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Adaptive quantum circuits employ unitary gates assisted by mid-circuit measurement, classical computation on the measurement outcome, and the conditional application of future unitary gates based on the result of the classical computation.
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We use the fairly standard definition that depth is the minimum number of required layers of two-qubit gates such that no layer contains gates having shared-support. Other definitions, for example in which single-qubit gates or measurement are included, would slightly change the code distance requirements for a 50% upper bound in the absence of feed-forward, but would not appreciably change the arguments made in this paper
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