# 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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### Get confused about the implementation of Amplitude Amplifier

I have a circuit $A$, which produces $$A|0^n\rangle _a |00\rangle _b = \phi_0 |00\rangle _b + \phi_1 |01\rangle _b+ \phi_2 |10\rangle _b + \phi_3 |11\rangle _b$$ And only $\phi_0 |00\rangle _b$ is ...
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### Can Amplitude Amplification amplify an unknown state?

If you have for example the basis states $|000\rangle$ and $|xxx\rangle$. The value of the second basis state is unknown, but the amplitude of both states is given. Also the amplitude of the second ...
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101 views

### How do I apply Amplitude Amplification for following state?

I have a multi qubit state that consists of two basis states and looks like the following for different number of qubits: 2 qubits: $|00⟩+|xx⟩$ 3 qubits: $|000⟩+|xxx⟩$ 4 qubits: $|0000⟩+|xxxx⟩$ ... (...
122 views

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### 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^{\...
210 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 ...
115 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 ...
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188 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 ...
127 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?
527 views

### What is the difference between amplitude amplification, amplitude estimation, and phase estimation?

I'm confused about the difference among Amplitude amplification (AA) , phase estimation (PE), and Amplitude Estimation. I thought I understood AA and PE somewhat but when I heard the amplitude ...
223 views

### Is it possible to tune the amplitude of superposition generated by Hadamard gates?

I had a question earlier about generating the superposition of all the possible states: Here. In that case, we could apply $H^{\otimes n}$ to the state $|0\rangle^{\otimes n}$, and each state has the ...
Montanaro A. 2015 Quantum speedup of Monte Carlo methods makes the following claim of an algorithm to estimate the mean output $\mu$ of an arbitrary algorithm A, with near-quadratic speedup over ...
I want to load a lognormal distribution and then use an IntegerComparator to flip a qubit ($|0\rangle$ to $|1\rangle$) if its value is less than a threshold. Then I want to use an Quantum Amplitude ...