Title: Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
Authors: Dehaene, Jeroen ×
De Moor, Bart #
Issue Date: Oct-2003
Publisher: American physical soc
Series Title: Physical Review A, Atomic, Molecular and Optical Physics vol:68 issue:4 pages:9042318_1-042318_10
Abstract: We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of a (2n + 1) X (2n + I) binary matrix product and binary quadratic forms. As an application we give two schemes to efficiently decompose Clifford group operations into one- and two-qubit operations. We also show how the coefficients of stabilizer states and Clifford group operations in a standard basis expansion can be described by binary quadratic forms. Our results are useful for quantum error correction, entanglement distillation, and possibly quantum computing.
ISSN: 1050-2947
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
Tutorial services, Faculty of Engineering
× corresponding author
# (joint) last author

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