Fractal Properties of Magic State Distillation

TL;DR

This paper reveals that magic state distillation protocols exhibit fractal properties when analyzed beyond traditional one-parameter restrictions, leading to more effective protocols that utilize low-fidelity states and require fewer iterations.

Contribution

It introduces the concept of fractal analysis in magic state distillation, demonstrating improved protocol effectiveness by removing one-parameter restrictions.

Findings

Fractal structures emerge in the analysis of distillation protocols.

Protocols become more effective with broader state considerations.

Fewer iterations are needed to reach high fidelity.

Abstract

Magic state distillation protocols have a complicated non-linear nature. Analysis of protocols is therefore usually restricted to one-parameter families of states, which aids tractability. We show that if we lift this one-parameter restriction and embrace the complexity, distillation exhibits fractal properties. By studying these fractals we demonstrate that some protocols are more effective when not restricted. Low fidelity states that are usually worthless for distillation are now usable, and fewer iterations of the protocols are needed to reach high fidelity.