  The Kitaev surface-code model is the most studied example of a topologically
ordered phase and typically involves four-spin interactions on a
two-dimensional surface. A universal signature of this phase is topological
entanglement entropy (TEE), but due to low signal to noise, it is extremely
difficult to observe in these systems, and one usually resorts to measuring
anyonic statistics of excitations or non-local string operators to reveal the
order. We describe a continuous-variable analog to the surface code using
quantum harmonic oscillators on a two-dimensional lattice, which has the
distinctive property of needing only two-body nearest-neighbor interactions for
its creation. Though such a model is gapless, satisfies an area law, and the
ground state can be simply prepared by measurements on a finitely squeezed and
gapped two-dimensional cluster state, which does not have topological order.
Asymptotically, the TEE grows linearly with the squeezing parameter, and we
show that its mixed-state generalization, the topological mutual information,
is robust to some forms of state preparation error and can be detected simply
using single-mode quadrature measurements. Finally, we discuss scalable
implementation of these methods using optical and circuit-QED technology.
