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

Experimentally scalable protocol for identification of correctable codes