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        "---\n",
        "title: Introduction\n",
        "description: A free IBM course on quantum information and computation\n",
        "---\n",
        "\n",
        "# Introduction\n",
        "\n",
        "In the previous lesson, we took a first look at quantum error correction, focusing specifically on the 9-qubit Shor code.\n",
        "In this lesson, we'll introduce the *stabilizer formalism*, which is a mathematical framework through which a broad class of quantum error correcting codes, known as *stabilizer codes*, can be specified and analyzed.\n",
        "This includes the 9-qubit Shor code along with many other examples, including codes that seem likely to be well-suited to real-world quantum devices.\n",
        "Not every quantum error correcting code is a stabilizer code, but many are, including every example that we'll see in this course.\n",
        "\n",
        "The lesson begins with a short discussion of Pauli matrices, and tensor products of Pauli matrices more generally, which can represent not only operations on qubits, but also measurements of qubits — in which case they're typically referred to as *observables*.\n",
        "We'll then go back and take a second look at the repetition code and see how it can be described in terms of Pauli matrix observables.\n",
        "This will both inform and lead into a general discussion of stabilizer codes, including several examples, basic properties of stabilizer codes, and how the fundamental tasks of encoding, detecting errors, and correcting those errors can be performed.\n",
        "\n",
        "## Lesson video\n",
        "\n",
        "In the following video, John Watrous steps you through the content in this lesson on stabilizer formalism. Alternatively, you can open the [YouTube video](https://youtu.be/3ib2JP_LeIU?list=PLOFEBzvs-VvqKKMXX4vbi4EB1uaErFMSO) for this lesson in a separate window. [Download the slides](https://ibm.box.com/public/static/umposbds8d27cv8rnpsayyaj1k2aw88o.pdf) for this lesson.\n",
        "\n",
        "<IBMVideo id=\"134212334\" title=\"In this video, John Watrous introduces stabilizer codes. Pauli operations and observables are reviewed.\" />\n",
        "\n"
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