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.

Filter by
Sorted by
Tagged with
1 vote
0 answers
12 views

What is the implementation of AQE on classic?

I want run the HHL, but if the matrices are big, I need to use HHL hybrid, but I was not able to found an implementation or pseudo algorithm of AQE or HHL hybrid. Can anyone help me, please?
user avatar
2 votes
1 answer
51 views

HHL for non power of 2 matrix

I'm trying to see how HHL does on a series of matrices coming from a linear problem I'm interested in. These matrices are always square, real, and symmteric. They are not, however, very often exactly ...
user avatar
0 votes
0 answers
13 views

HHL: What are those xor's for in the ancilla rotation

I'm working my way through the HHL algorithm. Several text books and also the reference Cirq Implementation perform an xor computation to determine where to place X-gates. I'm confused by both the ...
user avatar
  • 339
4 votes
1 answer
90 views

Representation of a vector in the HHL algorithm

Reading about the HHL algorithm, which is used to solve the equation $Ax=b$, on Wikipedia, they say to represent $b$ as $|b\rangle=\sum_{i \mathop =1}^N b_i|i\rangle.$ I'm assuming $b$ is a vector ...
user avatar
  • 43
2 votes
0 answers
29 views

How to extract solution from HHL statevector on qskit?

I want to extract the HHL solution from the StateVector. I am doing this on a $4\times4$ matrix. For a $2$ by $2$ the solution is available in the StateVector $8$, $9$. However for a $4$ by $4$ matrix ...
user avatar
3 votes
1 answer
80 views

Is it possible to compute a matrix inverse for an arbitrary matrix within a subroutine?

Suppose I want solve a lower diagonal linear system of equations given in block form by $ \left( {\begin{array}{cccc} I & 0 & \cdots & 0 &0\\ M & I & \cdots & 0 &...
user avatar
1 vote
2 answers
77 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 ...
user avatar
0 votes
0 answers
36 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 ...
user avatar
3 votes
0 answers
93 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?
user avatar
  • 37
3 votes
1 answer
62 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 $|x\rangle$...
user avatar
1 vote
0 answers
29 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.
user avatar
  • 131
0 votes
0 answers
30 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?
user avatar
  • 37
4 votes
1 answer
175 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]] ...
user avatar
1 vote
1 answer
208 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 ...
user avatar
3 votes
1 answer
98 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 ...
user avatar
2 votes
0 answers
42 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 ...
user avatar
  • 107
6 votes
0 answers
191 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 ...
user avatar
5 votes
0 answers
76 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 $...
user avatar
  • 183
3 votes
1 answer
124 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 ...
user avatar
3 votes
0 answers
55 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, ...
user avatar
  • 118
1 vote
1 answer
173 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 ...
user avatar
  • 118
2 votes
2 answers
251 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(\...
user avatar
  • 185
5 votes
1 answer
117 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 ...
user avatar
3 votes
1 answer
126 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 ...
user avatar
  • 183
3 votes
2 answers
180 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.
user avatar
  • 183
5 votes
1 answer
412 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 ...
user avatar
  • 183
1 vote
0 answers
105 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 ...
user avatar
  • 183
9 votes
2 answers
268 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 ...
user avatar
  • 185
3 votes
1 answer
200 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 ...
user avatar
1 vote
0 answers
62 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 $$ A=\begin{pmatrix} -\frac{1}{3} & 1 \\ 1 & -\frac{1}{3} \end{pmatrix} \,\,\,\, b=\begin{pmatrix} 0 \\ 1 \end{pmatrix}. $$ ...
user avatar
3 votes
1 answer
104 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 $U$ ...
user avatar
  • 185
4 votes
1 answer
218 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 ...
user avatar
3 votes
1 answer
104 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 ...
user avatar
  • 181
-3 votes
1 answer
69 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 ...
user avatar
9 votes
2 answers
169 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 ...
user avatar
3 votes
1 answer
264 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 ...
user avatar
4 votes
1 answer
295 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, ...
user avatar
  • 185
8 votes
1 answer
136 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 $...
user avatar
2 votes
1 answer
190 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 ...
user avatar
  • 1,380
0 votes
1 answer
140 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. ...
user avatar
4 votes
0 answers
44 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 ...
user avatar
2 votes
0 answers
119 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 ...
user avatar
1 vote
1 answer
118 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 ...
user avatar
1 vote
0 answers
188 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 ...
user avatar
2 votes
1 answer
280 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 \...
user avatar
1 vote
1 answer
245 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 ...
user avatar
2 votes
1 answer
59 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 ...
user avatar
3 votes
1 answer
128 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 ...
user avatar
10 votes
0 answers
194 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 ...
user avatar
  • 7,042
3 votes
0 answers
168 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 ...
user avatar