A Graphical-Model-Based Approach To Quantum Information Processing
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The Chinese University of Hong Kong

ISIT 2021, Melbourne, Victoria, Australia



The world we live in is a quantum world. Although our human bodies limit ourselves to experience a world that we call classical, and therefore makes it difficult for us to grasp quantum concepts, this should not stop us from designing and implementing devices that benefit from the unique features of the quantum world. Quantum information processing (QIP) is about understanding this quantum world and using it to our advantage to process, transmit, and store information.

This tutorial gives an introduction to QIP using a particular approach based on graphical models. Graphical models are a well-appreciated tool in the information and coding theory community. For example, low-density parity-check codes (which appear in the 5G Telecommunication standard) and their decoding via message-passing algorithms are naturally expressed in terms of graphical models.

Various graphical notations have been introduced over the last decades to visualize QIP concepts. The graphical notation and language that is used in this tutorial is based on so-called normal factor graphs (NFGs). One particular advantage of this approach is that the NFGs used for QIP are compatible with the NFGs used in classical information processing (CIP), like decoding of low-density parity-check codes, Kalman filtering, etc. Another advantage is that similarities/differences between the NFGs used for QIP and the NFGs used for CIP allow one to better appreciate similarities/differences between the quantum world and the classical world.

This tutorial is planned to be accessible to a broad audience within the information and coding theory community. Therefore, we only require a solid understanding of linear algebra, with relevant background from other areas being introduced and reviewed as necessary. Overall, this tutorial should allow newcomers to get started in the field and for people with some background knowledge in QIP to get a different perspective on QIP.

At the beginning, the tutorial will contain a step-by-step discussion of the topics, whereas later topics will be discussed at a higher level. Nevertheless, the slides will be such that the participants can study the details later on by themselves.

Tentative topics: introduction; normal factor graphs; closing-the-box operation, opening-the-box operation; sum-product algorithm as closing-the-box operation; factor-graph transforms; classical hidden Markov models; probability mass function vs. quantum mass function; unitary evolution and non-unitary evolution; measurements; quantum teleportation, superdense coding; Bell's game; Deutsch--Jozsa algorithm, Grover's algorithm; classical channel codes vs. quantum stabilizer codes; emergence of classical correlations; classical entropy vs. quantum entropy connections to other graphical representations like tensor network states, matrix product states, tree tensor states, projected entangled pair states, etc.