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Preparation of a CZ state on a four-qubit code in three steps. In the code-preparation step, the four-qubit code is prepared in the logical |+ +> state by measuring |+> with the S Z operator. We can use adaptive circuits or post-selection to correct for S Z = -1 outcomes. In the magic-state initialization step, we measure the W operator and post-select on the +1 outcome. In the final error-detection step, we identify the errors that may have occurred during preparation. We measure W a second time to identify if a measurement error occurred during the magic-state initialization step. We finally measure S X and S Z a second time to identify Pauli errors that may have occurred, and to determine if the initial S Z measurement gave a readout error.
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