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This page was last edited on 13 October 2024, at 11:35 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
Locally decodable codes are error-correcting codes for which single bits of the message can be probabilistically recovered by only looking at a small (say constant) number of positions of a codeword, even after the codeword has been corrupted at some constant fraction of positions.
That these codes allow indeed for quantum computations of arbitrary length is the content of the quantum threshold theorem, found by Michael Ben-Or and Dorit Aharonov, which asserts that you can correct for all errors if you concatenate quantum codes such as the CSS codes—i.e. re-encode each logical qubit by the same code again, and so on, on ...
In a quantum error-correcting code, the codespace is the subspace of the overall Hilbert space where all logical states live. In an -qubit stabilizer code, we can describe this subspace by its Pauli stabilizing group, the set of all -qubit Pauli operators which stabilize every logical state. The stabilizer formalism allows us to define the ...
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This page was last edited on 8 December 2024, at 16:03 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.