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.
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J2. Unitary Groups
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Mod-08 Lec-31 Pauli Spin Matrices and The Stern Gerlach Experiment
Transcription
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
- ^ Pauli group on GroupNames
2. https://arxiv.org/abs/quant-ph/9807006