# 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.

38 questions with no upvoted or accepted answers
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### 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 ...
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316 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 ...
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• 319
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### 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 ...
213 views

### Running HHL tutorial on real backend

I tried to follow the HHL tutorial. Since the 8x8 problem is not realistically simulable (I stopped after a few minutes), I tried to make it run on another backend, starting on the easiest example: <...
• 116
1 vote
45 views

### What is the intuition behind achieving Quantum advantage in simulating non-hermitian dynamics using Quantum computer?

There have been several works on simulating ODE for classical systems like here and here. They are quantum techniques to solve the ODE related to classical systems. A generic methodology is: To solve ...
• 520
1 vote
49 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 $[0.5, 0.2, 0.3, 0.6]$ ...
• 33
1 vote
107 views

### HHL phase estimation step

I have got an HHL circuit that looks as follows: In the phase estimation part we are trying to find the eigenvalues of the matrix A. But what is the role of the piece of circuit hightlighted below? ...
1 vote
157 views

### Amplitude Amplification applied to HHL Algorithm

I’m trying to understand and implement the amplitude amplification algorithm described in the HHL paper. I’m using the cirq implementation of the HHL algorithm as my starting point. I have a couple of ...
1 vote
115 views

### Changing the eigenvalues used in HHL algorithm

For an HHL algorithm implemented exactly as depicted in Figure 2 of this paper by Dutta et. al (https://arxiv.org/abs/1811.01726), how do I go about changing the eigenvalues that they use? Obviously, ...
1 vote
60 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. Any solution?
1 vote
51 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.
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1 vote
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### 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 ...
• 303
1 vote
339 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 ...
• 339
1 vote
44 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–...
1 vote