Quantum

Resumen de puertas y qubits comunes en quantum computing

Manuel H. AriasDeja un comentario

Me he preparado esta tabla con la definición de las puertas y qubits más frecuentes. Iré actualizanda conforme avanzo en el estudio de esta teoría.

IdentityI|0\rangle = |0\rangle
I|1\rangle = |1\rangle 		I = \begin{pmatrix}1&0\\0&1\end{pmatrix}
Pauli XX|j\rangle = |1 \oplus j\rangle \; \text{para j=\{0,1\}}
X|0\rangle = |1 \rangle
X|1\rangle = |0\rangle 		X = \begin{pmatrix}0&1\\1&0\end{pmatrix}
Pauli YY|j\rangle = (-i)^{j}|1\oplus j\rangle \; \text{para j=\{0,1\}}
Y|0\rangle = i|0\rangle
Y|1\rangle = -i|1\rangle 		Y = \begin{pmatrix}0&{-i}\\{i}&0\end{pmatrix}
Pauli ZZ|j\rangle = (-1)^j |j\rangle \; \text{para j=\{0,1\}}
Z|0\rangle = |0\rangle
Z|1\rangle = -|1\rangle 		Z = \begin{pmatrix}1&0\\0&-1\end{pmatrix}
Phase SS|0\rangle = |0\rangle
S|1\rangle = i|1\rangle 		S = \begin{pmatrix}1&0\\0&i\end{pmatrix}
TT|0\rangle = |0\rangle
T|1\rangle = e^{i\frac{\pi}{4}}|1\rangle 		T = \begin{pmatrix}1&0\\0&e^{i\frac{\pi}{4}}\end{pmatrix}
H
Hadamard		H|0\rangle = \frac{1}{\sqrt{2}}\left(|0\rangle+|1\rangle\right)
H|1\rangle = \frac{1}{\sqrt{2}}\left(|0\rangle-|1\rangle\right) 		H = \frac{1}{\sqrt{2}}\begin{pmatrix}1&1\\1&-1\end{pmatrix}
|+\rangle
|-\rangle 		|+\rangle = \frac{1}{\sqrt{2}}\left(|0\rangle+|1\rangle\right)
|-\rangle = \frac{1}{\sqrt{2}}\left(|0\rangle-|1\rangle\right)
|i\rangle
|-i\rangle 		|i\rangle = \frac{1}{\sqrt{2}}\left(|0\rangle+i|1\rangle\right)
|-i\rangle = \frac{1}{\sqrt{2}}\left(|0\rangle-i|1\rangle\right)
|\phi^{+}\rangle
|\phi^{-}\rangle
|\phi^{+}\rangle = \frac{1}{\sqrt{2}}\left(|00\rangle+|11\rangle\right)
|\phi^{-}\rangle = \frac{1}{\sqrt{2}}\left(|00\rangle-|11\rangle\right)
|\psi^{+}\rangle
|\psi^{-}\rangle 		|\psi^{+}\rangle = \frac{1}{\sqrt{2}}\left(|01\rangle+|10\rangle\right)
|\psi^{-}\rangle = \frac{1}{\sqrt{2}}\left(|01\rangle-|10\rangle\right)

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