2005/08/31 by David Poulin · 27 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physrevlett.95.230504
published as Phys. Rev. Lett. 95 230504 (2005) · Corrected claim based on exhaustive search
openalex publication_date 2005/12/01 · arxiv created 2006/06/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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.