  Continuous-variable (CV) cluster states are a universal quantum computing
platform that has experimentally out-scaled qubit platforms by orders of
magnitude. Room-temperature implementation of CV cluster states has been
achieved with quantum optics by using multimode squeezed Gaussian states. It
has also been proven that fault tolerance thresholds for CV quantum computing
can be reached at realistic squeezing levels. In this paper, we show that
standard approaches to design and characterize CV cluster states can miss
entanglement present in the system. Such hidden entanglement may be used to
increase the power of a quantum computer but it can also, if undetected, hinder
the successful implementation of a quantum algorithm. By a detailed analysis of
the structure of Gaussian states, we derive an algorithm that reveals hidden
entanglement in an arbitrary Gaussian state and optimizes its use for one-way
quantum computing.
