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The fact that the Pauli matrices, along with the identity matrix I, form an orthogonal basis for the Hilbert space of all 2 × 2 complex matrices , over , means that we can express any 2 × 2 complex matrix M as = + where c is a complex number, and a is a 3-component, complex vector.
The Pauli group is generated by the Pauli matrices, and like them it is named after Wolfgang Pauli. The Pauli group on n {\displaystyle n} qubits, G n {\displaystyle G_{n}} , is the group generated by the operators described above applied to each of n {\displaystyle n} qubits in the tensor product Hilbert space ( C 2 ) ⊗ n {\displaystyle ...
The Pauli gates (,,) are the three Pauli matrices (,,) and act on a single qubit. The Pauli X , Y and Z equate, respectively, to a rotation around the x , y and z axes of the Bloch sphere by π {\displaystyle \pi } radians.
This method of generalizing the Pauli matrices refers to a generalization from a single 2-level system to multiple such systems.In particular, the generalized Pauli matrices for a group of qubits is just the set of matrices generated by all possible products of Pauli matrices on any of the qubits.
Pauli matrices, also called the "Pauli spin matrices". Generalizations of Pauli matrices; Gamma matrices, which can be represented in terms of the Pauli matrices.
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= ¯ (′) where B μ is the U(1) gauge field; Y W is the weak hypercharge (the generator of the U(1) group); W μ is the three-component SU(2) gauge field; and the components of τ are the Pauli matrices (infinitesimal generators of the SU(2) group) whose eigenvalues give the weak isospin.
The Hamiltonian of a spin-1/2 particle in a magnetic field can be written as [3] =, where denote the Pauli matrices, is the magnetic moment, and B is the magnetic field.