  We present a Hamiltonian quantum computation scheme universal for quantum
computation (BQP). Our Hamiltonian is a sum of a polynomial number (in the
number of gates L in the quantum circuit) of time-independent, constant-norm,
2-local qubit-qubit interaction terms. Furthermore, each qubit in the system
interacts only with a constant number of other qubits. The computer runs in
three steps - starts in a simple initial product-state, evolves it for time of
order L^2 (up to logarithmic factors) and wraps up with a two-qubit
measurement. Our model differs from the previous universal 2-local Hamiltonian
constructions in that it does not use perturbation gadgets, does not need large
energy penalties in the Hamiltonian and does not need to run slowly to ensure
adiabatic evolution.
