University of Cambridge > Talks.cam > CQIF Seminar > Magic-State Distillation in All Prime Dimensions Using Quantum Reed-Muller Codes

Magic-State Distillation in All Prime Dimensions Using Quantum Reed-Muller Codes

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We propose families of protocols for magic-state distillation—important components of fault-tolerance schemes—for systems of odd prime dimension. Our protocols utilize quantum Reed-Muller codes with transversal non-Clifford gates. We find that, in higher dimensions, small and effective codes can be used that have no direct analogue in qubit (two-dimensional) systems. We present several concrete protocols, including schemes for three-dimensional (qutrit) and five-dimensional (ququint) systems. At the time of publication our five dimensional protocol was, by many measures, the best magic-state-distillation scheme yet discovered. It excels both in terms of error threshold with respect to depolarizing noise (36.3%) and the efficiency measure known as yield, where, for a large region of parameters, it outperforms all first-generation qubit protocols by many orders of magnitude.

This talk is part of the CQIF Seminar series.

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