Application of a Resource Theory for Magic States to Fault-Tolerant Quantum Computing

Mark Howard, Earl Campbell
2017 Physical Review Letters  
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
more » ... d 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.
doi:10.1103/physrevlett.118.090501 pmid:28306308 fatcat:icb25b2ypra6fnieyxkf2ksw4i