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# Tag Info

## Hot answers tagged amplitude-amplification

8 votes
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 ...
• 2,999
7 votes
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### 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 $$S|x\rangle|0\rangle=|x\rangle |\sqrt{x}\rangle,$$ ...
• 2,048
5 votes
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### 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 ...
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5 votes
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### 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 ...
• 59.2k
4 votes
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### 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 ...
• 59.2k
3 votes
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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 ...
• 1,846
3 votes

### 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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3 votes
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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 ...
• 59.2k
3 votes
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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 ...
• 611
3 votes
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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{...
• 59.2k
3 votes

### 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 ...
• 1,517
3 votes
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### 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 ...
• 38.5k
3 votes
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### How to increase the probability of successful measurement to find out the largest amplitude?

There can be no efficient algorithm for doing this. Consider the complexity class PP: it contains the problems for which there is a polynomial time algorithm that succeeds with probability strictly ...
• 2,605
3 votes
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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 ...
• 59.2k
3 votes
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### How to perform amplitude amplification when the initial amplitude of aiming state is unknown

Crudely, what you want to do is think of your grover iterator $G$ as a unitary, and your unknown rotation angle $\alpha$ corresponds to two eigenvalues of $G$, $e^{\pm i\alpha}$, and you can prepare ...
• 59.2k
2 votes

### 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 ...
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2 votes

### 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 ...
• 25.5k
2 votes
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### 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 ...
• 14.6k
2 votes

### In amplitude amplification, how are the amplitudes of qubits changed?

EDIT: I completely misunderstood your question and thought that you were confused about what a negative amplitude means, and not about physical mechanisms. I'm leaving this up in case that actually ...
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2 votes
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### The relationship between problem structure and exponential speedups under the query model

The Aaronson-Ambainis (AA) conjecture implies that there must be some structure that's exploitable by a quantum algorithm to have any hope to achieve an exponential speedup for decision problems in NP....
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2 votes

### The relationship between problem structure and exponential speedups under the query model

Gilyén and Vazirani, building on the recent breakthrough of Hastings, give a (sub)-exponential separation for a quantum adiabatic algorithm with no sign problem. They design a graph that can be ...
• 12.8k
2 votes
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Where did the article say M/N is the probability of error? M/N in the article is only for the use of normalization. For example(2 qubits), after $H^{\otimes 2}$ acted on initial $\mid 0\rangle^{\... • 2,999 2 votes ### How to define Q-operator in Quantum Amplitude Estimation Short answer: Check out qiskit.aqua.algorithms.amplitude_estimators.q_factory.QFactory which constructs$Q$if you provide it with$A$. You can use the ... • 2,953 2 votes ### Is Grover's algorithm only applicable to a pure state? The problem is that you have only two states in your database. So when you mark state$|00\rangle$its amplitude is$-1$while the other state has amplitued$1$(note that I ignore normalization ... • 14.6k 2 votes Accepted ### Noise-induced amplitude amplification? It could have something to do with cross-talk and decoherence. By introducing the messy circuits, the other qubits are on idle as long as the messy circuits are being computed. Hence decoherence ... • 88 2 votes Accepted ### Setting the$\texttt{state_preparation}$for$\texttt{AmplificationProblem()}$in the scope of Grover's algorithm You have to pass a circuit, but you can just remove the resets from your circuit with the initialize instruction as ... • 2,953 2 votes Accepted ### Qiskit: Get number of iterations for Iterative Amplitude Estimation For the number of iterations, you can do for i,j in enumerate(result_delta._estimate_intervals): print(i,np.mean(j)) For the circuit result, you can try to do <... • 632 2 votes ### How to increase the probability of successful measurement to find out the largest amplitude? The problem is ill-defined. What if the largest$|c_n|$is not unique? What is the largest$|c_n|$if you have a uniform superposition? These issues aside, let's start with a simpler situation. First, ... • 2,684 2 votes Accepted ### In the quantum mean computation circuit, how to apply the controlled rotation to the extra qubit? Self-answer: This is actually a bit simpler than I thought. For two qubits (and this can be easily generalized to more qubits), the circuit would have to look like the following, where the$\theta_i$... • 1,018 2 votes ### How to perform amplitude amplification to return$|\psi_{\rm good}⟩$from$\cos\theta|\psi_{\rm good},\phi⟩+\sin\theta|\psi_{\rm bad},\phi^\perp⟩\$?

For question 1 - A state is a valid quantum state if it is normalised (i.e. the sum of the absolute value of its coefficients squared add to 1). For question 2 - This question is basically asking you ...
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