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| [[File:Cayley_graph_Pauli.svg|thumb|The [[Möbius–Kantor graph]], the [[Cayley graph]] of the Pauli group <math>G_1</math> with generators ''X'', ''Y'', and ''Z'']]
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| In [[physics]] and [[mathematics]], the '''Pauli group''' <math>G_1</math> on 1 [[qubit]] is the 16-element [[matrix group]] consisting of the 2 × 2 [[identity matrix]] <math>I</math> and all of the [[Pauli matrices]]
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| :<math>X = \sigma_1 = | |
| \begin{pmatrix}
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| 0&1\\
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| 1&0
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| \end{pmatrix},\quad
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| Y = \sigma_2 =
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| \begin{pmatrix}
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| 0&-i\\
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| i&0
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| \end{pmatrix},\quad
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| Z = \sigma_3 =
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| \begin{pmatrix}
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| 1&0\\
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| 0&-1
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| \end{pmatrix}</math>,
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| together with the products of these matrices with the factors <math>-1</math> and <math>\pm i</math>:
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| :<math>G_1 \ \stackrel{\mathrm{def}}{=}\ \{\pm I,\pm iI,\pm X,\pm iX,\pm Y,\pm iY,\pm Z,\pm iZ\} \equiv \langle X, Y, Z \rangle</math>.
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| The Pauli group is [[Generating_set_of_a_group|generated]] by the Pauli matrices, and like them it is named after [[Wolfgang Pauli]].
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| The Pauli group on n qubits, <math>G_n</math>, is the group generated by the operators described above applied to each of <math>n</math> qubits in the [[tensor product]] [[Hilbert space]] <math>(\mathbb{C}^2)^{\otimes n}</math>.
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| ==References==
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| * {{cite book |title= Quantum Computation and Quantum Information|last= Nielsen|first= Michael A|authorlink= |coauthors= Chuang, Isaac L|year= 2000|publisher= [[Cambridge University Press]]|location= [[Cambridge]]; [[New York City|New York]]|isbn= 978-0-521-63235-5|oclc= 43641333|pages= }}
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| [[Category:Finite groups]]
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| [[Category:Quantum information science]]
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| {{quantum-stub}}
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Latest revision as of 07:55, 19 October 2014
I am Oscar and I completely dig that name. Since she was 18 she's been working as a receptionist but her promotion by no means arrives. South Dakota is exactly where me and my husband reside. Playing baseball is the pastime he will never quit performing.
My blog ... www.hard-ass-porn.com