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One-way measurement based quantum computations (1WQC) may describe unitarytransformations, via a composition of CPTP maps which are not all unitarythemselves. This motivates the following decision problems: Is it possible todetermine whether a ``quantum-to-quantum'' 1WQC procedure (having non-trivialinput and output subsystems) performs a unitary transformation? Is it possibleto describe precisely how such computations transform quantum states, bytranslation to a quantum circuit of comparable complexity? In this article, wepresent an efficient algorithm for transforming certain families ofmeasurement-based computations into a reasonable unitary circuit model, inparticular without employing the principle of deferred measurement.

Unitary-circuit semantics for measurement-based computations