quantum-error-correction
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| Any single-qubit error can be decomposed as a linear combination of the four Pauli operators $\{I, X, Y, Z\}$, so it suffices to detect and correct only bit-flip ($X$), phase-flip ($Z$), and combined ($Y$) errors. The [[list-of-quantum-error-correction-codes|quantum error correction codes]] that do this rely on measuring error syndromes — multi-qubit observables that reveal which error occurred without revealing the logical state. The threshold theorem states that if the physical error rate is below a code-dependent threshold, arbitrarily long computations are possible by concatenating or tiling error-correcting codes. | Any single-qubit error can be decomposed as a linear combination of the four Pauli operators $\{I, X, Y, Z\}$, so it suffices to detect and correct only bit-flip ($X$), phase-flip ($Z$), and combined ($Y$) errors. The [[list-of-quantum-error-correction-codes|quantum error correction codes]] that do this rely on measuring error syndromes — multi-qubit observables that reveal which error occurred without revealing the logical state. The threshold theorem states that if the physical error rate is below a code-dependent threshold, arbitrarily long computations are possible by concatenating or tiling error-correcting codes. | ||
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| - | ## List of quantum error correction concepts | ||
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| - | - [[pure-state]] | ||
| - | - [[mixed-state]] | ||
| - | - [[density-matrix]] | ||
| - | - [[von-neumann-equation]] | ||
| - | - [[lindblad-equation]] | ||
| - | - [[kraus-operator]] | ||
| - | - [[nisq]] | ||
| - | - [[list-of-quantum-error-correction-codes]] | ||
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quantum-error-correction.1781134424.txt.gz · Last modified: by 127.0.0.1