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Statements

Subject Item
dbr:Bacon-Shor_code
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dbr:Glossary_of_quantum_computing
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Bacon–Shor code
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The Bacon–Shor code is a Subsystem error correcting code. In a Subsystem code, information is encoded in a subsystem of a Hilbert space. Subsystem codes lend to simplified error correcting procedures unlike codes which encode information in the subspace of a Hilbert space. This simplicity led to the first demonstration of fault tolerant circuits on a quantum computer. ZZ ZZ q0---q1--q2XX| | |XX | | | q6--q2--q8XX| | |XX | | | q3--q4--q5 ZZ ZZ
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dbr:Stabilizer_code dbr:Hilbert_space dbr:Gauge_symmetry dbr:Space_(mathematics) dbc:Quantum_computing dbr:Gauge_group dbr:System dbr:Quantum_error_correction dbr:Five-qubit_error_correcting_code
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The Bacon–Shor code is a Subsystem error correcting code. In a Subsystem code, information is encoded in a subsystem of a Hilbert space. Subsystem codes lend to simplified error correcting procedures unlike codes which encode information in the subspace of a Hilbert space. This simplicity led to the first demonstration of fault tolerant circuits on a quantum computer. Given the stabilizer generators of Shor's code: , 4 stabilizers can be removed from this generator by recognizing gauge symmetries in the code to get: . Error correction is now simplified because 4 stabilizers are needed to measure errors instead of 8. A gauge group can be created from the stabilizer generators:. Given that the Bacon–Shor code is defined on a square lattice where the qubits are placed on the vertices; laying the qubits on a grid in a way that corresponds to the gauge group shows how only 2 qubit nearest-neighbor measurements are needed to infer the error syndromes. The simplicity of deducing the syndromes reduces the overheard for fault tolerant error correction. ZZ ZZ q0---q1--q2XX| | |XX | | | q6--q2--q8XX| | |XX | | | q3--q4--q5 ZZ ZZ
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wikipedia-en:Bacon–Shor_code?oldid=1101079432&ns=0
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