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

TLDR

The authors develop a resource theory for magic states to support fault‑tolerant quantum computation. They construct this theory and analyze the synthesis of unitaries using magic states interleaved with Clifford gates, Pauli measurements, and stabilizer ancillas, showing the synthesis class is hard to characterize. They prove robustness of magic is a monotone that quantifies classical simulation overhead, use the framework to bound and optimize magic‑state synthesis for non‑Clifford gates, and identify new optimal synthesis examples.

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.