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The leading approach to fault tolerant quantum computing requires a continualsupply of magic states. When a new magic state is first encoded, its initialfidelity will be too poor for use in the computation. This necessitates aresource-intensive distillation process that occupies the majority of thecomputer's hardware; creating magic states with a high initial fidelityminimises this cost and is therefore crucial for practical quantum computing.Here we present the surprising and encouraging result that raw magic states canhave a fidelity significantly better than that of the two-qubit gate operationsused to construct them. Our protocol exploits post-selection withoutsignificantly slowing the rate of generation and tolerates finite error ratesin initialisations, measurements and single-qubit gates. This approach maydramatically reduce the size of the hardware needed for a given quantumcomputing task.

A magic state's fidelity can be superior to the operations that created it