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arXiv · 1609.07488

Application of a resource theory for magic states to fault-tolerant quantum computing

Mark Howard·Earl T. Campbell
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Abstract

Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. We first show that robustness of magic is a well-behaved magic monotone that operationally quantifies the classical simulation overhead for a Gottesman-Knill type scheme using ancillary magic states. Our framework subsequently finds immediate application in the task of synthesizing non-Clifford gates using magic states. When magic states are interspersed with Clifford gates, Pauli measurements and stabilizer ancillas - the most general synthesis scenario - then the class of synthesizable unitaries is hard to characterize. Our techniques can place non-trivial lower bounds on the number of magic states required for implementing a given target unitary. Guided by these results we have found new and optimal examples of such synthesis.

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Mark Howard, Earl T. Campbell. 2016-09-23. Application of a resource theory for magic states to fault-tolerant quantum computing. https://doi.org/10.1103/physrevlett.118.090501

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