  A translation-invariant gapped local Hamiltonian is in the trivial phase if
it can be connected to a completely decoupled Hamiltonian with a smooth path of
translation-invariant gapped local Hamiltonians. For the ground state of such a
Hamiltonian, we show that the expectation value of a local observable can be
computed in time $\text{poly}(1/\delta)$ in one spatial dimension and
$e^{\text{poly}\log(1/\delta)}$ in two and higher dimensions, where $\delta$ is
the desired (additive) accuracy. The algorithm applies to systems of finite
size and in the thermodynamic limit. It only assumes the existence but not any
knowledge of the path.
