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arXiv:quant-ph/9705052quant-ph

Stabilizer Codes and Quantum Error Correction

Daniel Gottesman

Abstract

Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed to meet this challenge. A group-theoretical structure and associated subclass of quantum codes, the stabilizer codes, has proved particularly fruitful in producing codes and in understanding the structure of both specific codes and classes of codes. I will give an overview of the field of quantum error correction and the formalism of stabilizer codes. In the context of stabilizer codes, I will discuss a number of known codes, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation.

arXiv comments
114 pages, LaTeX. Caltech Ph.D. Thesis
Journal reference
DOI
Subjects
quant-phQuantum Physics

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    • I had a lot of finals, and the answer to this comment that I did not write was essentially accurate. The people who think about computers this way are the people who have to implement them on analog devices, aka the electrical engineers. There is a discrete analog (lol) in the…

      ouidView on HNParent context

  2. Twist: MIT’s Quantum Programming Language 1 comment

    • > your goals (e.g. compilation into realistic gates) are very different from the goals of these language designers (study of abstract structure of quantum algorithms) But the abstract structure of quantum algorithms is all about the carefully orchestrated structure within…

      StrilancView on HNParent context

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