How does one devise a Grover quantum oracle despite the no-cloning theorem?
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From what I understand, the Oracle operator takes an index register of qubits |x⟩|x⟩ (that will later be measured to find the solution) and a function f(x)f(x) where f(x)=1f(x)=1 for the correct solution xx such that
|x⟩−→−−Oracle(−1)f(x)|x⟩
|x⟩→Oracle(−1)f(x)|x⟩
Nielsen and Chaung's text has the idea of setting aside qubits as an Oracle workspace to provide extra room for the computing of f(x)f(x). In addition, the above statement suggests that the Oracle must keep |x⟩|x⟩ "intact" with the exception of inverting the sign of the correct answer.
Without a Oracle workspace, I imagine that the Oracle operator would transform |x⟩|x⟩ into |f(x)⟩|f(x)⟩ (but reversibly so, of course). Unless I've misunderstood, this is undesirable because we wish to measure xx.
How does one use the Oracle workspace? As I understand it, the no-cloning theorem means that one cannot copy qubits in and out from the |x⟩|x⟩ register and the Oracle workspace.
Hope it's helpful.
|x⟩−→−−Oracle(−1)f(x)|x⟩
|x⟩→Oracle(−1)f(x)|x⟩
Nielsen and Chaung's text has the idea of setting aside qubits as an Oracle workspace to provide extra room for the computing of f(x)f(x). In addition, the above statement suggests that the Oracle must keep |x⟩|x⟩ "intact" with the exception of inverting the sign of the correct answer.
Without a Oracle workspace, I imagine that the Oracle operator would transform |x⟩|x⟩ into |f(x)⟩|f(x)⟩ (but reversibly so, of course). Unless I've misunderstood, this is undesirable because we wish to measure xx.
How does one use the Oracle workspace? As I understand it, the no-cloning theorem means that one cannot copy qubits in and out from the |x⟩|x⟩ register and the Oracle workspace.
Hope it's helpful.
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