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# Questions tagged [amplitude-amplification]

For questions about the amplitude-amplitude algorithm. Do NOT use for general Grover's algorithm related question. Amplitude amplification is a technique in quantum computing which generalizes the idea behind Grover's search algorithm and gives rise to a family of quantum algorithms. It was discovered by Gilles Brassard and Peter Høyer in 1997 and independently rediscovered by Lov Grover in 1998. (Wikipedia)

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### Which applications of quantum singular value transformation use block-encodings in apriori unknown bases?

Quantum singular value transformation (QSVT) algorithm allows performing polynomial transformations on matrices that are block-encoded in a unitary. Typically, block encoding is assumed to be 'the top-...
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### Grover's algorithm for complex phases

Grover's algorithm traditionally inputs a phase oracle, $U_\omega$ such that $U_\omega | x \rangle = (-1)^{f(x)} | x \rangle$. The task is to find some $x$ such that $f(x) = 1$. In other words, the ...
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### In generals Amplitude Amplification algorithm, the initial state does not need to attain equally superposition?

In the beginning of this paper about amplitude amplification algorithm, the author stated the conventions of amplitude amplification which I quoted the important part for your convenience as follows: ...
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### Understanding Qiskit 0.32 's $\texttt{AmplificationProblem()}$ behaviour

This is related to my previous question. To apply amplitude amplification in Qiskit, one needs to use AmplificationProblem() or ...
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### Setting the $\texttt{state_preparation}$ for $\texttt{AmplificationProblem()}$ in the scope of Grover's algorithm

I am having trouble setting the state_preparation parameter of AmplificationProblem() from ...
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### Amplifying entangled qubits

Suppose I have a three-qubit entangled state of the following form: $$|00\rangle|\psi_1\rangle + |01\rangle|\psi_2\rangle + |10\rangle|\psi_3\rangle + |11\rangle|\psi_4\rangle$$ I refer to the ...
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### How to understand picking a random subcube in the Aaronson/Ambainis spatial search algorithm?

I am referring to the Quantum Search of Spatial Regions paper. I must confess that the paper itself is a bit heavy for my level of mathematical fluency. Trying to understand it nevertheless and having ...
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### BHT algorithm implementation

Summary of Method Amplitude Amplification Summary The BHT algorithm uses amplitude amplification, a nice generalisation of Grover's algorithm, where there is a subset $G\subset X$ of good elements in ...
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### Noise-induced amplitude amplification?

I wanted to share some results from an experiment which I find thought were deeply surprising. The basic idea is to prepare a superposition in a main register then conditionally apply lots of random ...
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### How does the amplitude amplification in Grover's algorithm work?

As the question says - how does the amplitude amplification in Grover's algorithm work? I am fine with adding the negative phase on the winning state, but how does one generate the diffuser to ...
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I am running an instance of amplitude amplification using Qiskit (v 26) on Google Colab. The circuit is approximately 17 qubits in space and $O(ck)$ in depth where $k \in \left \{1,2,3....,22 \right \... 2 votes 1 answer 190 views ### Amplitude Amplification for searching$|0\rangle$in an unknown state For one known (invertible) function that does: $$f:H^{\otimes 2n}\times H^{\otimes 2n}:|x⟩|0⟩\mapsto|x⟩|y⟩$$ I want to find a similar (invertible) function that does:$$g:H^{\otimes 2n}\times H^{\... 3 votes 1 answer 233 views ### Combining Amplitude Amplification with HHL I'm recently learning about how to apply Grover search techniques to other places. An example I've come across is to amplify the probability of measure a$\lvert 1 \rangle$of the ancilla qubit in HHL ... 2 votes 1 answer 131 views ### Manipulating the amplitude of state based on the state information In the past, I thought I have seen quantum circuits/algorithm techniques to change the amplitude of state based on the state?$\lvert \psi \rangle = \sum_x \ C_x \lvert x \rangle$, here$C_x$is just ... • 1,111 1 vote 0 answers 239 views ### How to load time-series stock data into quantum amplitude estimation Now I got some time-series data as showing example below: I have spent a period of time realizing the QAE from qiskit, and I found that the tutorial used uncertainty model to reproduce data, while I ... • 33 0 votes 1 answer 134 views ### In the amplitude amplification algorithm in Nielsen and Chuang's book, why is the error probability$M/N\$?

I was able to follow til the yellow-highlighted sentences, which seems to be important to understand. Why M/N is the probability of error? If so 1 - M/N would be the probability of success?
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