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# Tag Info

### What could be the possible future applications for HHL algorithm?

A couple years ago it was shown in Quantum algorithms and the finite element method by Montanaro and Pallister that the HHL algorithm could be applied to the Finite Element Method (FEM) which is a "...
• 1,626
Accepted

### Quantum phase estimation and HHL algorithm - knowledge of eigenvalues required?

You should know a bound on the eigenvalues (both upper and lower). As you say, you can then normalise $A$ by rescaling $t$. Indeed, you should do this to get the most accurate estimate possible, ...
• 58.7k
Accepted

• 13.9k
Accepted

### Quantum algorithm for linear systems of equations (HHL09): Step 2 - What is $|\Psi_0\rangle$?

1. Definitions Names and symbols used in this answer follow the ones defined in Quantum linear systems algorithms: a primer (Dervovic, Herbster, Mountney, Severini, Usher & Wossnig, 2018). A ...
• 4,987

### Quantum circuit to implement matrix exponential

There is actually a nice way to do this in Qiskit, since it has decompositions for single-qubit unitaries built in. The QuantumCircuit.squ method takes a unitary ...
• 2,933

### Problem with HHL algorithm on Qiskit

These aren't error messages, they are just outputs. The first message simply means it will be using your credentials for the session. This has probably popped up because you have run ...
• 3,251
Accepted

### Quantum algorithm for linear systems of equations (HHL09): Step 1 - Confusion regarding the usage of phase estimation algorithm

It depends on the papers but I saw 2 approaches: In most of the papers I read about the HHL algorithm and its implementation, the Hamiltonian evolution time $t$ is taken such that this factor ...
• 4,987
Accepted

### Solving linear systems represented by NxN matrices with N not power of 2

This is indeed a correct way to solve linear systems with dimension not equal to a power of 2. Solve the smallest possible system of dimension 2$^n$ that contains the system you want to solve, and pad ...
Accepted

### Practical implementation of Hamiltonian Evolution

I don't know why/how the authors of that paper do what they do. However, here's how I'd go about it for this special case (and it is a very special case): You can write the Hamiltonian as a Pauli ...
• 58.7k
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• 58.7k