**Efficient algorithms for simulating general dynamics on a quantum computer**

Feynman motivated the quantum computer as an efficient tool for simulating the dynamics of general quantum systems. I will discuss what it means to be both "efficient" and "general" and show that a quantum computer can simulate evolution of a system representable by n qubits over time t with a cost that is almost linear in t (and can't be sublinear, hence optimal) and almost constant in n (really log*n, which probably never exceeds 5 in our universe).