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 .
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.
In mathematical physics and mathematics, the Pauli matrices are a set of three 2 × 2 complex matrices that are Hermitian, involutory and unitary. Usually...
In physics and mathematics, the Pauligroup G 1 {\displaystyle G_{1}} on 1 qubit is the 16-element matrix group consisting of the 2 × 2 identity matrix...
The Clifford group encompasses a set of quantum operations that map the set of n-fold Pauligroup products into itself. It is most famously studied for...
Wolfgang Ernst Pauli (/ˈpɔːli/; German: [ˈvɔlfɡaŋ ˈpaʊli]; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers...
of the Clifford group, a set of mathematical transformations which normalize the n-qubit Pauligroup, i.e., map tensor products of Pauli matrices to tensor...
In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously...
{\textstyle \mathrm {CNOT} } . Note that if a Clifford gate A is not in the Pauligroup, A {\displaystyle {\sqrt {A}}} or controlled-A are not in the Clifford...
Anna Pauline "Pauli" Murray (November 20, 1910 – July 1, 1985) was an American civil rights activist, advocate, legal scholar and theorist, author and...
mathematics contains the finite groups of small order up to group isomorphism. For n = 1, 2, … the number of nonisomorphic groups of order n is 1, 1, 1, 2,...
physicist Wolfgang Pauli through correspondence and in their 1952 work The Interpretation of Nature and the Psyche. This culminated in the Pauli–Jung conjecture...
In quantum mechanics, the Pauli equation or Schrödinger–Pauli equation is the formulation of the Schrödinger equation for spin-½ particles, which takes...
the term generalized Pauli matrices refers to families of matrices which generalize the (linear algebraic) properties of the Pauli matrices. Here, a few...
Hanna Hirsch, later Hanna Pauli (Stockholm, 13 January 1864 – 29 December 1940, Solna), was a Swedish painter; primarily of genre scenes and portraits...
the football club FC St. Pauli. Littmann toured throughout West Germany for years with the "Familie Schmidt" theatre group before setting up the "Schmidt...
Hamburger SV and FC St. Pauli. In total, the two sides met 107 times since 1919, of which Hamburger SV won 68 games and FC St. Pauli won 23 games. Earlier...
professional footballer who plays as a left winger for 2. Bundesliga club FC St. Pauli. Born in Germany to Tunisian parents, he is a former international for the...
Micarea pauli is a species of corticolous and lignicolous (bark- and wood-dwelling), crustose lichen in the family Pilocarpaceae. It is only known to...
Australian professional soccer player who plays for Bundesliga club FC St. Pauli, which he captains, and the Australia National team. Playing as a midfielder...