Pauli-Z gate clarification

Question

In this following document: https://people.cs.umass.edu/~strubell/doc/quantum_tutorial.pdf

Page 16 says the following about Pauli Z gate

However the right-hand most (ket-bra) side of the equation doesn't seem to evaluate to the 2x2 matrix. Is this a typo in the document or am I doing something wrong?

|1><0| = [0 0
          1 0]          ---- (1)
|0><1| = [0 1           ---- (2)
          0 0]

(1) - (2) = [0 -1
             1  0]


```

Siong Thye Goh · Accepted Answer · 2019-07-10T08:15:11.897

1

$\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bra}[1]{\left<#1\right|}$

Looks like a typo while copying from $X$ and $Y$ pauli matrices.

It should be $$\ket{0}\bra{0} - \ket{1}\bra{1}$$

edited Jul 10 '19 at 08:15

answered Jul 10 '19 at 08:04

Siong Thye Goh

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Pauli-Z gate clarification

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