diff options
Diffstat (limited to 'content/know/concept/quantum-gate/index.pdc')
| -rw-r--r-- | content/know/concept/quantum-gate/index.pdc | 16 |
1 files changed, 15 insertions, 1 deletions
diff --git a/content/know/concept/quantum-gate/index.pdc b/content/know/concept/quantum-gate/index.pdc index cd09094..189145f 100644 --- a/content/know/concept/quantum-gate/index.pdc +++ b/content/know/concept/quantum-gate/index.pdc @@ -208,6 +208,10 @@ but not always in the basis of $\ket{0}_1$, $\ket{1}_1$, $\ket{0}_2$ and $\ket{1 With that said, the first two-qubit gate is $\mathrm{SWAP}$, which simply swaps $\ket{\psi_1}$ and $\ket{\psi_2}$: +<a href="swap.png"> +<img src="swap.png" style="width:22%;display:block;margin:auto;"> +</a> + $$\begin{aligned} \boxed{ \mathrm{SWAP} = @@ -233,6 +237,10 @@ $$\begin{aligned} Next, there is the **controlled NOT gate** $\mathrm{CNOT}$, which "flips" (applies $X$ to) $\ket{\psi_2}$ if $\ket{\psi_1}$ is true: +<a href="cnot.png"> +<img src="cnot.png" style="width:22%;display:block;margin:auto;"> +</a> + $$\begin{aligned} \boxed{ \mathrm{CNOT} = @@ -252,7 +260,13 @@ $$\begin{aligned} &= c_{00} \ket{00} + c_{01} \ket{01} + c_{11} \ket{10} + c_{10} \ket{11} \end{aligned}$$ -More generally, each one-qubit gate $U$ can be turned into a **controlled** $U$ **gate**: +More generally, from every one-qubit gate $U$, +we can define a two-qubit **controlled U gate** $\mathrm{CU}$, +which applies $U$ to $\ket{\psi_2}$ if $\ket{\psi_1}$ is true: + +<a href="cu.png"> +<img src="cu.png" style="width:22%;display:block;margin:auto;"> +</a> $$\begin{aligned} \boxed{ |