# Tag Info

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### How is the oracle in Grover's search algorithm implemented?

The function $f$ is simply an arbitrary boolean function of a bit string: $f\colon \{0,1\}^n \to \{0,1\}$. For applications to breaking cryptography, such as , , or , this is not actually a ‘...
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### Is there a layman's explanation for why Grover's algorithm works?

There is a good explanation by Craig Gidney here (he also has other great content, including a circuit simulator, on his blog). Essentially, Grover's algorithm applies when you have a function which ...
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### Can anyone provide me with an example of the for Grover's algorithm on one qubit?

The case of 1 qubit turns out to be pretty bad for understanding Grover's algorithm. There are several scenarios for the function you're looking at: Both inputs are solutions to $f(x) = 1$. The ...
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### How is Grover's algorithm used to estimate the mean and median of a set of numbers?

The idea for estimating the mean is roughly as follows: For any $f(x)$ that gives outputs in the reals, define a rescaled $F(x)$ that gives outputs in the range 0 to 1. We aim to estimate the mean of ...

### How is the Grover-Algorithm applied to a database?

I've been working on this problem as well. As a beginner and a classical programmer (i.e., I don't speak Quantum Mechanics), it is difficult to get an understanding of the concepts without complete ...
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### Nielsen and Chuang, Exercise 6.5: How to simulate oracle for n+1 qubits using one oracle gate for n qubits and one extra qubit?

The simplest solution is to use an ancilla in the $|+\rangle$ state. Swap that ancilla for the oracle's output qubit, conditioned on the control qubit being false, before and after applying the oracle....
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### Can adiabatic quantum computing be faster than Grover's algorithm?

Good question. For unstructured search, adiabatic quantum computation indeed gives the exact same $\sqrt{N}$ speedup that the standard gate-based Grover's algorithm does, as proven in this important ...
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### Is there any (really) quantum procedure that's an algorithm and not a Las Vegas algorithm?

It sounds like you're looking for algorithms that succeed deterministically with probability 1, instead of probabilistic algorithms that succeed with probability bounded from a 1/2 by a finite amount, ...
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### Significance of the term "diffusion" in Grover's diffusion operator

I had forwarded this question to Dr. Lov Grover and received the following response. I guess inversion about average is a better name for the $\mathrm{W}\mathbb I_0\mathrm{W}$ transformation. When I ...