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We present a translation from the standard network model of quantum computation to the one-way model of quantum computation. The translation is compositional, i.e., it preserves the structure of computations, which allows us to abstract the concrete realizations in a monadic abstraction layer. We briefly review the By-Product and Measurement Calculus approaches to combining circuits in the one-way model, and show how the procedures can be expressed in the exact same notation, bearing a directdoi:10.1016/j.entcs.2011.01.018 fatcat:b4fxpuknhrhodk6sbwpmxyfnmm