(4/11) Stabilizer codes II: symplectic representation, codes over GF(4). (4/6) Stabilizer codes II: symplectic representation, codes over GF(4). (4/4) Stabilizer codes I: basic properties, CSS codes. (3/30) Bit and phase-flip codes, 4- and 9-qubit codes, QECC conditions. (3/28) Noisy quantum mechanics, QECC Basics. Lecture 16a Polar codes and Reed-Muller codes (Recording posted to ELMS) Ch.11 (more detailed than we did in class) Youtube lectures of Telatar and Urbanke | My notes (3/14) Achieving the Shannon capacity: Polar codes. (3/9) Linear programming bounds for codes and sphere packings. Linear programming bounds for binary codes. (3/2) Locally testable codes (LTC) on 2D complexes. (2/28) Expander codes, codes on 2D complexes, and families of good locally testable codes (LTCs). Expander codes, parameters and decodingĪ survey on expanders | Madhu Sudan's lectures 13,14 (2/23) Expander graphs: Spectral expanders. Lecture 9 (2/21) Maximum rank distance codes: construction and Welch-Berlekamp decoding Reading on rank metric codes: Introduction | More on parameters, Coding in the matrix space: Rank metric codes. 10.3, 10.4Įxercises: (not collected or graded) (2/14) Codes on algebraic curves Hermitian codes, their parameters (2/7) Interpolation decoding of Reed-Solomon codes: Unique and ListīW Algorithm in brief |, Ch.15 Ch.7 (2/2) Reed-Solomon (RS) codes their properties, and their decoding (1/26) Shannon's perspective of packing: Capacity of the BSC and BEC. (1/24) Metric spaces of Coding Theory, Linear codes and their duals. Project presentations: May 9, 11, starting at 11:00am.ĭetailed contents of the course: (tentative outline will be adjusted as we progress) Entries can be related to topics chosen for the course project.Ĭourse project A list of topics for the course project is posted here Entries will include a description of the code, its error-correcting properties, protected gates, rate, threshold, decoder, encoder, and other properties. An entry can be a single code or a family of codes. You will provide three entries into the EC Zoo - an online database of classical and quantum error-correcting codes.Toric/surface codes and topological error correctionĪssignments: There will be two home assignments in addition to the assignment described in the next paragraph.Stabilizer codes, CSS codes, Polynomial codes.Connections between classical and quantum codes.Fourier analysis on $\^n$, linear programming, and bounds on codes.Expander codes, codes on 2D complexes, and families of good locally testable codes.Reed-Solomon codes Codes on algebraic curves and their decoding.Project topics and materials will be distributed halfway into the course (please wait for the announcement).Ĭourse contents: We plan to cover the following topics: Grading: Homeworks (1/3), Final exam (1/3), Course project/End of course presentation (1/3) The lectures draw on multiple sources, some of which are listed below. Information theory or quantum mechanics are notĪmong prerequisites the material will be discussed from the first principles. Most of the results are established from the first principles, so no specific background is required (except for good knowledge of basic linear algebra). Prerequisites The course focuses on mathematical reasoning, so general mathematical maturity and previous experience of similar kind is essential. On the classical part, we discuss families of algebraic codes and their decoding, spherical codes and combinatorial constructions, and the results of the last decade relating to achieving Shannon capacity of basic communication channels.On the quantum side, we describe why quantum error correction is possible, go over basic constructions such as the stabilizer formalism, CSS codes, and toric/surface codes, and touch upon related continuous-variable error-correcting codes. We discuss basic principles of and connections between classical and quantum coding theory. Important aspects of classical and quantum coding theory from a unified perspective. Instructor availability outside class hours: Please send us an email, including an online meeting requestĬourse description: This is an Advanced Topics graduate-level course covering several for Systems Research, (*)Department of CS, (*)Department of Mathematics (*)Joint Center for Quantum Information and Computer Science, (*)Department of Physics
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