Pauli Group
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Pauli Group
The Möbius-Kantor graph, the Cayley graph of the Pauli group with generators X, Y, and Z

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 n 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]

References

  • Nielsen, Michael A.; Chuang, Isaac L. (2000). Quantum Computation and Quantum Information. Cambridge; New York: Cambridge University Press. ISBN 978-0-521-63235-5. OCLC 43641333.

External links

  1. ^ Pauli group on GroupNames



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