6
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 ...
- 2,782
5
votes
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 $$S|x\rangle|0\rangle=|x\rangle |\sqrt{x}\rangle,$$ ...
- 1,771
5
votes
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 ...
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4
votes
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 ...
- 52.3k
4
votes
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 ...
- 52.3k
3
votes
Accepted
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 ...
- 1,312
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 ...
- 7,559
3
votes
Accepted
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 ...
- 52.3k
3
votes
Accepted
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 ...
- 581
3
votes
Accepted
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{...
- 52.3k
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 ...
- 1,432
3
votes
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 ...
- 30.3k
3
votes
Accepted
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 ...
- 52.3k
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 ...
- 2,367
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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 ...
glS♦
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2
votes
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 ...
- 13.1k
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
Accepted
In the amplitude amplification algorithm in Nielsen and Chuang's book, why is the error probability $M/N$?
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^{\...
- 2,782
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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 ...
- 2,633
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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 ...
- 13.1k
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 ...
- 78
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
...
- 2,633
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 <...
- 619
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, ...
- 2,194
2
votes
Accepted
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 ...
- 2,258
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 $\theta_i$ ...
- 873
1
vote
Computing the CDF with QAE in Qiskit
I had to exchange len(qr_state) with num_uncertainty_qubits in the code you posted
...
- 2,633
1
vote
Accepted
Computing the CDF with QAE in Qiskit
I think it would be also useful to see your Quantum Circuit using %matplotlib inline
and qc.draw('mpl') to see whether all gates ...
- 56
1
vote
Computing the CDF with QAE in Qiskit
I am also working with IterativeAmplitudeEstimation in qiskit. I was able to run QAE for 'Credit Analysis with Quantum Computing'...
- 56
1
vote
Accepted
In amplitude amplification, isn't the speedup hindered by the realization of $S_o$?
No, not at all. Barenco et al.'s work is primarily saying that for certain specific gates (the multi-controlled phase gate, as required for $S_0$, being one), you can construct them in a time that is ...
- 52.3k
Only top scored, non community-wiki answers of a minimum length are eligible