In one-way quantum computation model (1WQC), the quantum correlations in an entangled state, called a cluster state or graph state, are used to perform universal quantum computations using single-qubit measurements. In 1WQC, the computations are shown by measurement pat
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In one-way quantum computation model (1WQC), the quantum correlations in an entangled state, called a cluster state or graph state, are used to perform universal quantum computations using single-qubit measurements. In 1WQC, the computations are shown by measurement patterns or simply patterns. The synthesis problem in the 1WQC model is defined as extracting the pattern from a given arbitrary unitary matrix. The important criteria in evaluating measurement patterns in the 1WQC model, are the size, the depth and the number of entanglements of the pattern. In this paper, a new approach is proposed to synthesize controlled-unitary U gates where U is a single-qubit gate. To this end, for the first time, the idea of applying the extended measurement calculus, which utilizes the measurements in different Bloch sphere planes, is used in the synthesis of the 1WQC model. Some optimizations are proposed for this method and a new approach is presented to synthesize controlled-U gates for the 1WQC model which improves the evaluation criteria of size, depth and the number of entanglements in this model as compared to the best previous result by 9.1%, 30% and 18.1%, respectively.
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