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Efficient Computations of Encodings for Quantum Error Correction

Richard Cleve·Daniel Gottesman
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Abstract

We show how, given any set of generators of the stabilizer of a quantum code, an efficient gate array that computes the codewords can be constructed. For an n-qubit code whose stabilizer has d generators, the resulting gate array consists of O(n d) operations, and converts k-qubit data (where k = n - d) into n-qubit codewords.

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Richard Cleve, Daniel Gottesman. 1996-08-01. Efficient Computations of Encodings for Quantum Error Correction. https://doi.org/10.1103/physreva.56.76

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