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Quantum Code and Error Detection

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Surface code

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A code with high fault-tolerance threshold making it suitable for quantum computation using physical qubits with higher error rates.

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Stabilizer codes

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A class of quantum error-correcting codes where errors can be detected and corrected by measuring stabilizer operators.

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Quantum Reed-Muller codes

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They are derived from classical Reed-Muller codes and are capable of correcting quantum errors.

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Shor's code

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A nine-qubit code that corrects arbitrary single-qubit errors through quantum error correction.

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Five-qubit code

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The smallest possible code that can correct single-qubit errors and is also known as the perfect quantum code.

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Color code

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A type of topological code that uses a lattice with qubits at vertices; encodes one logical qubit into several physical qubits.

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Topological codes

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Codes that encode information in the global features of entangled quantum states, protecting against local errors.

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Quantum Hamming code

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A quantum error-correcting code extending the classical Hamming code, typically capable of correcting single-qubit errors.

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Bacon-Shor code

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This code uses a rectangular array of qubits and can correct for errors along rows or columns.

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Quantum Convolutional code

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These codes are the quantum analog of classical convolutional codes and suitable for streaming quantum data.

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Quantum Polar code

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Based on the concept of channel polarization, they offer a constructive way to achieve channel capacity with low encoding and decoding complexity.

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Cat code

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A quantum error-correcting code that uses superpositions of coherent states (so-called 'cat states') to detect and correct errors.

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Steane code

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A seven-qubit code also known as the perfect code; it encodes one logical qubit into seven physical qubits.

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Toric code

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A topological code used to store quantum information in two dimensions, which is robust against local errors.

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GKP code

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Short for Gottesman-Kitaev-Preskill code; encodes quantum information into oscillators and corrects small displacement errors.

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