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

TL;DR

This paper develops a resource theory for magic states in quantum computing, providing tools to quantify, synthesize, and optimize non-Clifford gate implementation for fault-tolerant quantum computation.

Contribution

It introduces a well-behaved magic monotone called robustness of magic and applies it to quantify classical simulation overhead and optimize magic state synthesis.

Findings

Robustness of magic quantifies classical simulation cost.

New bounds on magic states needed for specific unitaries.

Identified optimal magic state synthesis protocols.

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.