Magic State Distillation at Intermediate Size

TL;DR

This paper analyzes intermediate-size magic state distillation protocols using BCH inner codes and various outer codes, demonstrating improved efficiency in reducing input magic states for a given output error.

Contribution

It extends previous asymptotic protocols to intermediate sizes, incorporating error correction and diverse code combinations for enhanced performance.

Findings

Protocols require fewer input magic states for target error rates.

Incorporating error correction improves protocol robustness.

Protocols perform well across various input error regimes.

Abstract

Recently we proposed a family of magic state distillation protocols that obtains asymptotic performance that is conjectured to be optimal. This family depends upon several codes, called "inner codes" and "outer codes." We presented some small examples of these codes as well as an analysis of codes in the asymptotic limit. Here, we analyze such protocols in an intermediate size regime, using hundreds to thousands of qubits. We use BCH inner codes, combined with various outer codes. We extend our protocols by adding error correction in some cases. We present a variety of protocols in various input error regimes; in many cases these protocols require significantly fewer input magic states to obtain a given output error than previous protocols.