The Bacon–Shor code is a subsystem
error correcting code.[1] 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.[2] This simplicity led to the first claim of fault tolerant circuit demonstration on a quantum computer.[3] It is named after
Dave Bacon and
Peter Shor.
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: .[4] 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:.[4] 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.[5]