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)

Filter by
Sorted by
Tagged with
2
votes
0answers
36 views

How to understand picking a random subcube in the Aaronson/Ambainis spatial search algorithm?

I am referring to the Quantum Search of Spatial Regions paper. I must confess that the paper itself is a bit heavy for my level of mathematical fluency. Trying to understand it nevertheless and having ...
5
votes
1answer
119 views

BHT algorithm implementation

Summary of Method Amplitude Amplification Summary The BHT algorithm uses amplitude amplification, a nice generalisation of Grover's algorithm, where there is a subset $G\subset X$ of good elements in ...
2
votes
1answer
84 views

Noise-induced amplitude amplification?

I wanted to share some results from an experiment which I find thought were deeply surprising. The basic idea is to prepare a superposition in a main register then conditionally apply lots of random ...
0
votes
0answers
52 views

How does the amplitude amplification in Grover's algorithm work?

As the question says - how does the amplitude amplification in Grover's algorithm work? I am fine with adding the negative phase on the winning state, but how does one generate the diffuser to ...
2
votes
0answers
29 views

Managing memory while running a high depth circuit simulation (amplitude amplification) using Qiskit

I am running an instance of amplitude amplification using Qiskit (v 26) on Google Colab. The circuit is approximately 17 qubits in space and $O(ck)$ in depth where $k \in \left \{1,2,3....,22 \right \...
2
votes
1answer
67 views

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^{\...
2
votes
1answer
53 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 ...
2
votes
1answer
61 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 ...
1
vote
0answers
88 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 ...
0
votes
1answer
75 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?
4
votes
2answers
138 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 ...
4
votes
1answer
74 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 ...
3
votes
0answers
32 views

Is it possible to nest quantum Markov chain Monte Carlo, mean and minimum algorithms?

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 ...
2
votes
3answers
209 views

Computing the CDF with QAE in Qiskit

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 ...
2
votes
0answers
64 views

A question about Grover's paper "Fixed-Point Quantum Search"

I am reading Grover's paper "Fixed-Point Quantum Search," (arXiv version with a different name) which improves on his earlier quantum research algorithm. However, I'm having difficulty in ...
2
votes
1answer
88 views

Is Grover's algorithm only applicable to a pure state?

I've been trying to perform Grover's algorithm on entangled states, e.g. $|00\rangle + |11\rangle$. However, the algorithm apparently doesn't seem to amplify the amplitude of the state $|11\rangle$ ...
2
votes
1answer
40 views

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 ...
2
votes
2answers
33 views

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 ...
3
votes
0answers
32 views

Amplitude estimation over subspace of problem

I've been searching about quantum amplitude estimation techniques and read that it is customary to use an extra qubit to separate good and bad states using algorithm $A$ as $$ A|{0} \rangle^{\otimes^{...
1
vote
1answer
38 views

Alternative Grover's Diffuse Operator [duplicate]

I was wondering if there is any good references where I could read to understand the construction of Unitary Operators such as the Diffuse Operator in Grover's Algorithm. I am looking to build my own ...
3
votes
2answers
108 views

Lemma 1 in the paper by Brassard, Hoyer, Tapp (1998) on Quantum counting

In the paper by Brassard, Hoyer, Tapp (1998) on Quantum Counting we have the following expression for the state: $$|Y\rangle =\sum_{i\in\mathbb{Z}}x_i|i\rangle |Y_i\rangle.$$ Now we have a quantum ...
3
votes
1answer
167 views

How to define Q-operator in Quantum Amplitude Estimation

I'm trying to implement a circuit for Quantum Amplitude Estimation in Qiskit using elementary gates. I have created the circuit that represent my algorithm $A$ but now from the theory I know that I ...
1
vote
0answers
45 views

Amplitude amplification for known state but unknown amplitude

I have a circuit that prepares a state $|s\rangle$ which is a superposition of the basis states $$\sum_{x=0}^{2^{n-1}}\alpha_x|x\rangle$$ with amplitude $\alpha_x$ for a circuit of $n$ qubits. ...
7
votes
1answer
434 views

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 ...
4
votes
3answers
177 views

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 ...
5
votes
1answer
104 views

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 ...
1
vote
1answer
292 views

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 ...
2
votes
1answer
55 views

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 ...
4
votes
1answer
283 views

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 ...
3
votes
2answers
60 views

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 ...
2
votes
3answers
202 views

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 ...
3
votes
2answers
85 views

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 ...
2
votes
1answer
278 views

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 ...
3
votes
0answers
63 views

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 ...
6
votes
1answer
125 views

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 (...
7
votes
2answers
728 views

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

I am relatively new to quantum computing and I feel like I don't fully understand the power of quantum computing due to a lack of understanding of how amplitude amplification works. What is ...