Hamiltonian is the basic building block for VQE algorithm. Basically, we try to minimize the expectation of the Hamiltonian to find the lowest eigenvalue of the Hamiltonian matrix which is apparently very useful for many problems ranging from chemistry to finance.
Find more details on:
Did you have a look to the following chapters in the Qiskit Textbook?
Simulating Molecules using VQE:
Variational Quantum Linear Solver:
Qiskit has an optimization module and you can find tutorials that illustrate its functionality here.
To solve the example you posted, e.g., with the Quantum Approximate Optimization Algorithm (QAOA), you can do the following:
from qiskit import Aer
from qiskit.optimization import QuadraticProgram
from qiskit.aqua.algorithms import QAOA
I'm not sure if the 286 qubit estimate has ever been fully explained, but we can backwards reason about how to get to the figure.
First off, accuracy of quantum chemistry simulations via Trotterization is a function of the basis set (in both classical and quantum simulations). The basis set is kinda like a coordinatization the electron orbitals. There are a ...