Transcription of Cli ord group - LU
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Cli ord group - LU
Clifford groupMaris OzolsJuly 31, 2008 AbstractThis is a survey on the Clifford group onnqubits. I will discuss its properties andapplications in quantum Pauli matricesThePauli matriceson a single qubit areI=(1 00 1),X=(0 11 0),Y=(0 ii0),Z=(1 00 1). Onnqubits the set of Pauli matrices isPn={ 1 n| i {I,X,Y,Z}},|Pn|= 4n. ThegroupPn/U(1) is isomorphic to a vector space overF2with dimension 2nvia identification:ZY| |IX (0,1)(1,1)| |(0,0)(1,0)(1)where the multiplication of matrices corresponds to the addition of Clifford DefinitionTo define the Clifford group , we do not have to turn the Pauli matrices into a group .
Cli ord group Maris Ozols July 31, 2008 Abstract This is a survey on the Cli ord group on nqubits. I will discuss its properties and applications in quantum computing. 1 Pauli matrices The Pauli matrices on a single qubit are I= 1 0 0 1, X= 0 1 1 0, Y = 0 i i 0, Z= 1 0 1. On
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