We show how to diagnose and rehabilitate bit-flip errors in a classical error correcting model. We compare logical versus physical bits, define codewords, and introduce a classical error-correcting model. We illustrate elements of the latter, including logical versus physical bits, codewords and the notion of an error correcting code. Quantum codes must consider the no-cloning theorem, the collapse hypothesis, and the possibility of continuous errors. We present encoding, syndrome measurement, and recovery circuits for single qubit bit-flip and phase shift errors. We review the Shor code, introduce the stabilizer formalism, and illustrate stabilizers role in its implementation. We demonstrate the use of the stabilizer formalism in the analysis of quantum error-detection in the Laflamme and Steane codes and the development of surface codes. We discuss the threshold theorem and its role in allowing for fault-tolerant quantum computing.

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Computare Errare Est: Quantum Error Correction

  • Bernard Zygelman

摘要

We show how to diagnose and rehabilitate bit-flip errors in a classical error correcting model. We compare logical versus physical bits, define codewords, and introduce a classical error-correcting model. We illustrate elements of the latter, including logical versus physical bits, codewords and the notion of an error correcting code. Quantum codes must consider the no-cloning theorem, the collapse hypothesis, and the possibility of continuous errors. We present encoding, syndrome measurement, and recovery circuits for single qubit bit-flip and phase shift errors. We review the Shor code, introduce the stabilizer formalism, and illustrate stabilizers role in its implementation. We demonstrate the use of the stabilizer formalism in the analysis of quantum error-detection in the Laflamme and Steane codes and the development of surface codes. We discuss the threshold theorem and its role in allowing for fault-tolerant quantum computing.