# 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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### In amplitude amplification, isn't the speedup hindered by the realization of $S_o$?

In brassard et al. Amplitude Amplification work, they define the Q operator as $$\mathbf{Q} = -AS_{o}A^{-1}S_{\chi}$$ where $S_{o}$ is an operator which flips the sign of the $|0 \rangle$ state. Which ...
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### Qiskit implementation of Brassard Amplitude implementaion's Q operator

In Brassard's et al. work, the $Q$ operator is defined as $$Q =-\mathcal{A}\mathcal{S_0}\mathcal{A}^{-1}\mathcal{S_\chi}$$ I was wondering how is the negative sign at the leftmost side implemented ...
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### Preparing a quantum state from a classical probability distribution

Suppose I have a black-box unitary $U_p$ which is described as follows: given a finite probability distribution $p:\{1,\ldots,n\}\rightarrow \mathbb{R}_{\geq0}$, where $\sum_{x=1}^n p(x)=1$, the ...
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### What is an exact quantum algorithm?

In the literature, there is a distinction between exact and error-bounded quantum algorithms. The former must solve a problem with a zero probability of error, whereas the latter only needs to bound ...
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### The relationship between problem structure and exponential speedups under the query model

What problem structure(s) are required to admit an exponential speedup in the universal quantum model of computation under the query model? Intuitively, it would seem that much of the benefit of the ...
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### Grover diffusion operator for a 3 qubit system

I want to make a three qubit system that marks the states where the last qubit is 0. I have made an oracle function but when I try to run the reflection the amplitudes are only higher than the others ...
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### Negating amplitude in amplitude amplification when second qubit is 0 not working

I have experimented a bit with Grover's Algorithm, and I wanted to search for the states $|00\rangle$ and $|10\rangle$. I tried making a Quantum Circuit, which looks like the one below, but measuring ...
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### What is the difference between Grover's and Amplitude Amplification?

I'm confused about what precisely is the difference between Grover's Algorithm and Amplitude Amplification. I've heard some sources say they are different algorithms and others say they are the same ...
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### Is there a quantum algorithm allowing to efficiently determine the state with the highest probability of occurring?

Is there a quantum algorithm allowing to determine the state with the highest probability of occurring (i.e. highest square amplitude), more efficiently than repeatedly measuring and estimating a ...
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### How to amplify a specific part of the quantum state

I understand that, according to amplitude amplification, I can amplify states according to a partition over the state space. However, suppose I want to amplify or de-amplify a specific portion of the ...
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### Amplitude suppression

On contrary to amplitude amplification, can I do some reflection such that my marked states' probability will vanish (ideally become zero but if there are small residuals also acceptable)? In order to ...
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### Amplitude Estimation Algorithm — Lambda (Q) Operator

I'm working on an implementation of the algorithms described Brassard et al. in the following paper: arXiv:quant-ph/0005055v1. I managed to make the amplitude amplification cases working but I'm ...
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### Does Brassard's algorithm for calculating the mean make implicit assumptions on distribution?

In An optimal quantum algorithm to approximate the mean and its application for approximating the median of a set of points over an arbitrary distance Brassard presents a quantum algorithm for finding ...
### Computing of the action of the amplification operator $\mathbf Q$ over $|\Psi_i\rangle$ in the quantum amplitude amplification algorithm
$\newcommand{\Q}{\mathbf{Q}}\newcommand{\S}{\mathbf{S}}\newcommand{\A}{{\mathcal A}}\newcommand{\H}{\mathcal H}$In the quantum amplitude amplification algorithm, as explained in Brassard et al. 2000 (...