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A Theory of Fault-Tolerant Quantum Computation

Daniel Gottesman
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Abstract

In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant operations based on symmetries of the code stabilizer. This allows a straightforward determination of which operations can be performed fault-tolerantly on a given code. I demonstrate that fault-tolerant universal computation is possible for any stabilizer code. I discuss a number of examples in more detail, including the five-qubit code.

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Daniel Gottesman. 1997-02-12. A Theory of Fault-Tolerant Quantum Computation. https://doi.org/10.1103/physreva.57.127

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