Hadamard-poort

Hadamard state machine

De Hadamard-poort is een kwantummechanische functie die qubits in een toestand van superpositie plaatst.

$H|0⟩=\left[\begin{array}{cc}1/\sqrt{2}& 1/\sqrt{2}\\ 1/\sqrt{2}& -1/\sqrt{2}\end{array}\right]\left[\begin{array}{c}1\\ 0\end{array}\right]=\left[\begin{array}{c}1/\sqrt{2}\\ 1/\sqrt{2}\end{array}\right]$

$H|1⟩=\left[\begin{array}{cc}1/\sqrt{2}& 1/\sqrt{2}\\ 1/\sqrt{2}& -1/\sqrt{2}\end{array}\right]\left[\begin{array}{c}0\\ 1\end{array}\right]=\left[\begin{array}{c}1/\sqrt{2}\\ -1/\sqrt{2}\end{array}\right]$

Reversiebele eigenschap

Aangezien de operatie reversiebel is, kunnen we de uitkomst van bovenstaande voorbeelden hergebruiken als input, en komen we opnieuw bij de originele beginwaarden uit:

$H(\left[\begin{array}{c}1/\sqrt{2}\\ 1/\sqrt{2}\end{array}\right])=\left[\begin{array}{cc}1/\sqrt{2}& 1/\sqrt{2}\\ 1/\sqrt{2}& -1/\sqrt{2}\end{array}\right]\left[\begin{array}{c}1/\sqrt{2}\\ 1/\sqrt{2}\end{array}\right]=\left[\begin{array}{c}1\\ 0\end{array}\right]=|0⟩$

$H(\left[\begin{array}{c}1/\sqrt{2}\\ -1/\sqrt{2}\end{array}\right])=\left[\begin{array}{cc}1/\sqrt{2}& 1/\sqrt{2}\\ 1/\sqrt{2}& -1/\sqrt{2}\end{array}\right]\left[\begin{array}{c}1/\sqrt{2}\\ -1/\sqrt{2}\end{array}\right]=\left[\begin{array}{c}0\\ 1\end{array}\right]=|1⟩$