Experimentally scalable protocol for identification of correctable codes

TL;DR

This paper introduces a scalable method for identifying correctable quantum codes by leveraging partial information obtained through twirling, simplifying the process of protecting quantum information against physical errors.

Contribution

It demonstrates that correctable codes for twirled channels can be found efficiently without exponential complexity, using partial channel information and a new postprocessing scheme.

Findings

Correctable codes for twirled channels are also correctable for original channels.

Twirling over Pauli operators and permutations allows scalable experimental characterization.

A postprocessing scheme avoids exponential matrix operations.

Abstract

The task of finding a correctable encoding that protects against some physical quantum process is in general hard. Two main obstacles are that an exponential number of experiments are needed to gain complete information about the quantum process, and known algorithmic methods for finding correctable encodings involve operations on exponentially large matrices. However, we show that in some cases it is possible to find such encodings with only partial information about the quantum process. Such useful partial information can be systematically extracted by averaging the channel under the action of a set of unitaries in a process known as "twirling". In this paper we prove that correctable encodings for a twirled channel are also correctable for the original channel. We investigate the particular case of twirling over the set of Pauli operators and qubit permutations, and show that the resulting quantum operation can be characterized experimentally in a scalable manner. We also provide a postprocessing scheme for finding unitarily correctable codes for these twirled channels which does not involve exponentially large matrices.