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# Tag Info

Accepted

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

To find the differences between them, you only need to know the aim of the problems. The aim of AA is to find the answers from unstructured data(or more directly, amplify the probability of the right ...
Accepted

### Preparing a quantum state from a classical probability distribution

Suppose we have two quantum circuits, the first one $S$ computes (or at least approximates) the classical squareroot function ($\sqrt{\cdot}$) via $$S|x\rangle|0\rangle=|x\rangle |\sqrt{x}\rangle,$$ ...
Accepted

### What is the difference between Grover's and Amplitude Amplification?

Grover's algorithm is a special case of the amplitude amplification algorithm where the number of good entries $G$ in the $N$-item database is $1$. In a nutshell: In the Grover's algorithm Wiki page ...
Accepted

### How to amplify a specific part of the quantum state

If you know, in advance, that the state you want to deamplify is specifically $|000\rangle$, there are a couple of strategies that you could follow. For example, introduce an ancilla and perform the ...
Accepted

### In generals Amplitude Amplification algorithm, the initial state does not need to attain equally superposition?

You've understood it correctly. The whole point of amplitude amplification is that it generalises Grover's Search so that it works with non-uniform superpositions. One of the key applications of this ...
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### Is it possible to tune the amplitude of superposition generated by Hadamard gates?

Yes indeed you can! First a simple example: if you want to increase all the amplitudes of the all the states that look like $|\cdot \cdot \cdot 1\rangle$ then you just need to apply an $R_y$ gate on ...

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

The original Amplitude Estimation algorithm (Brassard et al., 2002) uses Phase Estimation. So, it is OK to notice the similarity between them. Other approaches, however, have emerged in recent years ...
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### Amplitude suppression

Any state $|\Psi\rangle$ can be decomposed using a two-dimensional subspace comprising marked and unmarked states, $$|\Psi\rangle=\alpha|\Psi_m\rangle+\beta|\Psi_u\rangle.$$ Part of the assumption ...
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### Amplitude Estimation Algorithm — Lambda (Q) Operator

There are several different answers to your question, but let me give the answer that computer scientists will find most satisfying here. As it comes to implementing general unitary operators $U$, I ...
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### Computing of the action of the amplification operator $\mathbf Q$ over $|\Psi_i\rangle$ in the quantum amplitude amplification algorithm

The trick here is to not calculate $\mathcal{A}^{-1}|\Psi\rangle$ at all, because it's insufficiently defined! Instead, look at  \mathcal{A}(\mathbb{I}-2|0\rangle\langle 0|)\mathcal{A}^{-1}=\mathbb{...

### What is an exact quantum algorithm?

Only a partial answer, the Deutsch-Jozsa algorithm is an example of an exact algorithm. In my view, the algorithms differ exactly in how the answer is given. Either with probability 1 for exact ...
Accepted

### Amplifying entangled qubits

The operation you're asking for is equivalent to postselection. You're trying to force a measurement result of the address register. If that were possible it would make BQP = PostBQP. There's no proof ...
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### Grover's algorithm for complex phases

In your specific case, there's a very easy way: apply $U^4$ as your Grover oracle as this converts it into a "standard" oracle with $\pm 1$ eigenvalues. But that's just a lucky coincidence ...

### What is an exact quantum algorithm?

I asked basically the same question on CS stack exchange before this community was created. The answer is that the class of exact quantum algorithms has a name (EQP) but isn't very natural to study ...

### What is an exact quantum algorithm?

Say you want to factorise a large integer $N$. We know (inefficient) classical algorithms to do this, a naive example being: just check all combinations of smaller numbers until you find one that ...
Accepted

### Negating amplitude in amplitude amplification when second qubit is 0 not working

It seems that there is a missing $\mathrm{X}$ and $\mathrm{H}$ gates on qubit $q_2$. I used this Grover algoritm shape: Note 1: controlled $\mathrm{Z}$ is replaced by $\mathrm{CNOT}$ and Hadamards on ...