Gaining Information About a Quantum Channel Via Twirling

Abstract

Finding correctable encoding that protects against a quantum process is in general a difficult task. 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.

In this thesis we discuss how useful partial information of a quantum channel can be systematically extracted by averaging the channel under the action of a set of unitaries in a process known as twirling. We show that in some cases it is possible to find correctable encodings for the channel using the partial information obtained via twirling.

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. A post-processing scheme for finding unitarily correctable codes for these twirled channels is presented which does not involve exponentially large matrices. A test for non-Markovian noise using such a twirling process is also discussed.