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Bacon–Shor Code
The Bacon–Shor code is a subsystem Quantum error correction, error correcting code. In a subsystem code, information is encoded in a System#Subsystem, subsystem of a Hilbert space. Subsystem codes lend to simplified error correcting procedures unlike codes which encode information in the Space (mathematics), subspace of a Hilbert space. This simplicity led to the first claim of fault tolerant circuit demonstration on a quantum computer. It is named after Dave Bacon and Peter Shor. Given the Stabilizer code, stabilizer generators of Quantum error correction#Shor code, Shor's code: \langle X_X_X_X_X_X_, X_X_X_X_X_X_, Z_Z_, Z_Z_, Z_Z_, Z_Z_, Z_Z_, Z_Z_\rangle, 4 stabilizers can be removed from this generator by recognizing Gauge symmetry, gauge symmetries in the code to get: \langle X_X_X_X_X_X_, X_X_X_X_X_X_, Z_Z_Z_Z_Z_Z_, Z_Z_Z_Z_Z_Z_ \rangle. Error correction is now simplified because 4 stabilizers are needed to measure errors instead of 8. A gauge group can be created from the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Error Correction
Quantum error correction (QEC) is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is theorised as essential to achieve fault tolerant quantum computing that can reduce the effects of noise on stored quantum information, faulty quantum gates, faulty quantum preparation, and faulty measurements. Classical error correction employs redundancy. The simplest albeit inefficient approach is the repetition code. The idea is to store the information multiple times, and—if these copies are later found to disagree—take a majority vote; e.g. suppose we copy a bit in the one state three times. Suppose further that a noisy error corrupts the three-bit state so that one of the copied bits is equal to zero but the other two are equal to one. Assuming that noisy errors are independent and occur with some sufficiently low probability ''p'', it is most likely that the error is a single-bit error and the tran ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
