# 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.

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### 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?
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### Confusing notation in Block-Encoding

I'm reading the lecture notes from Ronald de Wolf and got confused at the part where it introduces Block encoding, specifically by this notation at page 76: More generally we can define an $a$-qubit ...
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### Simulation of algorithms with QFT on a classical computer

In paper The Quantum Fourier Transform Has Small Entanglement the authors showed that strong entanglement of qubits caused by QFT comes mainly from ordering the qubits. QFT itself prepares only weak ...
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### HHL algorithm: how running the process $N$ times gives the vector components of the solution?

In the HHL paper the authors have mentioned that if the user wants to get all the components of vector $\vec{x}$, one needs to run the process at least $N$ times, where $N$ is the dimension of the ...
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### What useful information can be efficiently extracted from solutions provided by the HHL-algorithm?

The result of the HHL-algorithm is the (amplitude-encoded) solution vector $|x\rangle$. I was wondering, which useful information could be extracted from this solution without loosing the algorithms ...
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### 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
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### 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, ...
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### Implementation of conditional Rotation on ancilla qubit in HHL

In HHL algorithm, after we have encoded the eigenvalues onto the clock register qubits, we apply conditional rotation on ancilla qubit such that it changes from $|0\rangle$ to: To achieve this ...
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### I think I’m having endianness problems replicating the results of this paper?

So I am trying to implement the HHL algorithm depicted in this paper titled 'Quantum Circuit Design for Solving Linear Systems of Equations' by Cao et. al (https://arxiv.org/abs/1110.2232v2), but if I ...
1 vote
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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, ...
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1 vote
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### 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 ...
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### 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 ...
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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 ...