Given any quantum error correcting code permitting universal fault-tolerant quantum computation and transversal measurement of logical X and Z, we describe how to perform time-optimal quantum computation, meaning the execution of an arbitrary Clifford circuit followed by a layer of independent T gates and any necessary feedforward measurement determined corrective S gates all in the time of a single physical measurement. We assume fast classical processing and classical communication, and argue the reasonableness of this assumption. This enables fault-tolerant quantum computation to be performed orders of magnitude faster than previously thought possible, with the execution time independent of the error correction strength.
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