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.

133 questions
Filter by
Sorted by
Tagged with
62 views

Optimal dependency of HHL (or any QLSP) algorithm on condition number $\kappa$

This is conserning the optimal dependency on condition number for Quantum linear system problem (QLSP). For solving QLSP, the HHL (algorithm) paper mentions any polylog($\kappa$) quantum algorihm ...
74 views

What is the total number of qubits required for the Harrow-Hassidim-Lloyd algorithm?

I am fairly new to Quantum Computing and I know a bit of Linear Algebra. I am currently working on the HHL algorithm, I'm having confusion as to how many qubits are actually required in the circuit ...
382 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 ...
3k views

What could be the possible future applications for HHL algorithm?

Note on the vocabulary: the word "hamiltonian" is used in this question to speak about hermitian matrices. The HHL algorithm seems to be an active subject of research in the field of quantum ...
758 views

Implementation of matrix A in HHL algorithm circuit

In HHL algorithm, how do we implement matrix $A$ (where $A|x\rangle = |b\rangle$) in the circuit?
1 vote
177 views

No module named 'qiskit.algorithms.linear_solvers'

I am trying to execute HHL algorithm. I referred to the code from https://quantumpedia.uk/quantum-algorithm-4-hhl-algorithm-for-linear-systems-of-equations-40619daec41d. I tried implementing all the ...
100 views

HHL for the pseudoinverse in Qiskit

The HHL algorithm can be modified to compute the pseudoinverse of $A$ as is shown here and here. Is there anyway to do this in Qiskit without coding the entire thing manually?
49 views

How to estimate the negative amplitude of multiple qubits?

The probability of measurement is the square of amplitude. After measurement, how to guess the original amplitude of state?? For example, in linear problem, we would like to know the exact solution, ...
1 vote
31 views

Can I get valid solution with HHL algorithm even if the QPE is not completely correct?

Can I get the valid solution of linear problem using HHL algorithm even if the QPE is not completely correct? My example is $A=diag(0.5, 0.2, 0.3, 0.6)$, so the solution is $[0.5, 0.2, 0.3, 0.6]$ ...
400 views

128 views

210 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 ...
174 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 ...
75 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 ...
1 vote
224 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 ...
226 views

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 $... 1 vote 0 answers 49 views Plots of the result for the qiskit HHL tutorial Could anyone make explicit the code which gives the two plots at the end of the HHL tutorial. They show the results of the jobs on a real IBM quantum device. 4 votes 0 answers 124 views Is the exponential speedup and output$\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$without losing the exponential speedup? 3 votes 1 answer 132 views Which observable$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$... 5 votes 1 answer 459 views HHL algorithm, How can I get result from register$|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 ...