Loading AI tools
From Wikipedia, the free encyclopedia
In physics and mathematics, the Pauli group on 1 qubit is the 16-element matrix group consisting of the 2 × 2 identity matrix and all of the Pauli matrices
together with the products of these matrices with the factors and :
The Pauli group is generated by the Pauli matrices, and like them it is named after Wolfgang Pauli.
The Pauli group on qubits, , is the group generated by the operators described above applied to each of qubits in the tensor product Hilbert space . That is,
The order of is since a scalar or factor in any tensor position can be moved to any other position.
As an abstract group, is the central product of a cyclic group of order 4 and the dihedral group of order 8.[1]
The Pauli group is a representation of the gamma group in three-dimensional Euclidean space. It is not isomorphic to the gamma group; it is less free, in that its chiral element is whereas there is no such relationship for the gamma group.
Seamless Wikipedia browsing. On steroids.
Every time you click a link to Wikipedia, Wiktionary or Wikiquote in your browser's search results, it will show the modern Wikiwand interface.
Wikiwand extension is a five stars, simple, with minimum permission required to keep your browsing private, safe and transparent.