Qutrit Magic State Distillation

TL;DR

This paper extends magic state distillation protocols to qutrit systems, demonstrating the distillation of non-stabilizer states and their conversion into resources for universal quantum computation.

Contribution

It introduces a general approach for qutrit MSD and analyzes a 5-qutrit stabilizer code protocol, revealing attractor states and their utility for non-Clifford gates.

Findings

The protocol successfully distills non-stabilizer magic states.

Identifies two attractor states in the distillation process.

Shows conversion of states into non-Clifford gate resources.

Abstract

Magic state distillation (MSD) is a purification protocol that plays a central role in fault tolerant quantum computation. Repeated iteration of the steps of a MSD protocol, generates pure single non-stabilizer states, or magic states, from multiple copies of a mixed resource state using stabilizer operations only. Thus mixed resource states promote the stabilizer operations to full universality. Magic state distillation was introduced for qubit-based quantum computation, but little has been known concerning MSD in higher dimensional qudit-based computation. Here, we describe a general approach for studying MSD in higher dimensions. We use it to investigate the features of a qutrit MSD protocol based on the 5-qutrit stabilizer code. We show that this protocol distills non-stabilizer magic states, and identify two types of states, that are attractors of this iteration map. Finally, we show how these states may be converted, via stabilizer circuits alone, into a state suitable for state injected implementation of a non-Clifford phase gate, enabling non-Clifford unitary computation.