# Hamiltonian simulation in quantum computation

What is the goal of Hamiltonian simulation?

Is it going to simulate a quantum system on a classical computer or quantum computer or none of them?

What is the relationship between a quantum algorithm and the Hamiltonian simulation?

• Hi Ramim! Welcome to QCSE! What have you researched, what is the background of your question? Can you edit your question to provide motivation for why you are asking, even if it's idle curiosity? – Mark S Jun 22 '19 at 12:56

If we have a certain quantum system which is in a state $$|\psi\rangle$$ and has a Hamiltonian $$H$$, then if we look at the state after a time $$t$$ it will have evolved to $$|\psi_t\rangle = e^{it H}|\psi\rangle$$. The goal of Hamiltonian simulation is to answer some questions about $$|\psi_t\rangle$$ given a (usually simple) input state $$|psi\rangle$$, Hamiltonian $$H$$ and time $$t$$.