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New construction of nine-qubit error-correcting code

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arxiv 2110.05130 v4 pith:DXSE2WH4 submitted 2021-10-11 quant-ph

New construction of nine-qubit error-correcting code

classification quant-ph
keywords nine-qubitcodecodesconstructionerror-correctingquantumdifferenterror-correction
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We report new construction of nine-qubit error-correcting code, which introduces two new nine-qubit codes and one new three-qubit code. Because both the new two nine-qubit codes have the normal logical operators, as opposed to the nine-qubit Shor code, it results in different performance when the three codes are applied in concatenated quantum error-correction. On the other hand, one of the two nine-qubit codes has the same stabilizer generators as the nine-qubit Shor code, they are more suitable for the high-wight bit-flip noise, and the other code has the different stabilizer generators, which is more suitable for the high-wight phase-flip noise. This work is enlightening to the construction of quantum error-correcting codes, and adds more options for optimizing the performance of quantum error-correction.

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  1. Three-Qubit State Preparation: Classification and Explicit Circuits

    quant-ph 2026-03 conditional novelty 6.0

    A deterministic five-type classification of three-qubit pure states yields explicit, connectivity-aware circuit templates whose gate parameters are computed directly from the target amplitudes.