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The distillation of magic states is an often-cited technique for enabling universal quantum computing once the error rate for a special subset of gates has been made negligible by other means. We present a routine for magic-state distillation that reduces the required overhead for a range of parameters of practical interest. Each iteration of the routine uses a four-qubit error-detecting code to distill the +1 eigenstate of the Hadamard gate at a cost of ten input states per two improved output states. Using this routine in combination with the 15-to-1 distillation routine described by Bravyi and Kitaev allows for further improvements in overhead.
Meier, A.
, Eastin, B.
and Knill, E.
(2012),
Magic-state distillation with the four-qubit code, Quantum Information & Computation
(Accessed June 7, 2023)