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We show that universal parity quantum computing employing a recently introduced constant depth decoding procedure is equivalent to measurement-based quantum computation (MBQC) on a bipartite graph using only yz-plane measurements. We further show that unitary MBQC using only yz-plane measurements must occur on a bipartite graph. These results have a number of consequences and open new research avenues for both frameworks. Published by the American Physical Society 2024
Smith et al. (Tue,) studied this question.