User:Ketulmehta22/sandbox

Quantum Simulation
One of the original motivations for Quantum Computing, by Richard Feynman was to perform simulation of quantum systems. Simulations have different interpretations in the Quantum context. One of them being performing the time evolution under some Hamiltonian (H).

$$|\psi(t)>=\exp(-iHt/h)|\psi(0)>$$. Another common interpretation is to find the ground state of a given Hamiltonian.

There are two kind of Quantum simulators:


 * 1) Analog Simulators (also called Quantum emulators): They directly mimic the desired Hamiiltonian, with a system that is more controllable experimentally. The main disadvantage of this approach is that if the quantum simulator doesn't have the same form of H as desired than it become difficult to run the simulation. Additionally, the method is prone to analog errors, and thus no error correction is possible.
 * 2) Digital Simulators: Its the method of running algorithms on the Quantum computer. The main advantage of this method is that, its in some way Universal as it can simulate any Hamiltonian. Additionally, the method lends itself well to Quantum Error Correction.