black box can only give us one bit of information. In
particular, one use of the black box with input a A a B reveals only the parity of a A a B according
to the hidden parameters b A and b B . Each use of the black box can therefore only help
us distinguish between two subsets of the four possible parities. At least two uses of the
black box are therefore necessary. Two uses are also sufficient. To determine which of the
four parities is involved, use the black box first with input a A a B = 10 and then with input
a A a B = 01. As a result of this argument, one can consider the parity problem as a simple
example of a case in which there is a more efficient quantum algorithm than is possible
Table I. Quantum Network Elements
Gate Names
and Their
Abbreviations
Add/Prepare, add
Measure, meas
Not, not, σ x
Hadamard, H
a i
Phase Change, S(e iφ )
Gate
Symbols Algebraic Form Matrix Form
0
Z b
or
H
e i
If applied to an existing qubit
{|〉〈|, |〉〈|}
(operator mixture)
Quantum Information Processing
⎛1
0⎞
⎛0
1⎞
⎜ ⎟ ⎜ ⎟
⎜ ⎟ or ⎜ ⎟
⎜
⎝0
0
⎟ ⎜
⎠ ⎝0
0
⎟
⎠
{:|〉〈|,:|〉〈|} ⎛1
0⎞
⎛0
0⎞
⎜ ⎟ ⎜ ⎟
⎜ ⎟ or ⎜ ⎟
⎜ ⎟ ⎜ ⎟
⎝0
0⎠
⎝0
1⎠
|〉〈| + |〉〈| ⎛0
1⎞
⎜ ⎟
⎜ ⎟
⎜ ⎟
⎝1
0⎠
e –iσ y π / 4 σz
e iφ / 2 e –iσ zφ / 2
⎛1
1⎞
1 ⎜ ⎟
⎜ ⎟
2 ⎜ ⎟
⎝1
−1⎠
1 0
0 e iφ
⎛ ⎞
⎜ ⎟
⎝ ⎠
Number 27 2002 Los Alamos Science 25