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edited Nov 24, 2020 at 18:58

glS ♦

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Decomposition of a matrix How are arbitrary $2\times 2$ matrices decomposed in the Pauli basis?

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asked Jul 28, 2019 at 15:12

lufydad

Decomposition of a matrix in the Pauli basis

I read in this article (Apendix III p.8) that for $A\in \mathcal{M}_2$, since the normalized Pauli matrices $\{I,X,Y,Z\}/\sqrt{2}$ form an orthogonal matrix basis. $$A=\frac{Tr(AI)I+Tr(AX)X+Tr(AY)Y+Tr(AZ)Z}{2} $$

I don't understand, where does the Trace coefficient come from ?

pauli-gates