Stabilizer formalism for operator quantum error correction.
By David Poulin. Physical Review Letters, 2005
344 citations recorded by the source corpus.
Operator quantum error correction is a recently developed theory that provides a generalized and unified framework for active error correction and passive error avoiding schemes. In this Letter, we describe these codes using the stabilizer formalism. This is achieved by adding a gauge group to stabilizer codes that defines an equivalence class between encoded states. Gauge transformations leave the encoded information unchanged; their effect is absorbed by virtual gauge qubits that do not carry useful information. We illustrate the construction by identifying a gauge symmetry in Shor's 9-qubit code that allows us to remove 3 of its 8 stabilizer generators, leading to a simpler decoding procedure and a wider class of logical operations without affecting its essential properties. This opens the path to possible improvements of the error threshold of fault-tolerant quantum computing.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/8ec4b1d133b098670c9be7f4dc1a874d4f553d2b
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In Artificial Intelligence
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In Atomic and Molecular Physics, and Optics
- Daniel Gottesman
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Citations in the corpus
- Quantum error correction for quantum memories (2013, positive): “Subsystem stabilizer codes can be viewed as stabilizer codes in which some logical qubits, called gauge qubits, are not used to encode information (Poulin, 2005).”
- Single-Shot Fault-Tolerant Quantum Error Correction (2014, background): “A gauge group G ⊆ P with S as its center (up to phases) fixes the decomposition C 1⁄4 A ⊗ B [27].”
- Quantum memories at finite temperature (2014, neutral): “(Poulin, 2005).”
- An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation (2009, background): “One tool that has garnered interest over the last few years is known as operator quantum error correction or subsystem codes [ 33, 36 ].”