  We show that, for even n, evolving n qubits according to a simple Hamiltonian
can be used to exactly implement an (n+1)-qubit parity gate, which is
equivalent in constant depth to an (n+1)-qubit fanout gate. We also observe
that evolving the Hamiltonian for three qubits results in an
inversion-on-three-way-equality gate, which together with single-qubit
operations is universal for quantum computation.
