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In the quantum computation circuit for the Deutsch-Jozsa algorithm, it is said that $U_f$ oracle will affect certain specific operations on the qubits using $f(x)$ and finally will give the answer in just one query. My doubts are,

  1. How does this $U_f$ oracle know what $f(x)$ is?
  2. Even if there is no need to know $f(x)$ for every $x$, but only what is to be known is whether $f(x)$ is constant or balanced; how is this latter knowledge known to oracle?

If my question is vague, let me put it in another way: I have $f(x)$ with me; I go to a quantum technician who will find out the nature of my function. If I don't tell him, the nature of $f(x)$, how does the technician proceed?

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  • $\begingroup$ I feel that the resource person who has provided the answer is not only giving the answer but is also trying to help me understand the answer. I am trying my best to follow the answer. $\endgroup$ Apr 5 at 19:26

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In the Deutsch-Jozsa scheme, you want to determine if your function is balance or constant. You do not have any information on the intern functioning of the function but you can access it as a black box. You submit an input and you get the output.

Now that we go to the quantum computer, we do not implement f on the quantum device but we assume the unitary $U_f$ acting like $f$ is given.

In the classical scheme, we have a black-box function and we need at least 2 queries to know about its nature.

While in the quantum scheme, we have a black-box unitary transformation and we only need one query to know about its nature.

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  • $\begingroup$ I feel that the resource person who has provided the answer is not only giving the answer but is also trying to help me understand the answer. I am trying my best to follow the answer. I was trying to give a real lfe example to the problem so as to understand the solution. I thought as follows. A, B both eat Apple on Monday, both eat Bread on Tuesday. A eats Apple while B eats Bread on Wednesday. A eats Bread while B eats Apple on Thursday. On Friday, they follow one of the above four choices. I wish to know if they ate the same item or if they ate different items on Friday. $\endgroup$ Apr 5 at 19:38

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