# Questions tagged [grovers-algorithm]

Grover's search algorithm is an algorithm that can perform a search in the order of square root of the input size. This is a provable speed up over the best classical algorithm, which requires a time of order N to perform a search.

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### Quantum attack on hash functions

The line of questioning is inspired by the pick one trick in Section 4 of the PDF version of the paper Quantum Attacks on Classical Proof Systems - The Hardness of Quantum Rewinding (Ambainis et al., ...
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### Can we speed up the Grover's Algorithm by running parallel processes?

In classical computing, we can run the key search (for example AES) by running parallel computing nodes as many as possible. It is clear that we can run many Grover's algorithms, too. My question is;...
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### Why does Grover's search invert about the mean?

Let $\vert s\rangle = \frac{1}{\sqrt{N}}\sum_{i=1}^N\vert x_i\rangle$ be an equal superposition over states from which we need to find one solution state $\vert w\rangle$. The phase flip operator in ...
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### How significant are the variants of Grover's Algorithm?

I found a paper by Grover titled "How significant are the known collision and element distinctness quantum algorithms?", in which he expressed criticism to several famous algorithms, including ...
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### How many qubits does it take to break a 10 characters password?

Let's assume we developed a hashcat-like programs for quantum computer. How many qubits we need to find the correct hash (WPA, MD5,...) from a 10 characters password make from upper, lower & ...
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### Has there been any truly ground breaking advance in quantum algorithms since Grover and Shor?

(Sorry for a somewhat amateurish question) I studied quantum computing from 2004 to 2007, but I've lost track of the field since then. At the time there was a lot of hype and talk of QC potentially ...
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### In amplitude amplification, how are the amplitudes of qubits changed?

I am relatively new to quantum computing and I feel like I don't fully understand the power of quantum computing due to a lack of understanding of how amplitude amplification works. What is ...
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### Grover's algorithm: a real life example?

I'm fairly confused about how Grover's algorithm could be used in practice and I'd like to ask help on clarification through an example. Let's assume an $N=8$ element database that contains colors ...
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### Can adiabatic quantum computing be faster than Grover's algorithm?

It has been proven that adiabatic quantum computing is equivalent to "standard", or gate-model quantum computing. Adiabatic computing, however, shows promises for optimisation problems, where the ...
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### Implementation of the oracle of Grover's algorithm on IBM Q using three qubits

I am trying to get used to IBM Q by implementing three qubits Grover's algorithm but having difficulty to implement the oracle. Could you show how to do that or suggest some good resources to get ...
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### How does the Grover diffusion operator work and why is it optimal?

In this answer, Grover's algorithm is explained. The explanation indicates that the algorithm relies heavily on the Grover Diffusion Operator, but does not give details on the inner workings of this ...
Grover's algorithm is often described as a way to search a database in $O(\sqrt{N})$ time. For using it we need an oracle gate that represents some function $f$ such that $f^{-1}(1)$ is the answer. ...