title: Application of a Resource Theory for Magic States to Fault-Tolerant Quantum Computing.
abstract: Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. First, we 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 nontrivial 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.
authors.affiliation: Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom.
authors.forename: Mark
authors.initials: M
authors.lastname: Howard
authors.affiliation: Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, United Kingdom.
authors.forename: Earl
authors.initials: E
authors.lastname: Campbell