We introduce three compact graph states that can be used to perform a measurement-based Toffoli gate. Given a weighted graph of six, seven, or eight qubits, we show that success probabilities of $1∕4$, $1∕2$, and 1, respectively, can be achieved. Our study puts a measurement-based version of this important quantum logic gate within the reach of current experiments. As the graphs are setup independent, they could be realized in a variety of systems, including linear optics and ion traps.
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Tame et al. (2009) studied this question.
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