  We propose a scheme for parameter estimation with cluster states. We find
that phase estimation with cluster states under a many-body Hamiltonian and
separable measurements leads to a precision at the Heisenberg limit. As noise
models we study the dephasing, depolarizing, and pure damping channels.
Decoherence reduces the sensitivity but our scheme remains superior over
several reference schemes with states such as maximally entangled states and
product states. For small cluster states and fixed evolution times it remains
at the Heisenberg limit for approximately 2 times as many qubits than
alternative schemes.
