A Polar Decomposition for Quantum Channels: Theory and Applications
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Date
2019-08-23
Authors
Alexander, Matthew
Advisor
Emerson, Joseph
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Every potential benefit of quantum computers would be lost without methods to protect the computations from error. Quantum channels provide a framework for understanding error in quantum systems. In general, for a system of size d, a quantum channel may require as many as ~d^4 parameters to characterize it. We introduce the leading Kraus approximation, a simplification which reduces the number of parameters to ~d^2, while accurately approximating two figures of merit important to the experimentalist: the unitarity and average process fidelity. Additionally, applying the leading Kraus approximation declutters investigations into the set of quantum channels. When applied, a natural decomposition of channels arises, separating behaviour into coherent and decoherent contributions. We find that eliminating the coherent contribution provides the greatest increase to the fidelity, while decoherent processes provide a generalization of depolarizing channels.
Description
Keywords
quantum theory, quantum computers