  In measurement-based quantum computing (MBQC), computation is carried out by
a sequence of measurements and corrections on an entangled state. Flow, and
related concepts, are powerful techniques for characterising the dependence of
the corrections on previous measurement results. We introduce flow-based
methods for quantum computation with continuous variables graph states, which
we call CV-flow. These are inspired by, but not equivalent to, the notions of
causal flow and g-flow for qubit MBQC. We also show that an MBQC with CV-flow
approximates a unitary arbitrarily well in the infinite-squeezing limit,
addressing issues of convergence which are unavoidable in the
infinite-dimensional setting. In developing our proofs, we provide a method for
converting a CV-MBQC computation into a circuit form, analogous to the circuit
extraction method of Miyazaki et al, and an efficient algorithm for finding
CV-flow when it exists based on the qubit version by Mhalla and Perdrix. Our
results and techniques naturally extend to the cases of MBQC for quantum
computation with qudits of prime local dimension.
