The Bacon–Shor code is a subsystem
error correcting code
In computing, telecommunication, information theory, and coding theory, forward error correction (FEC) or channel coding is a technique used for controlling errors in data transmission over unreliable or noisy communication channels.
The centra ...
. In a subsystem code, information is encoded in a
subsystem
A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and is exp ...
of a
Hilbert space
In mathematics, a Hilbert space is a real number, real or complex number, complex inner product space that is also a complete metric space with respect to the metric induced by the inner product. It generalizes the notion of Euclidean space. The ...
. 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 claim of fault tolerant circuit demonstration on a quantum computer. It is named after
Dave Bacon and
Peter Shor
Peter Williston Shor (born August 14, 1959) is an American theoretical computer scientist known for his work on quantum computation, in particular for devising Shor's algorithm, a quantum algorithm for factoring exponentially faster than the ...
.
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 overhead for fault tolerant error correction.
See also
*
Five-qubit error correcting code
References
{{DEFAULTSORT:Bacon-Shor code
Quantum computing