| Topic: |
Science > Physics |
| User: |
"SkanderH" |
| Date: |
13 Feb 2005 11:35:08 PM |
| Object: |
about the Deutsh and Deutsh-Josza algorithms |
Deutsh's algorithm in quantum computing checks in one step if a binary
function is balanced f(0) diff f(1) or constant f(0) = f(1)
- Take 2 qubits 0 and 1 |0>|1>
- Apply Hadamard gate-->each qubit becomes a superposition of 0 and
1 1/2(|0>+|1>)(|0>-|1>)
- Apply a unitary transformation Uf that
turns |x>|y> into |x>|y xor f(x)>
- Apply Hadamard gate again to the first qubit --> this basically
removes the superposition without doing a measurment --> If the
function is constant the qubit is |0>, the amplitudes for |1>
cancel each other. If the function is balanced the qubit is in state
|1>.
- Measure the qubit, the outcome is deterministic: 0 = the function is
constant, 1 = the function is balanced.
Great, two computations for the price of one!! If you upgrade to the
Deutsh-Jozsa algorithm, than you get n computations for the price of
one!!
The question is, can a real world unitary transformation
[b:f2ced122ce]Uf[/b:f2ced122ce] be found for a given function? The
published practical implementations of the algorithms I've checked
just use truth tables. In the 2 bit case, is it possible at all for
an unkown function ?(if the function is known, what's the point
anyway?). In the n bit case, what happens when the function is
neither balanced, nor constant (probably the case of most useful
functions)?
Similar questions can be asked about the so called "oracle" in
Grover's search algorithm.
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