Contents
Is the HHL algorithm suitable for a quantum simulator?
For the quantum simulator, Qiskit already provides an implementation of the HHL algorithm requiring only the matrix A and | b⟩ as inputs in the simplest example. Although we can give the algorithm a general Hermitian matrix and an arbitrary initial state as NumPy arrays, in these cases the quantum algorithm will not achieve an exponential speedup.
When to use HHL to calculate running time?
The HHL is a quantum algorithm to estimate a function of the solution with running time complexity of O(log(N)s2κ2/ϵ) O (log (N) s 2 κ 2 / ϵ) (#hhl) when A A is a Hermitian matrix under the assumptions of efficient oracles for loading the data, Hamiltonian simulation and computing a function of the solution.
How is the HHL algorithm different from the classical algorithm?
This is an exponential speed up in the size of the system, however one crucial remark to keep in mind is that the classical algorithm returns the full solution, while the HHL can only approximate functions of the solution vector. 2. The HHL algorithm A. Some mathematical background
Why is less than lambda / 4 length required for impedance transformation?
From Microwave point of view: prove that less than lambda/4 length required for impedance transformation (inductive to capacitive and vice versa) in left handed/metatransmission lines? Can it be proved from the impedance graphs for short and open circuit RH and LH transmission lines?
Do you need previous knowledge of HHL algorithm?
For the purpose of illustrating the algorithm, we will cheat a bit and calculate the eigenvalues of AA to be able to choose tt to obtain an exact binary representation of the rescaled eigenvalues in the nlnl -register. However, keep in mind that for the HHL algorithm implementation one does not need previous knowledge of the eigenvalues.
Which is the running time complexity of HHL?
The HHL is a quantum algorithm to estimate a function of the solution with running time complexity of O(log(N)s2κ2 / ϵ)O(log(N)s2κ2/ϵ)[2] (#hhl) when AA is a Hermitian matrix under the assumptions of efficient oracles for loading the data, Hamiltonian simulation and computing a function of the solution.
What are the prerequisites for a Qiskit textbook?
Prerequisites 1. Quantum States and Qubits 2. Multiple Qubits and Entanglement 3. Quantum Protocols and Quantum Algorithms 4. Quantum Algorithms for Applications 5. Investigating Quantum Hardware Using Quantum Circuits 6. Investigating Quantum Hardware Using Microwave Pulses 7. Quantum Computing Labs Lab 1. Quantum Circuits Lab 2.
How is the HHL algorithm implemented in Qiskit?
In this tutorial, we introduce the HHL algorithm, derive the circuit, and implement it using Qiskit. We show how to run the HHL on a simulator and on a five qubit device. 1. Introduction
What kind of matrix do you need for HHL?
For the quantum simulator, Qiskit Aqua already provides an implementation of the HHL algorithm requiring the matrix A A and |b⟩ | b ⟩ as basic inputs. The main advantage is that it can take a general Hermitian matrix and an arbitrary initial state as inputs.
How to use Cirq in a quantum algorithm?
Use Cirq for intermediate-level subroutines and algorithms. Use the variational quantum eigensolver to find the ground state of the Ising model. Use a quantum computer to find approximately optimal cuts in a graph. Demonstration of classical and quantum random walks on a graph. Utilize Cirq features to implement advanced quantum algorithms.