Title: Theory / Unimportant / CS / Fundamental / Quantum / ZX-for the working quantum computer scientist / Equalities

Answer: equals
Page: 7
Chapter: 2
Context: ZX-calculus

Answer: equals
Page: 8, 19
Chapter: 2
Context: ZX-calculus
Name: Identity removal

Answer: equals
Page: 8
Chapter: 2
Context: ZX-calculus

Question: can be rewritten as
Page: 8
Chapter: 2
Context: ZX-calculus

Name: ZX-calculus identities
Page: 8
Section: 2
Under: switch of all colors

Name: A \(Z\)-spider
Definition: [$]\ket{0\dots0}\bra{0\dots0}+e^{i\alpha}\ket{1\dots1}\bra{1\dots1}[/$]
Page: 9
Chapter: 2
Section: 1
Notation: \(\enclose{circle}{\alpha}\)
Definition2: \[
\left(\begin{array}{lllll}
1&0&\dots&0&0\\
0&0&\dots&0&0\\
\vdots&&&&\vdots\\
0&0&\dots&0&0\\
0&0&\dots&0&e^{i\alpha}\\
\dots\end{array}\right)
\]
Example: \[\left(\begin{array}{ll} 1&0\\ 0&1 \end{array}\right)\]
Example2: [$]\sqrt2\ket+[/$]
Example3: [$]\sqrt2\ket-[/$]
Applied to: \(\enclose{circle}{ }\)
Example4: \(1+e^{i\alpha}\)

Name: A \(X\)-spider
Definition: [$]\ket{+\dots+}\bra{+\dots+}+e^{i\alpha}\ket{-\dots-}\bra{-\dots-}[/$]
Page: 9
Chapter: 2
Section: 1
Definition2: \[
\frac{1}{\sqrt2}
\left(\begin{array}{lllll}
1+e^{i\alpha}&1-e^{i\alpha}&\dots\\
1-e^{i\alpha}&1+e^{i\alpha}&\dots\\
\vdots&&&&\vdots\\
\dots\end{array}\right)
\]
Example: \[\left(\begin{array}{ll} 1&0\\ 0&1 \end{array}\right)\]
Example2: [$]\sqrt2\ket0[/$]
Example3: [$]\sqrt2\ket1[/$]

Question: What does it means if a spider label is empty
Answer: The spider label is 0
Page: 10
Chapter: 2
Section: 1
Context: Quantum computing

Question: How do you compose two ZX-diagram vertically?
Answer: Using a Kronecker product
Page: 11
Chapter: 2
Section: 1
Context: Quantum computing

Name: Kronecker product
Definition: [$$]C=\left(\begin{array}{lll}
a_{0,0}B&&a_{0,n-1}B\\
&&\\
a_{m-1,0}B&&a_{m-1,n-1}B\\
\end{array}
\right)[/$$], that is \((c_{ek+f,il+j})=a_{e,i}b_{f,j}\)
Page: 11
Chapter: 2
Section: 1
Variables: [$$]A=\left(\begin{array}{lll}
a_{0,0}&&a_{0,n-1}\\
&&\\
a_{m-1,0}&&a_{m-1,n-1}\\
\end{array}
\right)[/$$]
[$$]B=\left(\begin{array}{lll}
b_{0,0}&&b_{0,l-1}\\
&&\\
b_{k-1,0}&&b_{k-1,l-1}\\
\end{array}
\right)[/$$]
Context: Quantum computing
Notation: \(A\otimes B\)

Question: How do you compose two ZX-diagram horizontaly?
Answer: You multiply the matrices together
Page: 11
Chapter: 2
Section: 1
Context: Quantum computing

Question: What does represent a vertical line, such as in
Answer: equivalently one of and
Page: 12
Chapter: 2
Section: 1
Context: ZX-calculus

Answer: equals (e.g. ZX calculus is not braided)
Page: 12
Chapter: 2
Section: 1
Context: ZX-calculus

Answer: equals (e.g. spiders are symmetric in output)
Page: 14
Chapter: 2
Section: 1
Context: ZX-calculus

Answer: equals (e.g. spiders are symmetric in input)
Page: 14
Chapter: 2
Section: 1
Context: ZX-calculus

Name: The cup
Definition: \[\left(\begin{array}{l}1\\0\\0\\1\end{array}\right)\]
Page: 14
Chapter: 2
Section: 1
Context: ZX-calculus
Name2: The bell state
Extra: Z-spider with two output and no input

Name: The cap
Definition: \(\left(1 0 0 1\right)\)
Page: 14
Chapter: 2
Section: 1
Context: ZX-calculus
Definition2: The Bell effect
Extra: Z-spider with two input and no output

Name: The yanking equations
Page: 14
Chapter: 2
Section: 1
Context: ZX-calculus
Extra: Z-spider with two input and no output

Answer: equals
Page: 14
Chapter: 2
Section: 1
Context: ZX-calculus
Extra: Z-spider with two input and no output

Question: (X or Z spider)
Answer: equals
Page: 14
Chapter: 2
Section: 1
Context: ZX-calculus
Extra: Z-spider with two input and no output

Name: A scalar diagram
Definition: A diagram with no input nor output
Page: 14
Chapter: 2
Section: 1
Context: ZX-calculus

Answer: equals \(\sqrt2\)
Page: 15
Chapter: 3
Section: 4
Context: ZX-calculus

Answer: equals \(\sqrt2e^{i\alpha}\)
Page: 15
Chapter: 3
Section: 4
Context: ZX-calculus

Answer: equals \(\frac1{\sqrt2}\)
Page: 15
Chapter: 3
Section: 4
Context: ZX-calculus

Question: How should equality be understood for ZX-calculus
Answer: only up to a global non-zero scalar
Page: 16
Chapter: 3
Section: 4
Context: ZX-calculus

Name: The conjugate of \(M\)
Definition: The matrix obtained from \(M\) by pointwise complex conjugate
Page: 16
Chapter: 3
Section: 5
Variables: \(M\) a complex matrix
Context: ZX-calculus

Instruction: Inverse the phase of each spider of \(D\)
Page: 16
Effect: The diagram whose matrix is the conjugate of the matrix of \(D\)
Context: ZX-calculus
Chapter: 3
Section: 5
Variables: \(D\) a ZX-diagram

Page: 16
Effect: The diagram whose matrix is the transpose of the matrix of \(D\)
Context: ZX-calculus
Chapter: 3
Section: 5
Variables: \(D\) a ZX-diagram

Name: The Hadamard box
Definition: \[\frac1{\sqrt2}\left(\begin{array}{ll}1&1\\1&-1\end{array}\right)\]
Page: 17
Chapter: 3
Section: 6
Context: ZX-calculus

Answer: equals and respectively
Page: 17
Chapter: 4
Context: ZX-calculus
Name: Spider fusion

Answer: equals
using identity removal and spider fusion
Page: 17
Chapter: 4
Context: ZX-calculus

Answer: equals
Page: 21
Chapter: 4
Section: 2
Context: ZX-calculus
Index: 55

Answer: equals
Page: 21
Chapter: 4
Section: 2
Context: ZX-calculus
Index: 56