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Quantum Code and Error Detection
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Surface code
A code with high fault-tolerance threshold making it suitable for quantum computation using physical qubits with higher error rates.
Stabilizer codes
A class of quantum error-correcting codes where errors can be detected and corrected by measuring stabilizer operators.
Quantum Reed-Muller codes
They are derived from classical Reed-Muller codes and are capable of correcting quantum errors.
Shor's code
A nine-qubit code that corrects arbitrary single-qubit errors through quantum error correction.
Five-qubit code
The smallest possible code that can correct single-qubit errors and is also known as the perfect quantum code.
Color code
A type of topological code that uses a lattice with qubits at vertices; encodes one logical qubit into several physical qubits.
Topological codes
Codes that encode information in the global features of entangled quantum states, protecting against local errors.
Quantum Hamming code
A quantum error-correcting code extending the classical Hamming code, typically capable of correcting single-qubit errors.
Bacon-Shor code
This code uses a rectangular array of qubits and can correct for errors along rows or columns.
Quantum Convolutional code
These codes are the quantum analog of classical convolutional codes and suitable for streaming quantum data.
Quantum Polar code
Based on the concept of channel polarization, they offer a constructive way to achieve channel capacity with low encoding and decoding complexity.
Cat code
A quantum error-correcting code that uses superpositions of coherent states (so-called 'cat states') to detect and correct errors.
Steane code
A seven-qubit code also known as the perfect code; it encodes one logical qubit into seven physical qubits.
Toric code
A topological code used to store quantum information in two dimensions, which is robust against local errors.
GKP code
Short for Gottesman-Kitaev-Preskill code; encodes quantum information into oscillators and corrects small displacement errors.
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