Magic state distillation with permutation-invariant codes and a two-qubit example

TL;DR

This paper introduces a novel, efficient two-qubit magic state distillation protocol using permutation-invariant codes, capable of distilling arbitrary magic states with high error thresholds, and compatible with existing protocols.

Contribution

The paper presents a new two-qubit magic state distillation protocol based on permutation-invariant codes that achieves high thresholds and supports arbitrary magic state distillation.

Findings

Achieves a 0.5 error threshold and 1/2 distillation rate.

Uses as small as two qubits for the protocol.

Compatible with existing distillation protocols.

Abstract

Magic states, by allowing non-Clifford gates through gate teleportation, are important building blocks of fault-tolerant quantum computation. Magic state distillation protocols aim to create clean copies of magic states from many noisier copies. However, the prevailing protocols require substantial qubit overhead. We present a distillation protocol based on permutation-invariant gnu codes, as small as two qubits. The two-qubit protocol achieves a 0.5 error threshold and 1/2 distillation rate, surpassing prior schemes for comparable codes. Our protocol furthermore distils magic states with arbitrary magic by varying the position of the ideal input states on the Bloch sphere. We achieve this by departing from the usual magic state distillation formalism, allowing the use of non-Clifford gates in the distillation protocol, and allowing the form of the output state to differ from the input state. Our protocol is compatible for use in tandem with existing magic state distillation protocols to enhance their performance.