The Resource Theory of Stabilizer Computation

TL;DR

This paper develops a resource theory for stabilizer states in quantum computing, introducing measures to quantify non-stabilizer resources and providing bounds on magic state distillation efficiency.

Contribution

It introduces a novel resource theory for stabilizer states, including two quantitative monotones, and links negativity in Wigner representation to quantum resourcefulness.

Findings

Defined two monotones for stabilizer resources.

Established bounds on magic state distillation efficiency.

Connected negativity in Wigner representation to quantum advantage.

Abstract

Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the theory of entanglement, for resources for stabilizer codes. We introduce two quantitative measures - monotones - for the amount of non-stabilizer resource. As an application we give absolute bounds on the efficiency of magic state distillation. One of these monotones is the sum of the negative entries of the discrete Wigner representation of a quantum state, thereby resolving a long-standing open question of whether the degree of negativity in a quasi-probability representation is an operationally meaningful indicator of quantum behaviour.