**Quantum computer simulations of time dependent Hamiltonians**

In 1982, Feynman suggested a quantum computer would efficiently simulate quantum systems and illustrated this concept with Heisenberg chains (Int. J. Theor. Phys, 21, 467), which are difficult to solve on a classical computer. Since then a number of sophisticated quantum simulation schemes have been created to simulate time independent Hamiltonians, but to date only simplistic simulation schemes have been proposed for simulating time dependent Hamiltonians.
In this talk I will present a sophisticated quantum algorithm that can simulate the evolution of a sufficiently smooth and sparse time dependent Hamiltonian, which uses a number of gate operations that is comparable to the best known simulation schemes for time independent Hamiltonians. Applications of this algorithm to simulating Hamiltonian based quantum computing schemes in the circuit model (such as adiabatic quantum computing) will also be discussed.