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I'm sorry if this is a stupid question. I want to know about the behavior of Grover's algorithm with oracle having a low one-sided probability of error. So if $f(x)=0$ my oracle returns $0$ and if $f(x)=1$ my oracle returns $1$ with probability $1-p$. Is it true that if $p=o(\frac{1}{\sqrt(n)})$, where $n$ is the size of the codomain of $f$ then Grover's algorithm still returns $x$ with constant probability?

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  • $\begingroup$ Is $n$ the number of qubits (bits) used for the codomain of $f$? You can always amplify by repeating Grover and try until success. $\endgroup$ Commented Apr 28 at 23:54
  • $\begingroup$ Are you more interested in how a standard implementation of Grover works in this scenario, or whether the algorithm can be modified to work over a much greater range of $p$? $\endgroup$
    – DaftWullie
    Commented Apr 29 at 6:39
  • $\begingroup$ n is the size of the codomain of f. $\endgroup$
    – ivmihajlin
    Commented Apr 29 at 17:08
  • $\begingroup$ The range of p is not a concern for me. I want to understand how to do a search with a nonperfect oracle. $\endgroup$
    – ivmihajlin
    Commented Apr 29 at 17:11

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