Stabilizer states and Clifford operations for systems of arbitrary dimensions and modular arithmetic

By Erik Hostens, Jeroen Dehaene, B. De Moor. 2004

162 citations recorded by the source corpus.

We describe generalizations of the Pauli group, the Clifford group, and stabilizer states for qudits in a Hilbert space of arbitrary dimension d. We examine a link with modular arithmetic, which yields an efficient way of representing the Pauli group and the Clifford group with matrices over Z{sub d}. We further show how a Clifford operation can be efficiently decomposed into one and two-qudit operations. We also focus in detail on standard basis expansions of stabilizer states.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/122092b7586effec4df02df3db6095df719dccf8

Citations in the corpus

• Symmetric informationally complete–positive operator valued measures and the extended Clifford group (2004, unknown): “ar X iv :q ua nt -p h/ 04 12 00 1v 2 1 7 Ja n 20 05 SIC-POVMs AND THE EXTENDED CLIFFORD GROUP”