Hamiltonian Simulation
The Hamiltonian is a very important concept in physics, especially in classical mechanics and quantum mechanics. It represents the total energy of a system (kinetic energy + potential energy). In other words, it is an expression of the total energy of a system and can describe the time evolution of the system.
From the perspective of our high school(here we only consider the gravity potential) $$ H=mgh+\frac{1}{2}mv^2 $$ Actually, the Hamiltonian itself is to express the classical machanics, but then people use it express something like graviational field, electromagnetic field and even quantum field theory.
