# Simulate Quantum Systems¶

As described previously, the original idea
of quantum computing rose as a solution to simulating quantum systems.
Feynman’s idea relied on the **digital quantum simulator**.

A second kind of simulators relies on the mapping of the simulated quantum system
onto a simulator system, and is called an **analog quantum simulator**.
The simulator is able to partly reproduce the dynamics of the simulated system,
forms a many-body model of it, and can be controlled to some extend. [citation needed]

Two major problems can be addressed:

**Computing the energy levels**of a quantum system’s: this requires an eigensolver for the Hamiltonian. This topic is covered in Quantum Chemistry.**Simulating Hamiltonian dynamics**: this requires the discretization of the Hamiltonian.

The former problem is essential to Quantum Chemistry:

“Perhaps the

**most important quantity**in quantum chemistry simulation is the**ground state**, which is the minimum energy eigenvector of the Hamiltonian matrix. This is because for most molecules at room temperature quantities such as**reaction rates**are dominated by free energy differences between quantum states that describe the beginning and end of a step in a reaction pathway and at room temperature such intermediate state are usually ground states.” 1

For the latter problem, two discretization methods may be applied 2:

…

**Notes:**

- 1
Hartree–Fock Theory in the Azure Quantum Documentation [M27].

- 2
Simulating Hamiltonian Dynamics in the Azure Quantum Documentation [M27].

**Further readings:**

*Quantum Simulation*[R8], complemented by*Quantum Simulators*[R2].Nature Physics Insight – Quantum Simulation, Nature 2012 (incl. [R5], [R3]).