Questions tagged [hhl-algorithm]
For questions related to the quantum algorithm for inverting linear systems of equations, developed by Harrow, Hassidim and Lloyd in 2009.
102
questions
1
vote
2answers
39 views
How to extract a solution to HHL from the full statevector?
I am having a difficult time trying to extract an HHL matrix inversion solution from the full system statevector.
I have a 32x32 size matrix A and a 32x1 vector b, and I ran HHL on 13 qubits. HHL ...
0
votes
0answers
29 views
How to perform controlled rotations similar to what is done in HHL
How does one do the conditional rotation based on a binary encoding of the input? The rotation of D_i^t has to be done in the image below and I know that similar rotations can also be found in HHL and ...
2
votes
0answers
73 views
Is the exponential speedup and output $\langle x|M|x\rangle$ in contradiction in HHL algorithm?
Isn't the exponential speedup and the output $\langle x|M|x\rangle$ in contradiction in HHL algorithm? How can we print the solution vector $|x\rangle$ without losing the exponential speedup?
2
votes
1answer
54 views
Which observable $M$ provides the Absolute Average of a statevector?
My question should be fairly simple, though I did not find an answer to it here or anywhere else.
I have been working on an algorithm which, similarly to the HHL algorithm, provides a state $|x\rangle$...
1
vote
0answers
25 views
Plots of the result for the qiskit HHL tutorial
Could anyone make explicit the code which gives the two plots at the end of the HHL tutorial. They show the results of the jobs on a real IBM quantum device.
0
votes
0answers
24 views
In the HHL algorithm, does the controlled unitary depend on the Hermitian matrix coefficients?
In HHL algorithm, does the controlled unitary (Hamiltonian simulation part of Quantum phase estimation) depend on Hermitian matrix coefficients and how?
3
votes
1answer
136 views
HHL - the result is correct for one matrix but wrong for another one
I tried to run HHL algorithm in new version of Qiskit (0.29). Firstly I tried to solve a diagonal system 4x4 with matrix [[1,0,0,0],[0,2,0,0],[0,0,3,0],[0,0,0,4]] ...
1
vote
1answer
121 views
"Classical" phase estimation versus iterative phase estimation
In the article Arbitrary accuracy iterative phase estimation algorithm as a two qubit benchmark, the authors introduced implementation of phase estimation with two qubits only. The trick that bits ...
2
votes
1answer
76 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 ...
1
vote
0answers
36 views
Difference in HLL applications
I am new to Qiskit and I have seen two types of simple 2X2 $Ax=b$ system solutions. I am wondering what the difference is exactly. They both occur on a simulator backend, but the first gives me a ...
6
votes
0answers
151 views
Solving linear system $Ax=b$ with exponential speed-up via binary optimization?
The main disadvantage of HHL algorithm for solving $A|x\rangle = |b\rangle$ is that exponential speed-up is reached only in case we are interested in value $\langle x|M|x\rangle$, where $M$ is a ...
5
votes
0answers
61 views
What is the largest linear system of equations solved using HHL experimentally?
Can someone tell what is the largest system of equations solved using HHL algorithm experimentally?
I know the $8$ x $8$ system has been solved experimentally. Has someone gone beyond this to solve $...
3
votes
1answer
88 views
HHL algorithm for linear systems with a real matrix and a real right side
HHL algorithm can be used for solving linear system $A|x\rangle=|b\rangle$. If we put $|b\rangle$ (to be precise its normalized version) into the algorithm and measuring ancilla to be $|1\rangle$ we ...
3
votes
0answers
51 views
What are the correct eigenvalues to use in controlled rotation in HHL?
I'm studying the HHL algorithm from the qiskit textbook, but I don't understand what $\lambda$ we have to use. If my matrix $A$ has eigenvalues that can be written in a binary representation, then, ...
1
vote
1answer
156 views
In the HHL alghoritm, how can I transform my hermitian matrix into a unitary operator?
I'm studying the HHL algorithm and I'm trying to do an his implementation but, there are some points that I don't understand how I can transform my hermitian Matrix into its unitary operator?
In ...
2
votes
2answers
203 views
Question on qiskit.circuit.library.PiecewiseChebyshev Qiskit circuit library
This question follows the post https://quantumcomputing.stackexchange.com/posts/15070/.
I am working on an implementation of HHL algorithm, to do so, I need to map $|\lambda\rangle\mapsto |\arcsin(\...
4
votes
1answer
104 views
I don't understand unitary of ${e^{iAt}}$ from HHL algorithm
I tried to implement the following circuit in the image below but with the red circled gates replaced with a unitary controlled ${e^{iAt/2}}$ and controlled ${e^{iAt/4}}$
The image came from this ...
2
votes
1answer
100 views
Function in Qiskit to get the quantum circuit
Is there any way to view the quantum circuit of pre implemented quantum algorithm in Qiskit?
In the Qiskit textbook, there is an example given for HHL algorithm. Is there any function in Qiskit which ...
3
votes
2answers
128 views
Source code for a Qiskit algorithm: HHL Algorithm
Is it possible to view the source code of one of the Qiskit's algorithm?
Actually, I am trying to find how Qiskit implements the HHL algorithm. I want to see the source code for this algorithm.
3
votes
1answer
273 views
Quantum Circuit for $e^{iAt}$ Hamiltonian Simulation in HHL algorithm
In HHL algorithm, there is a step in Quantum Phase Estimation where we have to apply powers of $e^{iAt}$ to the register (see pic). I am not able to understand how to find the quantum circuit ...
1
vote
0answers
75 views
In HHL algorithm, how to find the angle of rotation of ancilla qubits?
In HHL algorithm, after the quantum phase estimation, what is the angle of rotation i.e. what is the value of $\theta$ in R$_y$($\theta$) that is used in rotating ancilla qubit? How to find this angle ...
9
votes
2answers
237 views
Quantum implementation of arcsin
I am looking to implement a quantum version of the arcsinus function. Such a problem is motivated by the HHL algorithm where $x\mapsto 1/x$ and $\arcsin$ can be used to get $1/x$ from the ...
3
votes
1answer
142 views
HHL algorithm, How to implement exp(iAt) gates?
From this paper Quantum Circuit Design for Solving Linear Systems of Equations, in figure 4
The paper shows what inside operator $e^{-iAt}$ but didn't shows how to connect the control qubit (register ...
1
vote
0answers
57 views
Why does solving linear systems of equations with HHL return imaginary numbers? [closed]
The textbook shows an example system of linear equations $Ax=b$ with
$$
A=\begin{pmatrix}
-\frac{1}{3} & 1 \\
1 & -\frac{1}{3}
\end{pmatrix} \,\,\,\,
b=\begin{pmatrix}
0 \\
1
\end{pmatrix}.
$$
...
3
votes
1answer
94 views
Efficient QFT-based QPEA complexity
The HHL algorithm lies on an implementation of the Quantum Phase Estimation algorithm. One popular implementation is based on the Quantum Fourier Transform which can be divided in three steps. Let $U$ ...
4
votes
1answer
160 views
HHL algorithm, How can I get result from register $|b\rangle$?
From the paper A survey on HHL algorithm: From theory to application in quantum machine learning ,
I use qasm code from here.
I try to follow the example in page 7. with Ax = b
and
the answer x ...
3
votes
1answer
84 views
HHL and choice of observable for calculating the expectation value thereof
The chapter about solving linear systems in the qiskit textbook describes the last (6th) step of the HHL algorithm as follows
Apply an observable $M$ to calculate $F(x):=\langle x |M|x\rangle$.
How ...
-3
votes
1answer
64 views
Query on the HHL Algorithm in the Qiskit Aqua Library [closed]
This is a question regarding the Qiskit Aqua package. I have been studying HHL algorithm from QISKIT textbook and after understanding the math I finally got to the code part, I am having a hard time ...
8
votes
2answers
126 views
How to recover the normalization constant of the HHL solution
HHL solves the linear equation $Ax=b$ by the quantum state $|x\rangle=A^{-1} |b\rangle$. However, the quantum state $|x\rangle$ is normalized and thus diffs a normalization constant from the solution ...
3
votes
1answer
200 views
Gate-level implementation of Eigenvalue-Inversion in HHL
I am trying to understand how does the gate-level implementation of eigenvalue-inversion step in the HHL algorithm works.
I am following this reference, where it is stated (Lemma 4) that this can be ...
4
votes
1answer
255 views
How to effectively compute eigenvalue rotation in HHL
In the HHL algorithm, how do you efficiently do the $\lambda-$controlled rotation on the ancillary qubit ? It seems to me after reading around some answers that this can be done in two steps :
First, ...
8
votes
1answer
113 views
Why is HHL the popular choice to solve QLSP and not the Childs et al. (2017) algorithm?
The Childs, Kthari, and Rolando (2017) (CKS) algorithm can solve the quantum linear systems problem (QLSP) in $\operatorname{poly}(\log N, \log(1/\epsilon))$ time while the HHL algorithm solves it in $...
2
votes
1answer
164 views
Given a matrix, how do I proceed with the quantum phase estimation algorithm and choose $\theta$?
Given a matrix, say $\begin{bmatrix} 1.5 & 0.5\\
0.5& 1.5
\end{bmatrix}$, with eigenvalues $1$ and $2$, how do I proceed with the quantum phase estimation algorithm?
In particular, how do I ...
0
votes
1answer
129 views
Qiskit HHL algorithm BrokenProcessPool error
I try to run HHL algorithm on qasm_simulator. I took the example from here. I try to solve 8x8 random matrix and adjust some parameters in create_eigs.
...
4
votes
0answers
42 views
In the HHL algorithm, how large should the eigenvalue estimation register be?
In the HHL algorithm, we need to estimate the eigenvalues of a matrix $A$. The result is stored in a register with $l$ qubits. Let $T = 2^l$. $T$ cannot be too small, otherwise the result would have a ...
2
votes
0answers
97 views
HHL example solution on Qiskit
In the example on the Qiskit page (https://qiskit.org/textbook/ch-applications/hhl_tutorial.html#A.-Some-mathematical-background) section 3 for the HHL algorithm the author is trying to solve the ...
1
vote
1answer
104 views
How to increase matrix size and getting high fidelity for HHL algorithm in Qiskit?
I have followed an example that Qiskit provides here.
I tried to increase the matrix size to 16x16 and change num_ancillae and ...
1
vote
0answers
148 views
Implementing the HHL algorithm with negative eigenvalues (Cirq)
How do I implement the HHL with negative eigenvalues?
This paper (https://arxiv.org/abs/1803.01486) says that:
what if $\lambda<0$? This problem actually does not hard to solve, since we can ...
2
votes
1answer
238 views
Error when running HHL algorithm in Qiskit
I tried to solve a simple system of two simultaneous linear equations in with HHL algorithm in Qiskit. In particular the system is $Ax=b$, where
$$
A = \begin{pmatrix}
1.5 & 0.5 \\
0.5 & 1.5
\...
1
vote
1answer
192 views
How to optimize my HHL algorithm on qiskit?
I am following this HHL tutorial to solve the $Ax=b$ problem and have been using the general (inefficient) approach with the BasicAer simulator that they describe in section 4a. I would now like to ...
1
vote
1answer
54 views
How can I use the quantum volume to design the scale of my experiment?
I am designing an experiment which involves solving a linear system of equations of the form $Ax=b$. To do this, I am using the HHL algorithm on the IBMQ system. My experiment is scalable such that ...
3
votes
1answer
117 views
Is it required to input full matrix when using Qiskit HHL algorithm for sparse matrices?
I am working with a very sparse matrix and it seems inefficient to load the full matrix as input into the Qiskit HHL algorithm. Is it possible to input only the non-zero elements, instead ? I am ...
1
vote
0answers
61 views
Help Understanding Line in Source Code
In Qiskit's implementation of the HHL algorithm, they have the following line at the end of their code that allows them to compute the global phase we need to add on to the solution.
...
9
votes
0answers
183 views
Is HHL still BQP-complete when the matrix entries are only in {0,1}?
I'm studying BQP-completeness proofs of a number of interesting problems of Janzing and Wocjan, and Wocjan and Zhang. Janzing and Wocjan show that estimating entries of matrix powers $(A^m)_{ij}$ with ...
3
votes
0answers
129 views
Comparison of matrix inversion algorithms
Since 2009, many matrix inversion algorithms have appeared.
Is there somewhere a table, or recently released overview, comparing the speed of matrix inversion algorithms, like done in this table taken ...
1
vote
0answers
29 views
Using matrix inversion and summation together. How to compute $(A+B^{-1})^{-1}|x\rangle$
I need to compute $(A+B^{-1})^{-1}|x\rangle$, where A and B is hermitian for simplicity.
I read out about matrix inversion algorithms (HHL, QSVE,...), and algorithms of summing up of matrices(LCU, Lie–...
3
votes
1answer
186 views
Confusion regarding time complexity in the HHL algorithm
In the paper of HHL algorithm (Quantum algorithm for linear systems of equations), the time complexity of simulating $e^{i A t}$ for a hermitian matrix A is $\tilde{O}\left(\log (N) s^{2} t_0\right)$. ...
1
vote
0answers
74 views
Adding Quantum State Tomography Step to HHL Algorithm (Cirq)
Over the past month, I have been learning about the HHL algorithm and am interested in extending the Cirq implementation to include the quantum state tomography step to extract the amplitudes or ...
4
votes
1answer
171 views
How do I optimize HHL algorithm in Qiskit?
How do I optimize HHL algorithm in Qiskit?
I tried to follow this tutorial on HHL in Qiskit. My project requires solving a very specific type of linear equations $Ax=b$ like the one below.
...
2
votes
1answer
152 views
The maximum depth possible on quantum computers
I hope you don't mind me having two questions.
Firstly, I was running a Qiskit HHL simulation on a 12x12 matrix and a 12x1 vector, leading to a 16x16 matrix after expansion, and it resulted in a ...
